# ************************************************ 
#     This table  has been made by using ../../Data/BaseM/Al 
#     with Bremsstrahlung formula: # 1
#     and  Pair creation  formula: # 1.
#     Tue Apr 20 20:13:13 GMT+0900 1999 by KASAHARA Katsuaki using
#     version epics.uv5.00  
# 
#name   Format    Alminum
Al 	1
#
#  Elem	 rho(g/cm^3)	Gas/Solid(1/0)  refl.index Birks c

1         2.70            0              0         0 0 0
# 	Z	A  	N
	13	26.98	1

 Excitation (Ionization) potential = 163.00 eV
 radation length=  8.89160596567383 cm  24.0073361073193 g/cm^2
 <Aeff>=  26.9800000000000 <Zeff=>  13.0000000000000 <Z2/A>=   6.26389918458117
 plasma energy=  3.286747044197750E-008 GeV no density=  6.026600848776872E+022 /cm^3
 <Z2eff=>  169.000000000000 <Z/A>=  .481838398813936
Migdal s1=  1.650922635396360E-004
 Conversion factors:
 g/cm^2 to cm=  .370370370370370
 mb to /(g/cm2)=  2.232074388435880E-005 mb to /cm=  6.026600848776872E-005 mb to /X0=  5.358616005971940E-004
 If a comound is specified as an Atom, use the
 following instead:   2.232074388435880E-005  6.026600848776872E-005  5.358616005971940E-004
 pi x Re**2 * N* Z /A *X0g  = 0.15 Z/A*X0g=  1.73783935965619
 media.A, Z, Z^2=  26.9800000000000  13.0000000000000  169.000000000000

 **** Sternheimers consts
 a, b, c =  7.401038157312493E-002  16.7721551145162 -4.20362431163979
 x0, x1 =  .200000002980232  3.00000000000000
 sa, xa =  .149527346896644  .912640981411220
 minimum dEdx_restricted=  1.356225069741623E-003 GeV/(g/cm^2)  with Tcut=  1.000000000000000E-004 GeV

 **** photoelectric consts
b0, b1, b2=  .711017167462358  1.67329892893568  1.63277196307458
fa, a, p=  1.08275406053135  5.087184999613300E-004  5.627140892436001E-004
l, ek=  7.59375000000000  2.298400000000000E-006

#-#-#-#-#-#-#-#-#-#-#-#-
 constant for Seltzer Brems sampling table 
  7.110000000000000E-004  1.000000000000000E-005 -3.14813039927023  .100000000000000  .100000000000000  1.00000000000000  21  4.736842105263160E-002  .107406519963512  .107406519963512  .000000000000000  .562341325190349  2.811706625951750E-002  21  20  21

Al      
Seltzer Brems total X-sec. table upto E=  .100000000000000 GeV
  7.110000E-04  3.98126
  9.104920E-04  3.73483
  1.165957E-03  3.90292
  1.493101E-03  4.25419
  1.912034E-03  4.69845
  2.448512E-03  5.19524
  3.135514E-03  5.71439
  4.015274E-03  6.23423
  5.141878E-03  6.76214
  6.584583E-03  7.27496
  8.432082E-03  7.77366
  1.079795E-02  8.24712
  1.382763E-02  8.71486
  1.770738E-02  9.15847
  2.267571E-02  9.59013
  2.903805E-02  10.0118
  3.718552E-02  10.4252
  4.761902E-02  10.8279
  6.097994E-02  11.2169
  7.808965E-02  11.5917
  .100000  11.4682

Selzter Brems sampling table; log(v/vmin)/(1-u)
    2.59463    2.50046    2.42653    2.36621    2.31562    2.27232    2.23486
    2.20187    2.17272    2.14671    2.12318    2.10196    2.08280    2.06527
    2.04932    2.03469    2.02128    2.00893    1.99738    1.98687

    3.09099    2.97550    2.88739    2.81697    2.75906    2.71034    2.66859
    2.63223    2.60065    2.57249    2.54733    2.52478    2.50448    2.48617
    2.46956    2.45449    2.44079    2.42822    2.41666    2.40630

    3.46439    3.33861    3.24417    3.16940    3.10860    3.05750    3.01444
    2.97684    2.94368    2.91444    2.88857    2.86564    2.84519    2.82695
    2.81060    2.79590    2.78269    2.77071    2.75995    2.74991

    3.80037    3.66841    3.57019    3.49336    3.43088    3.37945    3.33510
    3.29651    3.26300    3.23383    3.20835    3.18598    3.16631    3.14886
    3.13342    3.11969    3.10736    3.09634    3.08655    3.07753

    4.11874    3.98269    3.88228    3.80445    3.74224    3.69083    3.64719
    3.60977    3.57748    3.54945    3.52507    3.50375    3.48502    3.46858
    3.45402    3.44114    3.42974    3.41959    3.41059    3.40235

    4.42904    4.29114    4.18984    4.11173    4.04949    3.99783    3.95415
    3.91693    3.88512    3.85775    3.83419    3.81378    3.79603    3.78056
    3.76703    3.75519    3.74475    3.73560    3.72742    3.72032

    4.73267    4.59585    4.49594    4.41903    4.35747    4.30613    4.26286
    4.22623    4.19515    4.16864    4.14602    4.12659    4.10993    4.09549
    4.08303    4.07224    4.06273    4.05453    4.04731    4.04109

    5.03383    4.89949    4.80207    4.72704    4.66644    4.61574    4.57308
    4.53721    4.50694    4.48141    4.45978    4.44144    4.42582    4.41244
    4.40101    4.39124    4.38273    4.37542    4.36904    4.36361

    5.33047    5.19645    5.09893    5.02339    4.96160    4.90973    4.86634
    4.83006    4.79977    4.77445    4.75322    4.73537    4.72035    4.70763
    4.69689    4.68769    4.67989    4.67330    4.66742    4.66257

    5.62383    5.49089    5.39392    5.31838    5.25575    5.20302    5.15899
    5.12247    5.09220    5.06714    5.04636    5.02908    5.01467    5.00257
    4.99249    4.98396    4.97676    4.97062    4.96556    4.96111

    5.91454    5.78290    5.68658    5.61108    5.54756    5.49389    5.44925
    5.41244    5.38221    5.35744    5.33713    5.32038    5.30658    5.29513
    5.28567    5.27773    5.27115    5.26558    5.26111    5.25703

    6.20360    6.07369    5.97889    5.90420    5.84107    5.78725    5.74199
    5.70442    5.67345    5.64810    5.62734    5.61036    5.59641    5.58499
    5.57556    5.56775    5.56136    5.55603    5.55160    5.54778

    6.48940    6.36088    6.26685    6.19195    6.12792    6.07321    6.02739
    5.98967    5.95896    5.93405    5.91391    5.89760    5.88436    5.87366
    5.86493    5.85776    5.85197    5.84712    5.84315    5.83987

    6.77110    6.64356    6.54997    6.47451    6.40951    6.35409    6.30805
    6.27058    6.24042    6.21625    6.19695    6.18152    6.16919    6.15925
    6.15126    6.14479    6.13957    6.13525    6.13169    6.12896

    7.04980    6.92298    6.82957    6.75331    6.68722    6.63112    6.58503
    6.54794    6.51848    6.49517    6.47676    6.46223    6.45073    6.44159
    6.43434    6.42850    6.42385    6.42006    6.41717    6.41459

    7.32517    7.19872    7.10519    7.02789    6.96061    6.90391    6.85783
    6.82126    6.79255    6.77012    6.75265    6.73898    6.72833    6.71993
    6.71339    6.70813    6.70401    6.70075    6.69828    6.69595

    7.59655    7.47019    7.37642    7.29803    7.22975    7.17271    7.12696
    7.09113    7.06338    7.04198    7.02549    7.01279    7.00299    6.99535
    6.98940    6.98479    6.98110    6.97823    6.97593    6.97414

    7.86466    7.73825    7.64420    7.56485    7.49589    7.43898    7.39396
    7.35918    7.33258    7.31234    7.29695    7.28522    7.27624    7.26933
    7.26403    7.25999    7.25679    7.25426    7.25238    7.25080

    8.13104    8.00458    7.91032    7.83019    7.76103    7.70473    7.66083
    7.62739    7.60218    7.58322    7.56898    7.55822    7.55012    7.54399
    7.53933    7.53573    7.53294    7.53083    7.52915    7.52790

    8.39612    8.27027    8.17641    8.09616    8.02747    7.97231    7.92993
    7.89809    7.87436    7.85676    7.84370    7.83398    7.82670    7.82127
    7.81715    7.81409    7.81169    7.80998    7.80864    7.80746

    8.72955    8.63471    8.57421    8.53423    8.50718    8.48858    8.47561
    8.46651    8.46005    8.45546    8.45218    8.44981    8.44810    8.44685
    8.44594    8.44525    8.44475    8.44444    8.44420    7.74479


Seltzer Brems sampling tbl in B; log(v/vmin)
   11.80845   11.86852   11.81246   11.80370   11.78992   11.76237   11.70775
   11.63649   11.50780   11.31141   11.03282   10.67749   10.25795    9.79764
    9.31887    8.83526    8.35710    7.88984    7.43956    7.01018    6.60561

   25.83486   25.75573   25.82819   25.76677   25.62235   25.33053   24.83022
   24.04486   22.98205   21.67397   20.22907   18.74704   17.30440   15.94097
   14.67184   13.50050   12.42770   11.45204   10.56992    9.77373    9.05704

   43.66445   43.66937   43.59497   43.32968   42.65087   41.35081   39.33424
   36.69696   33.69456   30.61218   27.66645   24.96161   22.51990   20.33020
   18.38001   16.65446   15.13407   13.79456   12.61257   11.56677   10.64034

   62.06675   62.01962   61.87009   61.08893   59.18093   55.86077   51.36707
   46.31862   41.30893   36.68494   32.56175   28.93832   25.77543   23.03041
   20.65355   18.59654   16.81222   15.25885   13.90262   12.71334   11.66767

   79.70826   79.63353   79.26865   77.54754   73.57763   67.36617   60.00986
   52.67470   46.05155   40.30124   35.37872   31.17775   27.60189   24.55695
   21.95745   19.73034   17.81488   16.15788   14.71671   13.45834   12.35519

   94.86668   94.78315   94.02471   90.97528   84.36732   75.05807   65.09857
   55.99600   48.28409   41.86470   36.52330   32.07795   28.35571   25.21862
   22.55896   20.29175   18.34614   16.66499   15.20323   13.92592   12.80444

  109.58449  109.35341  108.03539  103.23294   93.00004   80.21079   67.96997
   57.55515   49.09769   42.25495   36.71460   32.19636   28.47153   25.36298
   22.74266   20.51472   18.60202   16.94484   15.49799   14.22721   13.10668

  123.06175  122.20211  120.47831  113.37498   98.80795   82.76834   68.82879
   57.60099   48.72709   41.71780   36.16446   31.71969   28.10234   25.11017
   22.59778   20.46380   18.62874   17.03149   15.62817   14.38764   13.28702

  136.63774  135.42054  132.64927  121.79774  102.82552   84.04069   68.73242
   56.86372   47.76318   40.76002   35.32250   31.03053   27.56956   24.71912
   22.33045   20.29726   18.54416   17.01363   15.66478   14.46863   13.40492

  149.85339  148.05904  143.97785  128.19086  104.80883   83.83939   67.65039
   55.48595   46.39626   39.53282   34.27616   30.17349   26.89020   24.20178
   21.95063   20.03364   18.37701   16.92524   15.64084   14.49765   13.47675

  162.70324  160.49930  154.15447  132.44027  105.06354   82.51986   65.85234
   53.67750   44.75666   38.12624   33.10318   29.21290   26.12279   23.60379
   21.49952   19.70605   18.15224   16.78671   15.57356   14.48893   13.51604

  174.89619  172.55183  162.63065  134.41865  103.78429   80.28925   63.49744
   51.53583   42.92076   36.59241   31.83573   28.17823   25.29225   22.94815
   20.99446   19.32889   17.88320   16.60868   15.47126   14.44905   13.52806

  186.90655  184.40803  169.56142  134.59711  101.39648   77.39462   60.80198
   49.23053   41.00693   35.02112   30.55607   27.13830   24.45628   22.28623
   20.48215   18.94419   17.60752   16.42442   15.36400   14.40562   13.53720

  198.10175  195.68745  174.25499  132.89232   98.02201   73.99264   57.88058
   46.82390   39.06424   33.45481   29.29224   26.12302   23.64494   21.64926
   19.99222   18.58043   17.34983   16.25705   15.27188   14.37579   13.55879

  208.90741  206.39065  176.97404  129.85424   94.06017   70.37378   54.85461
   44.41289   37.13741   31.91380   28.06022   25.13459   22.85864   21.03206
   19.52023   18.23110   17.10519   16.10110   15.18982   14.35534   13.58857

  219.35512  216.70886  177.79063  125.78941   89.74032   66.68309   51.89004
   42.04564   35.27315   30.43502   26.87921   24.19323   22.11298   20.45159
   19.08022   17.91016   16.88611   15.96781   15.12818   14.35246   13.63363

  229.45221  226.07050  176.92027  120.97093   85.09924   62.91118   48.94411
   39.77181   33.49445   29.03286   25.75869   23.29842   21.40511   19.90580
   18.67562   17.62725   16.70477   15.87047   15.09925   14.37845   13.70359

  239.16144  234.47591  174.39941  115.62679   80.29662   59.13999   46.05635
   37.58155   31.81997   27.72280   24.72155   22.47461   20.75608   19.41095
   18.31644   17.38518   16.56043   15.80624   15.09919   14.42913   13.79417

  248.45920  241.54399  170.31233  109.87829   75.51065   55.48537   43.32082
   35.50485   30.21836   26.48523   23.75492   21.71648   20.16969   18.96981
   17.99851   17.17436   16.43938   15.75966   15.11299   14.49089   13.89357

  257.35966  247.27498  165.10133  103.84875   70.77663   51.95928   40.70500
   33.53450   28.70372   25.30975   22.84937   21.02286   19.63758   18.56800
   17.71046   16.98781   16.33964   15.73122   15.14105   14.56293   13.99962

  255.07266  251.28766  156.04550   92.96407   62.17320   45.82820   36.24262
   30.14410   26.03406   23.12995   21.01634   19.45091   18.27148   17.36537
   16.64519   16.04342   15.50600   14.99616   14.49248   13.98814   13.48629


 constant for Brems sampling table at low energies
  63.8481205758033  1.000000000000000E-004  1.000000000000000E-002 -2.00000000000000  63.8481205758033  4.203703668382432E-002  .100000000000000  1.00000000000000  38  4.736842105263160E-002  .102841841025864  .102841841025864  .000000000000000  .562341325190349  2.811706625951750E-002  38  20  21

Al      
Brems total X-sec. table upto E=  63.8481205758034 GeV
  1.000000E-02  4.73383
  1.267190E-02  5.15898
  1.605771E-02  5.57424
  2.034818E-02  5.98362
  2.578501E-02  6.38896
  3.267452E-02  6.78195
  4.140483E-02  7.17321
  5.246780E-02  7.55511
  6.648669E-02  7.93065
  8.425129E-02  8.29651
  .106762  8.43868
  .135288  8.78655
  .171436  9.13089
  .217242  9.47209
  .275287  9.81053
  .348841  10.1465
  .442048  10.4804
  .560159  10.8125
  .709828  11.1429
  .899487  11.4720
  1.13982  11.7986
  1.44437  12.1317
  1.83029  12.4634
  2.31933  12.7857
  2.93903  13.0761
  3.72431  13.3312
  4.71941  13.5373
  5.98039  13.6862
  7.57830  13.7776
  9.60314  13.8105
  12.1690  13.7898
  15.4205  13.7195
  19.5406  13.6060
  24.7617  13.4556
  31.3778  13.2742
  39.7617  13.0668
  50.3856  12.8378
  63.8481  12.4540

Brems sampling table at low E for Small Eg
    4.01444    3.90536    3.82240    3.75628    3.70162    3.65520    3.61493
    3.57828    3.54408    3.51239    3.48328    3.45670    3.43261    3.41082
    3.39117    3.37351    3.35757    3.34320    3.33041    3.31858

    4.27578    4.16731    4.08479    4.01902    3.96477    3.91931    3.87900
    3.84211    3.80782    3.77607    3.74680    3.72005    3.69572    3.67375
    3.65398    3.63620    3.62024    3.60582    3.59306    3.58141

    4.53447    4.42614    4.34362    4.27773    4.22337    4.17749    4.13608
    4.09773    4.06207    4.02917    3.99912    3.97198    3.94757    3.92576
    3.90627    3.88901    3.87368    3.85991    3.84786    3.83703

    4.79204    4.68382    4.60122    4.53511    4.48064    4.43385    4.39105
    4.35114    4.31413    4.28028    4.24971    4.22239    4.19815    4.17675
    4.15787    4.14125    4.12666    4.11391    4.10250    4.09256

    5.04910    4.94100    4.85826    4.79186    4.73725    4.68921    4.64479
    4.60329    4.56507    4.53047    4.49964    4.47243    4.44860    4.42778
    4.40964    4.39383    4.38010    4.36812    4.35778    4.34860

    5.30252    5.19385    5.11053    5.04355    4.98824    4.93866    4.89242
    4.84941    4.81023    4.77523    4.74447    4.71767    4.69450    4.67447
    4.65725    4.64245    4.62968    4.61866    4.60917    4.60089

    5.55364    5.44416    5.36022    5.29275    5.23656    5.18546    5.13759
    5.09342    5.05373    5.01878    4.98849    4.96249    4.94029    4.92133
    4.90519    4.89143    4.87972    4.86969    4.86094    4.85373

    5.80417    5.69394    5.60933    5.54130    5.48412    5.43142    5.38214
    5.33725    5.29750    5.26306    5.23361    5.20865    5.18755    5.16979
    5.15488    5.14228    5.13162    5.12261    5.11490    5.10844

    6.05305    5.94199    5.85679    5.78841    5.73014    5.67606    5.62590
    5.58086    5.54159    5.50809    5.47987    5.45625    5.43656    5.42014
    5.40645    5.39507    5.38554    5.37756    5.37092    5.36515

    6.30016    6.18853    6.10315    6.03492    5.97578    5.92083    5.87042
    5.82584    5.78761    5.75548    5.72877    5.70670    5.68852    5.67349
    5.66114    5.65093    5.64253    5.63553    5.62976    5.62479

    6.58531    6.48989    6.42243    6.37360    6.33752    6.31039    6.28976
    6.27391    6.26162    6.25204    6.24452    6.23861    6.23391    6.23020
    6.22719    6.22481    6.22288    6.22138    6.21997    6.21901

    6.82974    6.73434    6.66753    6.61961    6.58451    6.55839    6.53871
    6.52373    6.51223    6.50338    6.49650    6.49111    6.48691    6.48359
    6.48094    6.47882    6.47721    6.47590    6.47466    6.47388

    7.07252    6.97711    6.91093    6.86389    6.82976    6.80461    6.78583
    6.77170    6.76094    6.75273    6.74641    6.74152    6.73775    6.73479
    6.73246    6.73066    6.72924    6.72808    6.72700    6.72640

    7.31375    7.21834    7.15276    7.10661    7.07345    7.04923    7.03132
    7.01798    7.00793    7.00033    6.99454    6.99012    6.98669    6.98404
    6.98203    6.98043    6.97918    6.97827    6.97750    6.97681

    7.55356    7.45814    7.39320    7.34793    7.31570    7.29241    7.27535
    7.26275    7.25335    7.24632    7.24102    7.23702    7.23395    7.23165
    7.22986    7.22848    7.22740    7.22648    7.22575    7.22533

    7.79210    7.69669    7.63240    7.58802    7.55673    7.53432    7.51807
    7.50619    7.49742    7.49094    7.48607    7.48246    7.47971    7.47761
    7.47602    7.47483    7.47395    7.47318    7.47259    7.47219

    8.02950    7.93412    7.87052    7.82704    7.79667    7.77513    7.75967
    7.74847    7.74031    7.73430    7.72989    7.72658    7.72414    7.72230
    7.72093    7.71989    7.71901    7.71843    7.71791    7.71759

    8.26587    8.17058    8.10770    8.06512    8.03567    8.01500    8.00029
    7.98975    7.98215    7.97661    7.97256    7.96959    7.96739    7.96576
    7.96452    7.96366    7.96293    7.96235    7.96203    7.96170

    8.50134    8.40620    8.34406    8.30241    8.27389    8.25405    8.24009
    8.23017    8.22309    8.21800    8.21431    8.21161    8.20966    8.20821
    8.20715    8.20631    8.20569    8.20535    8.20498    8.20471

    8.73603    8.64110    8.57977    8.53905    8.51143    8.49241    8.47917
    8.46986    8.46325    8.45858    8.45522    8.45280    8.45105    8.44977
    8.44884    8.44817    8.44765    8.44720    8.44697    8.44675

    8.97019    8.87560    8.81517    8.77546    8.74882    8.73071    8.71825
    8.70963    8.70365    8.69952    8.69667    8.69477    8.69355    8.69286
    8.69269    8.69308    8.69421    8.69722    8.70660    8.63647

    9.20303    9.10852    9.04864    9.00956    8.98344    8.96567    8.95337
    8.94467    8.93841    8.93377    8.93013    8.92711    8.92435    8.92151
    8.91824    8.91388    8.90713    8.88804    8.82881    8.82030

    9.43547    9.34115    9.28192    9.24348    9.21791    9.20049    9.18834
    9.17963    9.17314    9.16802    9.16367    9.15963    9.15547    9.15068
    9.14460    9.13594    9.11926    9.09819    9.09137    9.14357

    9.66846    9.57477    9.51659    9.47930    9.45478    9.43831    9.42705
    9.41912    9.41334    9.40895    9.40537    9.40213    9.39895    9.39538
    9.39090    9.38310    9.37007    9.41779    9.50691    9.65934

    9.90437    9.81273    9.75714    9.72265    9.70114    9.68785    9.68002
    9.67592    9.67453    9.67524    9.67775    9.68208    9.68849    9.69771
    9.71004    9.73180    9.80149    9.91749   10.11801   10.41335

   10.14360   10.05554   10.00422    9.97444    9.95803    9.95042    9.94892
    9.95207    9.95906    9.96972    9.98432   10.00368   10.02933   10.06413
   10.10871   10.20763   10.36627   10.61539   10.96999   11.46815

   10.38754   10.30523   10.26047   10.23802   10.22977   10.23130   10.24019
   10.25532   10.27638   10.30382   10.33882   10.38368   10.44205   10.51674
   10.64062   10.83543   11.12683   11.53288   12.09573   12.88227

   10.63707   10.56297   10.52751   10.51545   10.51887   10.53362   10.55767
   10.59037   10.63213   10.68433   10.74957   10.83216   10.93616   11.08508
   11.31013   11.62866   12.07508   12.68520   13.52779   14.72514

   10.89217   10.82878   10.80534   10.80677   10.82542   10.85749   10.90146
   10.95736   11.02647   11.11147   11.21676   11.34937   11.51891   11.76297
   12.10764   12.57867   13.21654   14.08600   15.30108   17.08513

   11.15303   11.10282   11.09418   11.11227   11.14977   11.20336   11.27215
   11.35696   11.46022   11.58620   11.74160   11.93442   12.19271   12.54959
   13.03182   13.67786   14.54737   15.74057   17.44484   20.06531

   11.41914   11.38443   11.39315   11.43075   11.49041   11.56937   11.66743
   11.78641   11.93009   12.10454   12.31919   12.58729   12.94822   13.43049
   14.06945   14.91810   16.06212   17.65269   19.99092   23.79765

   11.69014   11.67308   11.70147   11.76129   11.84619   11.95405   12.08552
   12.24355   12.43339   12.66327   12.94477   13.30179   13.77503   14.39529
   15.20880   16.28709   17.75000   19.81899   22.96413   28.44059

   11.96544   11.96785   12.01801   12.10237   12.21519   12.35505   12.52355
   12.72483   12.96586   13.25725   13.61073   14.06884   14.66341   15.43320
   16.43801   17.77227   19.59917   22.23322   26.38526   34.19161

   12.24442   12.26794   12.34158   12.45248   12.59550   12.77001   12.97860
   13.22676   13.52328   13.88133   14.31865   14.88097   15.60409   16.53369
   17.74525   19.36046   21.59566   24.88409   30.26863   41.29294

   12.52655   12.57253   12.67114   12.81024   12.98537   13.19673   13.44800
   13.74607   14.10171   14.52827   15.05884   15.73077   16.58850   17.68694
   19.11921   21.03852   23.72435   27.75692   34.61831   50.04069

   12.81134   12.88090   13.00573   13.17442   13.38327   13.63335   13.92943
   14.27996   14.69768   15.19821   15.82567   16.61162   17.60889   18.88395
   20.54932   22.79367   25.96950   30.83315   39.42953   60.79579

   13.09840   13.19251   13.34459   13.54401   13.78790   14.07821   14.42092
   14.82600   15.30814   15.88985   16.61152   17.51749   18.65843   20.11679
   22.02589   24.61380   28.31533   34.09234   44.68688   73.99715

   13.39632   13.51545   13.69534   13.92632   14.20623   14.53804   14.92885
   15.39027   15.93735   16.60244   17.42502   18.44977   19.73818   21.38590
   23.54846   26.49701   30.75775   37.52741   50.38919   90.24406


Brems sampling tbl at low E for large Eg
   99.55314   98.80048   95.90077   84.85107   69.36622   55.35485   44.63058
   36.57195   30.54040   25.99315   22.52092   19.82411   17.69203   15.97612
   14.56588   13.38213   12.36982   11.48960   10.71345   10.02128    9.39717

  109.87018  108.86898  104.20736   88.83279   70.46142   55.28035   44.06939
   35.89915   29.89679   25.44235   22.06654   19.46591   17.42054   15.78327
   14.44201   13.31887   12.35863   11.52300   10.78475   10.12410    9.52615

  119.87702  118.73117  111.40207   91.25792   70.46443   54.42837   43.04575
   34.92740   29.07796   24.76994   21.53620   19.05624   17.11380   15.56440
   14.29955   13.24185   12.33772   11.54965   10.85177   10.22445    9.65418

  129.74029  128.76641  117.47053   92.38458   69.64619   53.10922   41.73109
   33.79243   28.14081   24.02022   20.94737   18.60090   16.77165   15.31635
   14.13190   13.14339   12.29869   11.56106   10.90578   10.31414    9.77315

  139.51486  138.40656  122.29339   92.37491   68.18267   51.47662   40.22074
   32.53702   27.12975   23.21800   20.31449   18.11030   16.39699   15.04069
   13.93988   13.02336   12.24008   11.55536   10.94521   10.39149    9.88170

  148.83286  147.65196  125.54975   91.27444   66.16560   49.57064   38.61174
   31.22504   26.10125   22.41818   19.69670   17.63558   16.04223   14.78478
   13.76976   12.92641   12.20589   11.57464   11.00865   10.49151   10.01143

  158.07286  156.50345  127.64488   89.45368   63.75457   47.41927   36.88090
   29.88605   25.07330   21.63252   19.09205   17.16712   15.68610   14.52351
   13.59430   12.82794   12.17614   11.60216   11.08350   10.60383   10.15287

  167.03424  164.77178  128.15174   86.94679   61.08377   45.15750   35.11330
   28.53574   24.04346   20.84462   18.49009   16.71183   15.34722   14.28227
   13.43661   12.74302   12.15363   11.63311   11.15851   10.71481   10.29236

  175.80096  172.45793  127.45301   83.91917   58.24918   42.90437   33.38604
   27.22653   23.04279   20.08176   17.90891   16.27708   15.02848   14.05972
   13.29580   12.67266   12.14535   11.67731   11.24598   10.83658   10.44127

  184.28906  179.18195  125.64597   80.49830   55.30599   40.64400   31.69200
   25.96520   22.09373   19.35813   17.36553   15.87981   14.75058   13.87549
   13.18657   12.62758   12.15846   11.74010   11.35002   10.97295   10.60170

  200.01203  187.80332  122.66072   74.32523   49.77667   36.57662   28.76475
   23.79067   20.42112   18.04179   16.29743   14.99603   14.00709   13.24736
   12.65331   12.17633   11.77479   11.41782   11.08092   10.74927   10.41621

  209.24937  192.98740  118.59459   70.39959   47.04549   34.67570   27.41350
   22.81615   19.69382   17.49390   15.88877   14.69881   13.80542   13.12698
   12.60395   12.18668   11.83605   11.52069   11.21683   10.90976   10.59445

  218.27033  196.63999  113.86633   66.49148   44.43149   32.90060   26.17941
   21.90452   19.02732   16.99511   15.52466   14.44390   13.64206   13.04330
   12.58655   12.22593   11.92334   11.64597   11.37144   11.08584   10.78547

  227.10304  199.14304  108.68002   62.67030   41.95472   31.25972   25.02870
   21.07876   18.41093   16.54642   15.20579   14.23182   13.51990   12.99486
   12.60141   12.29438   12.03526   11.79296   11.54421   11.27688   10.98860

  235.77325  200.11590  103.22767   58.98864   39.62836   29.71935   23.94518
   20.30964   17.85785   16.14850   14.93515   14.06293   13.43552   12.98193
   12.64811   12.39069   12.17209   11.96026   11.73407   11.48202   11.20337

  244.30408  199.55918   97.64141   55.48009   37.45796   28.28185   22.96803
   19.60807   17.36238   15.80542   14.71292   13.93912   13.39154   13.00373
   12.72543   12.51397   12.33150   12.14739   11.94012   11.70037   11.42830

  252.71593  197.47341   92.06509   52.16626   35.44302   26.98635   22.07820
   18.98436   16.92456   15.51342   14.53668   13.85702   13.38437   13.05952
   12.83283   12.66281   12.51286   12.35221   12.16095   11.93056   11.66304

  261.02665  193.85909   86.59470   49.05685   33.58147   25.79279   21.25641
   18.41783   16.54438   15.27633   14.40894   13.81492   13.41407   13.14663
   12.96702   12.83472   12.71385   12.57395   12.39541   12.17146   11.90612

  269.25177  189.09813   81.27833   46.15914   31.86893   24.66018   20.52086
   17.91834   16.22762   15.09017   14.32462   13.81284   13.47697   13.26335
   13.12674   13.02878   12.93336   12.81073   12.64202   12.42211   12.15675

  277.40476  183.00021   76.19980   43.47328   30.29728   23.66368   19.85089
   17.49529   15.96167   14.95467   14.28606   13.84893   13.57304   13.40693
   13.30997   13.24296   13.16942   13.06102   12.89958   12.68131   12.41416

  285.46697  176.13788   71.38316   40.98755   28.85686   22.76012   19.26363
   17.12711   15.75203   14.86190   14.28306   13.91624   13.69614   13.57478
   13.51343   13.47372   13.41973   13.32235   13.16557   12.94682   12.67576

  293.65894  168.51145   66.86436   38.71854   27.55443   21.95228   18.76042
   16.82481   15.60518   14.82350   14.32829   14.02519   13.85489   13.77409
   13.74525   13.72937   13.69158   13.60283   13.44754   13.22585   12.94932

  301.79501  160.50267   62.63155   36.63564   26.36762   21.23098   18.33685
   16.58600   15.50763   14.82727   14.40623   14.16173   14.03691   13.99405
   13.99397   13.99910   13.97452   13.89154   13.73601   13.50962   13.22618

  309.68718  151.92098   58.67290   34.71059   25.27703   20.58831   17.95117
   16.39844   15.44615   14.85736   14.50649   14.31530   14.23229   14.22293
   14.24877   14.27258   14.25887   14.17953   14.02160   13.78922   13.49791

  316.79219  143.14805   54.91689   32.89863   24.24760   19.97067   17.61547
   16.22757   15.39444   14.89357   14.60324   14.45784   14.41374   14.43357
   14.48254   14.52273   14.51773   14.44088   14.28033   14.04207   13.74304

  323.03026  134.18400   51.36357   31.18799   23.27637   19.37685   17.29124
   16.07315   15.34632   14.92061   14.68897   14.58595   14.57513   14.62147
   14.69048   14.74425   14.74653   14.67124   14.50813   14.26415   13.95862

  328.06999  125.21968   48.00102   29.55747   22.34691   18.83936   16.97520
   15.90260   15.28270   14.93037   14.74576   14.68215   14.70035   14.76847
   14.85486   14.91986   14.92927   14.85561   14.69047   14.44207   14.13139

  331.71311  116.25518   44.79349   27.99294   21.44879   18.31470   16.66534
   15.73538   15.19680   14.90341   14.76587   14.73417   14.77697   14.86460
   14.96474   15.04063   15.05601   14.98438   14.81852   14.56798   14.25392

  333.95783  107.48129   41.76483   26.49440   20.58426   17.80379   16.34315
   15.53068   15.08289   14.84372   14.74184   14.73866   14.80383   14.90714
   15.02012   15.10436   15.12543   15.05750   14.89248   14.64128   14.32606

  334.77775   99.08880   38.90313   25.06185   19.75032   17.26622   16.00811
   15.31904   14.93463   14.74358   14.67615   14.69555   14.77715   14.89422
   15.01752   15.10945   15.13668   15.07256   14.91012   14.66085   14.34649

  334.29436   91.07774   36.20838   23.69766   18.94996   16.78161   15.66069
   15.08017   14.75832   14.60688   14.56885   14.60835   14.70313   14.83037
   14.96167   15.06058   15.09335   15.03444   14.87670   14.63093   14.31962

  332.60499   83.44814   33.69252   22.40889   18.18319   16.27156   15.31997
   14.81412   14.55397   14.43747   14.42245   14.47705   14.58301   14.71832
   14.85603   14.96091   14.99964   14.94676   14.79514   14.55502   14.24869

  329.86438   76.39075   31.33168   21.19318   17.45149   15.77589   14.96723
   14.54158   14.32162   14.23918   14.24200   14.30859   14.42298   14.56442
   14.70673   14.81728   14.86169   14.81577   14.67153   14.43875   14.13928

  326.22657   69.71483   29.13780   20.05525   16.75636   15.29521   14.60278
   14.25247   14.07352   14.01586   14.03256   14.10992   14.22918   14.37501
   14.52130   14.63546   14.68613   14.64737   14.51172   14.28779   13.99641

  321.83411   63.80188   27.11086   18.99273   16.09779   14.82952   14.24557
   13.94675   13.80965   13.76751   13.79918   13.88276   14.00785   14.15555
   14.30382   14.42181   14.47793   14.44757   14.32137   14.10719   13.82520

  316.81156   58.07967   25.22702   18.00562   15.47428   14.41739   13.89526
   13.63451   13.52988   13.50546   13.54679   13.63571   13.76258   13.91144
   14.06045   14.18158   14.24329   14.22092   14.10470   13.90152   13.63016

  311.26457   52.92969   23.49820   17.08920   14.88435   13.97983   13.53271
   13.32594   13.24020   13.22966   13.27788   13.37049   13.49710   13.64632
   13.79600   13.91899   13.98595   13.97177   13.86631   13.67475   13.41476

   12.36867   12.30243   12.37458   12.37094   12.37674   12.40422   12.41303
   12.44458   12.49397   12.57019   12.66942   12.79545   12.94604   13.11455
   13.28496   13.43345   13.53064   13.55240   13.48426   13.32893   13.10153


 constant for Brems sampling table at high energies
  6.384812057580330E-004  63.8481205758033  1.80514811795698  50  5.000000000000000E-002  .100000000000000  5071636.49074409  5.000000000000000E-002  .200000000000000  1.00000000000000  17  .000000000000000  .668740304976422  16  15  4.458268699842813E-002  50  7.500000000000000E-002  302098.186327657  4.00000000000000

Al      
Brems total X-sec. table with C.S+LPM upto E=  5071636.49074410 GeV
  63.8481  12.1847
  80.3800  11.8763
  101.192  11.6756
  127.394  11.4545
  160.379  11.2164
  201.905  10.9646
  254.184  10.7019
  319.999  10.4307
  402.854  10.1526
  507.164  9.86910
  638.481  9.57975
  803.800  9.28782
  1011.92  8.99205
  1273.94  8.69467
  1603.79  8.39792
  2019.05  8.09780
  2541.84  7.79676
  3199.99  7.49542
  4028.54  7.19744
  5071.64  6.89773
  6384.81  6.59922
  8038.00  6.30434
  10119.2  6.01014
  12739.4  5.71872
  16037.9  5.43194
  20190.5  5.14818
  25418.4  4.86983
  31999.9  4.59630
  40285.4  4.32925
  50716.4  4.06853
  63848.1  3.81546
  80380.0  3.56994
  101192.  3.33321
  127394.  3.10524
  160379.  2.88640
  201905.  2.67744
  254184.  2.47827
  319999.  2.28910
  402854.  2.11000
  507164.  1.94123
  638481.  1.78253
  803800.  1.63377
  1.011924E+06  1.49477
  1.273937E+06  1.36527
  1.603792E+06  1.24498
  2.019055E+06  1.13353
  2.541840E+06  1.03068
  3.199986E+06  .935907
  4.028544E+06  .848785
  5.071637E+06  .768871

Brems with LPM sampling tbl for small Eg
     .37521     .31178     .26187     .22187     .18946     .16306     .14145
     .12426     .11043     .09924     .09003     .08235     .07585     .07027
     .06536     .06090     .05642

     .38240     .31872     .26854     .22827     .19559     .16893     .14713
     .12977     .11578     .10437     .09494     .08704     .08033     .07453
     .06941     .06470     .05986

     .38866     .32503     .27482     .23444     .20162     .17478     .15296
     .13548     .12132     .10971     .10007     .09196     .08504     .07902
     .07367     .06872     .06348

     .39519     .33164     .28141     .24094     .20799     .18100     .15914
     .14154     .12721     .11539     .10554     .09721     .09006     .08381
     .07823     .07301     .06733

     .40203     .33858     .28834     .24780     .21473     .18754     .16568
     .14795     .13344     .12142     .11134     .10278     .09540     .08892
     .08309     .07759     .07142

     .40916     .34583     .29561     .25501     .22184     .19464     .17257
     .15471     .14002     .12779     .11749     .10869     .10106     .09434
     .08825     .08246     .07575

     .41645     .35327     .30308     .26244     .22914     .20188     .17994
     .16193     .14704     .13459     .12404     .11499     .10711     .10013
     .09377     .08767     .08036

     .42409     .36108     .31094     .27029     .23688     .20956     .18761
     .16947     .15439     .14171     .13092     .12162     .11349     .10624
     .09961     .09318     .08521

     .43197     .36917     .31912     .27847     .24500     .21790     .19566
     .17738     .16212     .14921     .13818     .12862     .12023     .11271
     .10579     .09903     .09034

     .44001     .37743     .32749     .28688     .25340     .22632     .20421
     .18579     .17032     .15718     .14589     .13607     .12739     .11960
     .11238     .10526     .09578

     .44837     .38605     .33625     .29562     .26229     .23525     .21308
     .19453     .17886     .16550     .15396     .14387     .13492     .12684
     .11932     .11183     .10150

     .45696     .39494     .34532     .30468     .27162     .24460     .22237
     .20369     .18783     .17423     .16244     .15209     .14286     .13449
     .12665     .11879     .10752

     .46580     .40411     .35469     .31424     .28136     .25440     .23209
     .21328     .19723     .18340     .17136     .16073     .15123     .14256
     .13440     .12615     .11386

     .47487     .41355     .36435     .32410     .29154     .26463     .24225
     .22330     .20706     .19301     .18071     .16982     .16003     .15106
     .14257     .13391     .12053

     .48424     .42331     .37424     .33446     .30209     .27536     .25280
     .23372     .21730     .20303     .19048     .17932     .16925     .15998
     .15116     .14209     .12753

     .49382     .43334     .38456     .34520     .31310     .28640     .26383
     .24461     .22801     .21352     .20073     .18930     .17894     .16936
     .16020     .15071     .13488

     .50370     .44370     .39523     .35634     .32443     .29780     .27525
     .25592     .23915     .22445     .21142     .19972     .18908     .17919
     .16969     .15976     .14256

     .51374     .45409     .40657     .36808     .33638     .30981     .28722
     .26777     .25083     .23591     .22263     .21067     .19974     .18954
     .17969     .16931     .15064

     .52415     .46519     .41810     .38006     .34860     .32212     .29951
     .27996     .26287     .24776     .23425     .22203     .21082     .20032
     .19011     .17929     .15905

     .53489     .47645     .42992     .39234     .36114     .33478     .31217
     .29255     .27532     .26002     .24630     .23383     .22235     .21154
     .20099     .18970     .16781

     .54575     .48826     .44257     .40538     .37438     .34810     .32547
     .30576     .28838     .27289     .25894     .24623     .23446     .22334
     .21243     .20068     .17700

     .55698     .50033     .45520     .41848     .38775     .36159     .33899
     .31922     .30172     .28607     .27192     .25897     .24695     .23553
     .22427     .21205     .18650

     .56837     .51297     .46861     .43231     .40181     .37574     .35314
     .33330     .31567     .29986     .28550     .27232     .26003     .24831
     .23669     .22400     .19644

     .58023     .52584     .48200     .44622     .41598     .39005     .36750
     .34762     .32990     .31394     .29941     .28601     .27347     .26147
     .24951     .23634     .20668

     .59228     .53926     .49621     .46080     .43080     .40499     .38245
     .36253     .34471     .32861     .31389     .30028     .28750     .27521
     .26290     .24924     .21747

     .60527     .55288     .51077     .47546     .44574     .42008     .39760
     .37767     .35978     .34356     .32869     .31489     .30187     .28931
     .27667     .26254     .22961

     .61807     .56701     .52526     .49072     .46125     .43573     .41330
     .39335     .37539     .35906     .34404     .33005     .31681     .30398
     .29099     .27639     .24227

     .63167     .58130     .54048     .50604     .47688     .45152     .42918
     .40924     .39124     .37482     .35967     .34551     .33207     .31899
     .30568     .29061     .25532

     .64512     .59603     .55560     .52191     .49301     .46781     .44554
     .42561     .40758     .39107     .37580     .36148     .34784     .33451
     .32089     .30535     .26888

     .65923     .61089     .57137     .53781     .50923     .48422     .46206
     .44217     .42412     .40755     .39218     .37773     .36390     .35035
     .33643     .32043     .28281

     .67321     .62612     .58702     .55419     .52588     .50105     .47898
     .45913     .44107     .42446     .40899     .39441     .38042     .36665
     .35244     .33599     .29721

     .68770     .64143     .60322     .57056     .54257     .51796     .49602
     .47623     .45819     .44155     .42602     .41133     .39719     .38322
     .36873     .35184     .31194

     .70206     .65702     .61927     .58733     .55962     .53520     .51339
     .49368     .47565     .45899     .44340     .42862     .41435     .40019
     .38543     .36811     .32711

     .71680     .67264     .63578     .60427     .57666     .55248     .53082
     .51120     .49321     .47656     .46093     .44608     .43169     .41736
     .40236     .38463     .34258

     .73138     .68846     .65208     .62107     .59400     .57003     .54851
     .52898     .51105     .49440     .47876     .46384     .44935     .43486
     .41962     .40149     .35842

     .74624     .70423     .66878     .63822     .61147     .58752     .56618
     .54677     .52891     .51229     .49664     .48168     .46711     .45249
     .43704     .41852     .37449

     .76084     .72014     .68536     .65511     .62872     .60523     .58406
     .56476     .54698     .53040     .51475     .49976     .48512     .47038
     .45472     .43583     .39090

     .77561     .73583     .70183     .67224     .64619     .62293     .60194
     .58277     .56507     .54855     .53292     .51792     .50322     .48838
     .47254     .45329     .40751

     .79013     .75173     .71845     .68937     .66347     .64050     .61972
     .60069     .58310     .56665     .55106     .53606     .52133     .50640
     .49039     .47082     .42427

     .80469     .76744     .73474     .70620     .68086     .65814     .63755
     .61868     .60119     .58482     .56927     .55429     .53953     .52453
     .50837     .48848     .44123

     .81905     .78286     .75114     .72310     .69813     .67567     .65528
     .63655     .61919     .60290     .58742     .57246     .55770     .54264
     .52635     .50617     .45830

     .83310     .79832     .76739     .73988     .71528     .69295     .67278
     .65424     .63701     .62082     .60541     .59049     .57574     .56064
     .54424     .52378     .47539

     .84703     .81347     .78334     .75625     .73206     .71018     .69023
     .67185     .65475     .63867     .62334     .60847     .59374     .57862
     .56212     .54141     .49257

     .86066     .82823     .79898     .77259     .74879     .72719     .70745
     .68924     .67229     .65632     .64107     .62627     .61157     .59644
     .57985     .55891     .50973

     .87396     .84289     .81448     .78866     .76524     .74393     .72441
     .70638     .68957     .67372     .65857     .64385     .62919     .61405
     .59741     .57625     .52683

     .88687     .85725     .82968     .80444     .78143     .76028     .74101
     .72318     .70653     .69081     .67577     .66112     .64652     .63140
     .61471     .59336     .54380

     .89949     .87117     .84447     .81970     .79713     .77644     .75740
     .73975     .72325     .70766     .69273     .67817     .66363     .64854
     .63180     .61028     .56068

     .91170     .88471     .85882     .83479     .81263     .79224     .77343
     .75597     .73963     .72416     .70935     .69488     .68041     .66535
     .64860     .62693     .57739

     .92350     .89777     .87291     .84948     .82774     .80765     .78906
     .77179     .75560     .74028     .72558     .71121     .69682     .68181
     .66504     .64325     .59389

     .93479     .91054     .88656     .86375     .84242     .82264     .80429
     .78720     .77117     .75598     .74140     .72714     .71283     .69787
     .68111     .65921     .61013


Brems with LPM smp tbl; (sqrt(v)-sqrt(vmin)/(1-u)
   11.97079   11.96449   11.97387   11.98818   12.01205   12.08679   12.20363
   12.38442   12.62339   12.88158   13.07621   13.10594   12.92361   12.56519
   12.11012   11.63276

   11.84133   11.84381   11.84367   11.86682   11.88238   11.95193   12.07088
   12.24651   12.48191   12.73702   12.93134   12.96642   12.79283   12.44396
   11.99710   11.52587

   11.69809   11.69294   11.70026   11.69502   11.73677   11.81055   11.92270
   12.09522   12.32444   12.57586   12.77108   12.81179   12.64783   12.30941
   11.87166   11.40743

   11.54283   11.54208   11.54553   11.56882   11.59038   11.65001   11.75915
   11.92889   12.15412   12.40213   12.59714   12.64361   12.49013   12.16313
   11.73534   11.27867

   11.37599   11.39121   11.37947   11.39255   11.41295   11.48306   11.58641
   11.75258   11.97189   12.21508   12.41001   12.46290   12.32022   12.00543
   11.58837   11.14002

   11.19911   11.21016   11.20209   11.21405   11.23483   11.30328   11.40444
   11.56458   11.77780   12.01677   12.21154   12.27063   12.13945   11.83759
   11.43205   10.99259

   11.01720   11.02911   11.01905   11.03444   11.05638   11.11712   11.21637
   11.37167   11.57890   11.81363   12.00733   12.07265   11.95296   11.66433
   11.27065   10.84044

   10.82590   10.81788   10.82847   10.85335   10.86226   10.91829   11.01918
   11.16884   11.37023   11.59925   11.79276   11.86384   11.75617   11.48131
   11.10030   10.67993

   10.62850   10.63683   10.63033   10.62295   10.66776   10.71933   10.81277
   10.95944   11.15478   11.37885   11.57082   11.64792   11.55224   11.29168
   10.92373   10.51371

   10.42900   10.42560   10.43220   10.44038   10.45802   10.51417   10.60650
   10.74682   10.93758   11.15622   11.34675   11.42948   11.34546   11.09925
   10.74447   10.34511

   10.22304   10.21438   10.22463   10.25595   10.26290   10.30876   10.39403
   10.52927   10.71357   10.92626   11.11540   11.20306   11.13116   10.89950
   10.55857   10.17035

   10.01362   10.00315   10.01518   10.02335   10.05256   10.09715   10.17865
   10.30857   10.48584   10.69287   10.87979   10.97272   10.91239   10.69553
   10.36866    9.99188

    9.80142    9.79192    9.80384    9.79038    9.82694    9.87932    9.96032
   10.08470   10.25539   10.45603   10.64086   10.73844   10.68966   10.48772
   10.17525    9.81023

    9.58690    9.58069    9.58873    9.60449    9.61623    9.66137    9.73895
    9.85760   10.02220   10.21772   10.39988   10.50145   10.46384   10.27662
    9.97869    9.62581

    9.36938    9.36946    9.37173    9.37042    9.40549    9.44346    9.51460
    9.62902    9.78729    9.97594   10.15514   10.26059   10.23391   10.06142
    9.77832    9.43783

    9.15096    9.15823    9.15285    9.13600    9.17947    9.21932    9.29039
    9.39893    9.55066    9.73332    9.90925   10.01799   10.00185    9.84422
    9.57592    9.24811

    8.93039    8.91682    8.93209    8.94901    8.95329    8.99516    9.06318
    9.16734    9.31232    9.48857    9.66136    9.77276    9.76683    9.62360
    9.37039    9.05554

    8.71074    8.70559    8.71322    8.71461    8.74251    8.77109    8.83608
    8.93593    9.07524    9.24550    9.41400    9.52822    9.53167    9.40279
    9.16450    8.86269

    8.48814    8.49436    8.49057    8.47947    8.51633    8.54702    8.60601
    8.70302    8.83545    8.99903    9.16384    9.27989    9.29252    9.17760
    8.95450    8.66609

    8.26381    8.25295    8.26604    8.29176    8.29001    8.31668    8.37603
    8.46694    8.59398    8.75111    8.91171    9.02933    9.05050    8.94951
    8.74158    8.46678

    8.04226    8.04172    8.04340    8.05665    8.06389    8.09272    8.14921
    8.23601    8.35669    8.50670    8.66308    8.78118    8.81053    8.72274
    8.52985    8.26866

    7.81721    7.83049    7.81888    7.82118    7.83768    7.86877    7.91941
    8.00025    8.11475    8.25897    8.41040    8.52908    8.56582    8.49126
    8.31334    8.06752

    7.59503    7.58909    7.59624    7.58609    7.61161    7.64492    7.68974
    7.76802    7.87704    8.01477    8.16122    8.28004    8.32340    8.26125
    8.09815    7.86732

    7.37016    7.37786    7.37172    7.39841    7.38540    7.41480    7.46017
    7.53262    7.63665    7.76785    7.90928    8.02763    8.07715    8.02723
    7.87879    7.66263

    7.14807    7.13645    7.14909    7.16334    7.15939    7.19106    7.23374
    7.30235    7.39943    7.52443    7.66082    7.77797    7.83299    7.79456
    7.66222    7.45880

    6.92415    6.92522    6.92458    6.92791    6.93329    6.96108    7.00438
    7.06896    7.16055    7.27958    7.41086    7.52613    7.58632    7.55887
    7.44203    7.24319

    6.70291    6.71399    6.70384    6.69324    6.72261    6.73746    6.77815
    6.83903    6.92585    7.03756    7.16351    7.27736    7.34154    7.32441
    7.22164    7.03512

    6.48068    6.47259    6.48122    6.50597    6.49664    6.51386    6.55201
    6.60759    6.68944    6.79535    6.91591    7.02728    7.09511    7.08776
    6.99756    6.81855

    6.26110    6.26136    6.26238    6.27170    6.27097    6.29043    6.32602
    6.37967    6.45623    6.55663    6.67176    6.78053    6.85099    6.85551
    6.77386    6.60862

    6.04137    6.05013    6.04165    6.03706    6.06036    6.07321    6.10310
    6.15185    6.22423    6.31826    6.42729    6.53334    6.60608    6.61919
    6.54225    6.39322

    5.82439    5.83890    5.82469    5.85094    5.83482    5.84992    5.88034
    5.92753    5.99444    6.08337    6.18668    6.28915    6.36369    6.38345
    6.31690    6.18393

    5.60802    5.59750    5.60774    5.61706    5.62450    5.63291    5.66068
    5.70334    5.76586    5.84945    5.94742    6.04626    6.12218    6.14628
    6.08694    5.97161

    5.39468    5.38627    5.39457    5.38395    5.39929    5.41606    5.44420
    5.48262    5.54143    5.61895    5.71153    5.80662    5.88574    5.91094
    5.86304    5.76545

    5.18266    5.17504    5.18328    5.19897    5.18933    5.20551    5.22779
    5.26533    5.31817    5.39065    5.47779    5.56879    5.64730    5.67187
    5.64072    5.55798

    4.97408    4.96381    4.97388    4.96662    4.97955    4.99506    5.01452
    5.04983    5.10002    5.16698    5.24860    5.33531    5.41170    5.43982
    5.41786    5.35714

    4.76744    4.75258    4.76826    4.78278    4.77000    4.78475    4.80439
    4.83776    4.88305    4.94547    5.02151    5.10564    5.17750    5.21049
    5.20157    5.15625

    4.56478    4.57153    4.56453    4.55157    4.57575    4.58074    4.60039
    4.62910    4.67112    4.72855    4.79976    4.88167    4.94795    4.98209
    4.98653    4.96266

    4.36529    4.36030    4.36646    4.36923    4.36672    4.38315    4.39652
    4.42388    4.46329    4.51559    4.58210    4.65877    4.71875    4.76174
    4.77925    4.77072

    4.16897    4.17925    4.17027    4.18727    4.17296    4.18563    4.19878
    4.22205    4.25854    4.30720    4.36808    4.43926    4.49735    4.54286
    4.57322    4.58540

    3.97711    3.96802    3.97786    3.95833    3.97948    3.98826    4.00417
    4.02527    4.05881    4.10334    4.16177    4.22504    4.27942    4.33371
    4.37399    4.40303

    3.78929    3.78697    3.78923    3.77787    3.80135    3.80343    3.81265
    3.83351    3.86310    3.90459    3.95821    4.01329    4.06999    4.12746
    4.18244    4.22632

    3.60553    3.60592    3.60626    3.59854    3.60848    3.61880    3.62730
    3.64516    3.67241    3.71035    3.75904    3.80993    3.86473    3.92841
    3.99458    4.05643

    3.42684    3.42487    3.42706    3.41997    3.43098    3.43429    3.44806
    3.46345    3.48764    3.52178    3.56582    3.61120    3.66937    3.73881
    3.81421    3.89080

    3.25291    3.24382    3.25352    3.24251    3.25386    3.26238    3.27194
    3.28512    3.30784    3.34011    3.37772    3.42127    3.47905    3.55435
    3.64187    3.73124

    3.08394    3.09294    3.08376    3.06581    3.09210    3.09058    3.09892
    3.11342    3.13299    3.16408    3.19633    3.23672    3.29845    3.37778
    3.47466    3.57794

    2.91998    2.91189    2.91965    2.93796    2.91558    2.92517    2.93503
    2.94671    2.96404    2.99184    3.01882    3.06088    3.12340    3.20999
    3.31451    3.43134

    2.76163    2.76101    2.76121    2.76350    2.76968    2.76612    2.77425
    2.78499    2.80193    2.82400    2.85078    2.89169    2.95687    3.04857
    3.16321    3.29020

    2.60870    2.61014    2.60843    2.59018    2.60903    2.61346    2.61958
    2.62988    2.64570    2.66416    2.68812    2.73163    2.79997    2.89521
    3.01736    3.15534

    2.46127    2.45926    2.46131    2.46568    2.46384    2.46715    2.47102
    2.47973    2.49436    2.50990    2.53405    2.57756    2.64905    2.75069
    2.87857    3.02694

    2.31943    2.30839    2.31984    2.34231    2.31902    2.32102    2.32856
    2.33618    2.34887    2.36119    2.38573    2.43144    2.50607    2.61221
    2.74693    2.90542


 constant for Pair  sampling table at low energies
  1.100000000000000E-003 -2.95860731484178  8.000000000000000E-003  63.8481205758033  12611.1111111111  47  47  5.000000000000000E-002  1.00000000000000  21  4.750000000000000E-002  .103559900713016  .000000000000000  .472870804501588  21  2.364354022507940E-002  .103559900713016  4.744788919871360E-002

Al      
total pair x-sec. at low E
  1.100000E-03  4.256889E-05
  1.396216E-03  2.464147E-03
  1.772199E-03  1.051920E-02
  2.249429E-03  2.462283E-02
  2.855172E-03  4.411537E-02
  3.624033E-03  6.812496E-02
  4.599939E-03  9.583604E-02
  5.838644E-03  .126550
  7.410916E-03  .159681
  9.406581E-03  .194893
  1.193965E-02  .231557
  1.515485E-02  .268762
  1.923585E-02  .306197
  2.441582E-02  .343612
  3.099069E-02  .380768
  3.933609E-02  .417377
  4.992880E-02  .453060
  6.337398E-02  .487385
  8.043978E-02  .519930
  .102101  .550360
  .129596  .578442
  .164494  .604047
  .208790  .627135
  .265015  .647738
  .336380  .665954
  .426963  .681930
  .541939  .695843
  .687876  .707884
  .873112  .718248
  1.10823  .727123
  1.40666  .734688
  1.78546  .741109
  2.26626  .746539
  2.87653  .751113
  3.65115  .754954
  4.63435  .758169
  5.88233  .760853
  7.46636  .763088
  9.47696  .764944
  12.0290  .766482
  15.2682  .767754
  19.3798  .768803
  24.5985  .769668
  31.2226  .770379
  39.6304  .770964
  50.3023  .771444
  63.8481  .771837

Pair table (v-.5)/(1-u) at low E
     .03277     .03176     .03105     .03050     .03006     .02970     .02940
     .02912     .02891     .02870     .02853     .02838     .02826     .02815
     .02805     .02797     .02790     .02785     .02784     .02779     .02781

     .12380     .11994     .11723     .11516     .11348     .11209     .11093
     .10991     .10905     .10829     .10765     .10708     .10660     .10618
     .10583     .10554     .10532     .10513     .10500     .10495     .10492

     .19547     .18937     .18511     .18186     .17923     .17705     .17521
     .17364     .17229     .17111     .17011     .16923     .16848     .16783
     .16730     .16687     .16650     .16624     .16600     .16597     .16588

     .25197     .24417     .23878     .23465     .23135     .22862     .22631
     .22436     .22268     .22122     .21998     .21890     .21798     .21719
     .21652     .21597     .21554     .21522     .21495     .21481     .21479

     .29661     .28760     .28142     .27674     .27301     .26994     .26737
     .26520     .26334     .26174     .26038     .25920     .25819     .25733
     .25663     .25602     .25557     .25524     .25498     .25482     .25475

     .33195     .32217     .31556     .31058     .30665     .30345     .30079
     .29855     .29664     .29503     .29365     .29247     .29147     .29060
     .28990     .28930     .28886     .28848     .28822     .28814     .28805

     .36008     .34990     .34311     .33808     .33413     .33096     .32835
     .32618     .32434     .32279     .32149     .32037     .31944     .31863
     .31799     .31744     .31703     .31668     .31649     .31639     .31630

     .38256     .37232     .36559     .36067     .35686     .35385     .35139
     .34937     .34768     .34628     .34511     .34411     .34330     .34263
     .34205     .34161     .34125     .34095     .34077     .34073     .34064

     .40067     .39061     .38410     .37943     .37588     .37310     .37087
     .36908     .36760     .36640     .36541     .36458     .36392     .36337
     .36292     .36258     .36229     .36207     .36192     .36189     .36184

     .41501     .40546     .39953     .39539     .39233     .39000     .38820
     .38678     .38568     .38480     .38413     .38359     .38316     .38284
     .38258     .38242     .38228     .38219     .38208     .38204     .38206

     .42766     .41880     .41340     .40971     .40706     .40510     .40365
     .40255     .40173     .40113     .40070     .40039     .40018     .40004
     .39994     .39991     .39987     .39985     .39989     .39985     .39987

     .43803     .42988     .42504     .42181     .41958     .41800     .41689
     .41612     .41560     .41528     .41508     .41500     .41499     .41505
     .41512     .41522     .41530     .41538     .41547     .41543     .41551

     .44661     .43918     .43489     .43213     .43030     .42909     .42833
     .42786     .42765     .42759     .42766     .42781     .42800     .42824
     .42846     .42871     .42890     .42906     .42922     .42926     .42932

     .45375     .44705     .44330     .44100     .43957     .43874     .43828
     .43814     .43820     .43840     .43870     .43907     .43948     .43989
     .44028     .44065     .44097     .44124     .44141     .44160     .44159

     .45978     .45378     .45055     .44869     .44765     .44717     .44705
     .44720     .44752     .44798     .44853     .44911     .44973     .45031
     .45089     .45138     .45181     .45217     .45241     .45253     .45264

     .46489     .45958     .45687     .45543     .45478     .45464     .45484
     .45529     .45590     .45663     .45742     .45824     .45906     .45985
     .46056     .46122     .46177     .46222     .46257     .46269     .46282

     .46928     .46465     .46244     .46145     .46119     .46139     .46194
     .46269     .46362     .46462     .46568     .46674     .46779     .46877
     .46967     .47050     .47119     .47170     .47211     .47239     .47246

     .47311     .46914     .46746     .46690     .46704     .46765     .46854
     .46965     .47089     .47218     .47352     .47485     .47613     .47735
     .47844     .47941     .48023     .48091     .48139     .48175     .48177

     .47647     .47317     .47203     .47196     .47253     .47352     .47479
     .47626     .47784     .47945     .48109     .48269     .48421     .48565
     .48693     .48809     .48904     .48982     .49036     .49072     .49084

     .47946     .47684     .47626     .47669     .47770     .47910     .48077
     .48257     .48449     .48642     .48835     .49022     .49201     .49365
     .49515     .49648     .49761     .49847     .49910     .49953     .49964

     .48214     .48023     .48021     .48112     .48259     .48442     .48645
     .48861     .49084     .49311     .49532     .49745     .49948     .50136
     .50306     .50452     .50580     .50677     .50750     .50794     .50811

     .48457     .48336     .48391     .48531     .48721     .48943     .49183
     .49435     .49689     .49942     .50192     .50432     .50659     .50868
     .51056     .51221     .51360     .51470     .51554     .51597     .51618

     .48678     .48627     .48736     .48923     .49154     .49413     .49689
     .49970     .50255     .50538     .50815     .51078     .51327     .51556
     .51763     .51944     .52095     .52220     .52309     .52353     .52379

     .48881     .48895     .49057     .49286     .49557     .49850     .50159
     .50470     .50785     .51094     .51394     .51681     .51951     .52200
     .52425     .52619     .52786     .52920     .53012     .53064     .53091

     .49066     .49144     .49353     .49625     .49930     .50254     .50593
     .50933     .51273     .51607     .51930     .52239     .52528     .52794
     .53034     .53245     .53422     .53561     .53664     .53732     .53749

     .49234     .49372     .49625     .49932     .50271     .50627     .50990
     .51358     .51720     .52075     .52420     .52748     .53057     .53339
     .53594     .53818     .54005     .54157     .54259     .54327     .54351

     .49389     .49579     .49873     .50214     .50581     .50962     .51350
     .51741     .52125     .52501     .52863     .53210     .53535     .53833
     .54100     .54336     .54533     .54692     .54800     .54868     .54897

     .49529     .49768     .50097     .50468     .50862     .51267     .51676
     .52085     .52488     .52883     .53263     .53625     .53963     .54274
     .54555     .54800     .55008     .55173     .55287     .55355     .55388

     .49656     .49939     .50300     .50697     .51112     .51538     .51967
     .52395     .52815     .53224     .53620     .53995     .54347     .54669
     .54962     .55215     .55431     .55603     .55722     .55806     .55826

     .49771     .50091     .50480     .50900     .51336     .51780     .52225
     .52668     .53104     .53526     .53935     .54322     .54685     .55020
     .55321     .55585     .55806     .55980     .56113     .56189     .56214

     .49872     .50226     .50641     .51080     .51534     .51993     .52453
     .52910     .53358     .53793     .54214     .54611     .54985     .55329
     .55637     .55908     .56134     .56318     .56445     .56521     .56556

     .49963     .50347     .50783     .51239     .51709     .52181     .52654
     .53121     .53580     .54029     .54456     .54865     .55246     .55598
     .55916     .56192     .56423     .56610     .56742     .56835     .56855

     .50045     .50455     .50907     .51380     .51862     .52346     .52830
     .53308     .53776     .54231     .54670     .55086     .55476     .55835
     .56155     .56440     .56675     .56868     .57006     .57082     .57116

     .50117     .50547     .51017     .51502     .51993     .52488     .52982
     .53468     .53945     .54409     .54854     .55277     .55674     .56037
     .56367     .56651     .56893     .57088     .57228     .57313     .57341

     .50180     .50629     .51112     .51607     .52109     .52611     .53112
     .53608     .54091     .54562     .55013     .55442     .55843     .56213
     .56545     .56838     .57082     .57279     .57417     .57510     .57536

     .50235     .50701     .51195     .51699     .52209     .52720     .53228
     .53728     .54217     .54693     .55150     .55584     .55990     .56364
     .56701     .56996     .57242     .57438     .57581     .57674     .57702

     .50283     .50763     .51265     .51779     .52295     .52812     .53324
     .53829     .54324     .54804     .55267     .55705     .56115     .56492
     .56832     .57130     .57381     .57580     .57728     .57821     .57844

     .50325     .50817     .51328     .51845     .52368     .52889     .53406
     .53917     .54417     .54899     .55366     .55807     .56220     .56602
     .56944     .57245     .57496     .57700     .57843     .57935     .57965

     .50362     .50862     .51381     .51904     .52431     .52957     .53477
     .53991     .54493     .54983     .55451     .55894     .56310     .56693
     .57039     .57340     .57594     .57798     .57949     .58033     .58067

     .50394     .50903     .51425     .51954     .52485     .53014     .53538
     .54054     .54559     .55051     .55520     .55968     .56385     .56773
     .57118     .57421     .57679     .57879     .58031     .58115     .58153

     .50420     .50936     .51463     .51996     .52530     .53062     .53589
     .54106     .54616     .55108     .55582     .56030     .56451     .56838
     .57186     .57490     .57749     .57955     .58104     .58196     .58225

     .50444     .50965     .51496     .52031     .52567     .53101     .53631
     .54152     .54662     .55155     .55631     .56082     .56504     .56892
     .57243     .57548     .57806     .58010     .58161     .58245     .58286

     .50464     .50989     .51523     .52062     .52599     .53136     .53666
     .54189     .54700     .55197     .55673     .56126     .56549     .56938
     .57289     .57597     .57855     .58064     .58210     .58310     .58336

     .50482     .51010     .51547     .52087     .52626     .53164     .53697
     .54222     .54733     .55229     .55709     .56160     .56585     .56975
     .57327     .57636     .57895     .58102     .58251     .58343     .58378

     .50495     .51027     .51565     .52108     .52648     .53188     .53722
     .54247     .54760     .55259     .55738     .56191     .56616     .57008
     .57360     .57669     .57928     .58134     .58291     .58375     .58413

     .50508     .51043     .51582     .52125     .52667     .53208     .53743
     .54270     .54782     .55282     .55761     .56216     .56642     .57033
     .57387     .57698     .57956     .58167     .58315     .58408     .58442

     .50518     .51055     .51596     .52139     .52683     .53225     .53759
     .54287     .54801     .55300     .55780     .56236     .56662     .57057
     .57408     .57721     .57980     .58189     .58340     .58424     .58466


Pair table at low E; v
     .53545     .53545     .53544     .53542     .53540     .53535     .53529
     .53519     .53509     .53495     .53478     .53458     .53436     .53410
     .53380     .53346     .53309     .53266     .53220     .53169     .53113

     .53786     .53785     .53784     .53782     .53780     .53774     .53768
     .53757     .53746     .53732     .53714     .53693     .53669     .53641
     .53609     .53573     .53533     .53488     .53439     .53384     .53324

     .54499     .54499     .54497     .54495     .54491     .54485     .54477
     .54466     .54452     .54434     .54413     .54389     .54360     .54326
     .54288     .54246     .54198     .54145     .54086     .54021     .53950

     .55663     .55663     .55661     .55658     .55654     .55646     .55636
     .55621     .55604     .55582     .55555     .55524     .55488     .55446
     .55398     .55344     .55284     .55217     .55143     .55061     .54972

     .57243     .57243     .57241     .57237     .57231     .57221     .57208
     .57189     .57167     .57139     .57105     .57065     .57019     .56965
     .56904     .56835     .56758     .56672     .56577     .56472     .56358

     .59192     .59191     .59189     .59185     .59177     .59164     .59148
     .59124     .59095     .59060     .59016     .58966     .58906     .58839
     .58761     .58673     .58575     .58467     .58346     .58214     .58068

     .61454     .61453     .61451     .61445     .61435     .61419     .61398
     .61370     .61333     .61288     .61235     .61172     .61098     .61013
     .60917     .60807     .60685     .60549     .60399     .60234     .60053

     .63966     .63965     .63962     .63955     .63942     .63924     .63897
     .63863     .63819     .63764     .63699     .63622     .63532     .63428
     .63310     .63176     .63027     .62862     .62678     .62476     .62255

     .66662     .66661     .66657     .66649     .66634     .66611     .66580
     .66539     .66486     .66421     .66343     .66250     .66142     .66018
     .65878     .65718     .65540     .65343     .65123     .64883     .64620

     .69474     .69473     .69468     .69459     .69441     .69415     .69378
     .69329     .69268     .69193     .69101     .68993     .68867     .68722
     .68557     .68370     .68162     .67930     .67675     .67393     .67085

     .72337     .72336     .72331     .72320     .72300     .72270     .72227
     .72171     .72101     .72013     .71908     .71784     .71640     .71473
     .71284     .71071     .70831     .70567     .70272     .69951     .69597

     .75190     .75189     .75184     .75171     .75148     .75114     .75066
     .75004     .74924     .74826     .74706     .74567     .74404     .74216
     .74002     .73762     .73492     .73193     .72861     .72498     .72100

     .77979     .77978     .77972     .77957     .77932     .77894     .77841
     .77771     .77682     .77573     .77441     .77285     .77104     .76896
     .76658     .76391     .76092     .75760     .75393     .74990     .74548

     .80655     .80654     .80648     .80632     .80604     .80562     .80504
     .80428     .80330     .80211     .80066     .79895     .79697     .79469
     .79209     .78917     .78589     .78226     .77825     .77384     .76903

     .83182     .83181     .83173     .83156     .83127     .83081     .83019
     .82935     .82830     .82701     .82544     .82359     .82145     .81898
     .81618     .81302     .80949     .80557     .80124     .79649     .79130

     .85529     .85528     .85520     .85502     .85470     .85422     .85354
     .85265     .85153     .85014     .84847     .84650     .84420     .84156
     .83857     .83521     .83144     .82726     .82265     .81760     .81207

     .87678     .87676     .87668     .87648     .87615     .87563     .87492
     .87398     .87278     .87131     .86955     .86746     .86504     .86226
     .85910     .85554     .85158     .84717     .84232     .83701     .83119

     .89615     .89613     .89605     .89584     .89549     .89495     .89420
     .89322     .89196     .89043     .88858     .88639     .88385     .88095
     .87765     .87395     .86981     .86523     .86018     .85464     .84858

     .91338     .91336     .91328     .91306     .91269     .91214     .91136
     .91034     .90902     .90743     .90550     .90325     .90062     .89762
     .89421     .89039     .88611     .88140     .87619     .87048     .86425

     .92850     .92848     .92839     .92817     .92779     .92721     .92641
     .92535     .92401     .92237     .92040     .91807     .91539     .91230
     .90883     .90490     .90055     .89572     .89041     .88459     .87824

     .94159     .94158     .94157     .94150     .94131     .94092     .94025
     .93925     .93786     .93611     .93395     .93142     .92851     .92521
     .92150     .91739     .91286     .90789     .90245     .89652     .89007

     .95277     .95276     .95275     .95268     .95247     .95206     .95138
     .95035     .94896     .94720     .94505     .94255     .93968     .93642
     .93277     .92871     .92423     .91931     .91391     .90802     .90160

     .96221     .96220     .96219     .96210     .96189     .96147     .96075
     .95970     .95831     .95654     .95444     .95197     .94915     .94597
     .94238     .93841     .93400     .92917     .92383     .91801     .91165

     .97007     .97006     .97005     .96996     .96973     .96929     .96854
     .96750     .96609     .96437     .96230     .95991     .95715     .95404
     .95055     .94668     .94238     .93763     .93241     .92667     .92039

     .97654     .97654     .97652     .97642     .97619     .97572     .97496
     .97390     .97252     .97083     .96884     .96652     .96385     .96084
     .95747     .95370     .94951     .94488     .93977     .93414     .92796

     .98180     .98180     .98178     .98168     .98143     .98094     .98018
     .97914     .97778     .97617     .97424     .97200     .96945     .96655
     .96330     .95965     .95560     .95108     .94610     .94060     .93454

     .98603     .98602     .98601     .98589     .98562     .98513     .98438
     .98335     .98206     .98051     .97867     .97653     .97410     .97133
     .96820     .96468     .96076     .95639     .95154     .94617     .94025

     .98939     .98938     .98936     .98925     .98896     .98847     .98772
     .98674     .98551     .98403     .98230     .98027     .97795     .97531
     .97231     .96895     .96516     .96094     .95624     .95101     .94523

     .99202     .99201     .99198     .99186     .99159     .99110     .99038
     .98944     .98829     .98691     .98526     .98335     .98116     .97865
     .97580     .97257     .96893     .96485     .96030     .95524     .94959

     .99406     .99405     .99402     .99390     .99362     .99313     .99247
     .99160     .99051     .98921     .98769     .98590     .98383     .98145
     .97874     .97566     .97218     .96826     .96387     .95895     .95348

     .99563     .99562     .99559     .99547     .99518     .99473     .99409
     .99329     .99229     .99110     .98966     .98800     .98604     .98381
     .98123     .97832     .97499     .97124     .96700     .96227     .95696

     .99681     .99680     .99677     .99665     .99638     .99596     .99536
     .99464     .99371     .99260     .99129     .98974     .98792     .98581
     .98339     .98061     .97744     .97385     .96979     .96522     .96010

     .99770     .99769     .99766     .99754     .99728     .99689     .99636
     .99569     .99485     .99383     .99262     .99118     .98949     .98752
     .98522     .98260     .97959     .97617     .97228     .96789     .96297

     .99836     .99835     .99832     .99820     .99796     .99761     .99713
     .99653     .99576     .99484     .99373     .99239     .99081     .98897
     .98682     .98434     .98148     .97823     .97452     .97032     .96558

     .99884     .99883     .99880     .99868     .99847     .99815     .99774
     .99719     .99650     .99565     .99463     .99340     .99194     .99020
     .98819     .98585     .98315     .98006     .97651     .97250     .96793

     .99919     .99918     .99915     .99904     .99885     .99857     .99819
     .99770     .99708     .99632     .99537     .99425     .99287     .99127
     .98939     .98718     .98463     .98169     .97831     .97446     .97005

     .99944     .99943     .99940     .99931     .99913     .99888     .99855
     .99812     .99756     .99686     .99600     .99495     .99368     .99219
     .99042     .98833     .98593     .98312     .97989     .97617     .97193

     .99962     .99961     .99958     .99949     .99935     .99912     .99883
     .99843     .99793     .99731     .99651     .99554     .99438     .99298
     .99131     .98935     .98706     .98438     .98127     .97768     .97357

     .99974     .99973     .99970     .99962     .99950     .99930     .99905
     .99869     .99824     .99766     .99694     .99604     .99496     .99365
     .99208     .99022     .98802     .98546     .98245     .97899     .97496

     .99983     .99982     .99979     .99973     .99962     .99945     .99922
     .99890     .99849     .99796     .99730     .99646     .99545     .99422
     .99274     .99096     .98885     .98638     .98347     .98008     .97614

     .99988     .99988     .99986     .99980     .99969     .99956     .99934
     .99907     .99870     .99821     .99760     .99683     .99586     .99470
     .99329     .99158     .98955     .98714     .98430     .98099     .97713

     .99992     .99992     .99990     .99986     .99976     .99964     .99946
     .99920     .99886     .99842     .99784     .99712     .99622     .99511
     .99375     .99210     .99012     .98777     .98500     .98173     .97792

     .99995     .99994     .99993     .99988     .99981     .99970     .99953
     .99930     .99900     .99858     .99805     .99736     .99651     .99544
     .99411     .99251     .99059     .98827     .98554     .98232     .97855

     .99997     .99996     .99995     .99991     .99985     .99975     .99961
     .99940     .99911     .99872     .99822     .99756     .99674     .99570
     .99442     .99285     .99096     .98868     .98597     .98278     .97904

     .99998     .99997     .99996     .99993     .99988     .99979     .99965
     .99947     .99919     .99884     .99835     .99773     .99694     .99591
     .99466     .99312     .99124     .98899     .98630     .98314     .97942

     .99999     .99998     .99998     .99995     .99990     .99983     .99970
     .99952     .99928     .99893     .99847     .99786     .99708     .99609
     .99485     .99333     .99147     .98922     .98657     .98341     .97970

     .99999     .99998     .99998     .99998     .99995     .99992     .99983
     .99969     .99950     .99919     .99878     .99821     .99748     .99654
     .99533     .99385     .99203     .98982     .98720     .98407     .98039


constant used in Pair cre. sampling with LPM
  12611.1111111111  25  2.500000000000000E-002  .100000000000000  .000000000000000  1.00000000000000  41  4.10075335208982  3167767.88862597

Al      
Pair total x-sec. with LPM
  12611.1  .773510
  15876.4  .772812
  19987.3  .772812
  25162.5  .772812
  31677.7  .772812
  39879.8  .772120
  50205.7  .772051
  63205.3  .772909
  79570.7  .772320
  100174.  .769975
  126111.  .766171
  158764.  .759351
  199873.  .748848
  251625.  .735286
  316777.  .717928
  398798.  .696706
  502057.  .672355
  632053.  .644905
  795707.  .614941
  1.001736E+06  .583008
  1.261111E+06  .549706
  1.587645E+06  .515664
  1.998726E+06  .481373
  2.516247E+06  .447394
  3.167768E+06  .414114

Pair table with LPM
    1.00000     .99027     .98040     .97041     .96027     .95000     .93960
     .92905     .91836     .90752     .89654     .88538     .87409     .86265
     .85105     .83929     .82737     .81528     .80306     .79066     .77810
     .76539     .75253     .73951     .72634     .71302     .69955     .68595
     .67221     .65834     .64437     .63027     .61607     .60178     .58740
     .57295     .55844     .54387     .52927     .51464     .50000

    1.00000     .99021     .98029     .97025     .96008     .94976     .93931
     .92872     .91798     .90710     .89608     .88490     .87357     .86210
     .85047     .83868     .82674     .81464     .80239     .78999     .77743
     .76472     .75185     .73883     .72567     .71237     .69892     .68534
     .67163     .65779     .64385     .62980     .61563     .60139     .58706
     .57266     .55820     .54370     .52915     .51458     .50000

    1.00000     .99021     .98029     .97025     .96008     .94976     .93931
     .92872     .91798     .90710     .89608     .88490     .87357     .86210
     .85047     .83868     .82674     .81464     .80239     .78999     .77743
     .76472     .75185     .73883     .72567     .71237     .69892     .68534
     .67163     .65779     .64385     .62980     .61563     .60139     .58706
     .57266     .55820     .54370     .52915     .51458     .50000

    1.00000     .99021     .98029     .97025     .96008     .94976     .93931
     .92872     .91798     .90710     .89608     .88490     .87357     .86210
     .85047     .83868     .82674     .81464     .80239     .78999     .77743
     .76472     .75185     .73883     .72567     .71237     .69892     .68534
     .67163     .65779     .64385     .62980     .61563     .60139     .58706
     .57266     .55820     .54370     .52915     .51458     .50000

    1.00000     .99021     .98029     .97025     .96008     .94976     .93931
     .92872     .91798     .90710     .89608     .88490     .87357     .86210
     .85047     .83868     .82674     .81464     .80239     .78999     .77743
     .76472     .75185     .73883     .72567     .71237     .69892     .68534
     .67163     .65779     .64385     .62980     .61563     .60139     .58706
     .57266     .55820     .54370     .52915     .51458     .50000

    1.00000     .99023     .98032     .97028     .96011     .94981     .93937
     .92878     .91805     .90719     .89617     .88502     .87370     .86224
     .85061     .83884     .82691     .81483     .80259     .79020     .77766
     .76496     .75210     .73910     .72596     .71267     .69923     .68562
     .67192     .65799     .64407     .62983     .61570     .60148     .58718
     .57251     .55809     .54361     .52910     .51456     .50000

    1.00000     .99023     .98032     .97028     .96012     .94982     .93937
     .92879     .91807     .90720     .89619     .88502     .87371     .86225
     .85062     .83886     .82693     .81486     .80262     .79023     .77764
     .76485     .75202     .73889     .72577     .71250     .69887     .68535
     .67170     .65792     .64402     .62970     .61561     .60143     .58716
     .57283     .55842     .54396     .52948     .51495     .50000

    1.00000     .99021     .98029     .97025     .96008     .94976     .93931
     .92870     .91798     .90710     .89606     .88488     .87356     .86208
     .85044     .83866     .82662     .81454     .80219     .78982     .77712
     .76446     .75163     .73866     .72529     .71205     .69867     .68514
     .67148     .65769     .64379     .62944     .61534     .60115     .58686
     .57251     .55809     .54361     .52910     .51456     .50000

    1.00000     .99023     .98031     .97027     .96011     .94979     .93935
     .92876     .91804     .90717     .89614     .88499     .87363     .86213
     .85044     .83869     .82668     .81464     .80245     .78992     .77744
     .76481     .75200     .73905     .72594     .71244     .69907     .68554
     .67189     .65809     .64417     .63013     .61599     .60137     .58706
     .57267     .55822     .54372     .52917     .51459     .50000

    1.00000     .99026     .98037     .97036     .96023     .94996     .93954
     .92899     .91830     .90746     .89643     .88526     .87402     .86253
     .85101     .83918     .82737     .81539     .80325     .79095     .77830
     .76569     .75293     .73999     .72690     .71365     .70024     .68641
     .67273     .65892     .64498     .63091     .61672     .60243     .58805
     .57357     .55903     .54443     .52979     .51511     .50000

    1.00000     .99030     .98048     .97051     .96043     .95020     .93986
     .92936     .91868     .90788     .89692     .88592     .87464     .86335
     .85191     .84029     .82838     .81646     .80436     .79211     .77966
     .76705     .75406     .74112     .72802     .71475     .70131     .68772
     .67396     .66006     .64602     .63183     .61753     .60280     .58831
     .57373     .55908     .54437     .52961     .51481     .50000

    1.00000     .99038     .98064     .97079     .96079     .95066     .94039
     .92995     .91941     .90879     .89796     .88708     .87603     .86472
     .85337     .84185     .83015     .81828     .80605     .79385     .78144
     .76885     .75608     .74311     .72997     .71664     .70313     .68921
     .67539     .66140     .64727     .63299     .61858     .60404     .58940
     .57465     .55983     .54493     .52998     .51500     .50000

    1.00000     .99052     .98092     .97120     .96134     .95135     .94123
     .93099     .92062     .91018     .89950     .88877     .87788     .86680
     .85555     .84400     .83241     .82061     .80863     .79644     .78407
     .77148     .75850     .74553     .73237     .71901     .70546     .69172
     .67780     .66370     .64943     .63501     .62043     .60572     .59089
     .57595     .56091     .54551     .53037     .51519     .50000

    1.00000     .99070     .98127     .97173     .96204     .95226     .94236
     .93235     .92223     .91192     .90151     .89092     .88007     .86915
     .85802     .84670     .83518     .82345     .81136     .79923     .78687
     .77431     .76152     .74852     .73529     .72185     .70820     .69435
     .68028     .66603     .65158     .63674     .62199     .60708     .59205
     .57689     .56164     .54631     .53090     .51546     .50000

    1.00000     .99091     .98171     .97240     .96296     .95344     .94381
     .93401     .92414     .91410     .90382     .89342     .88284     .87205
     .86106     .84972     .83833     .82668     .81481     .80271     .79038
     .77781     .76499     .75194     .73865     .72512     .71119     .69722
     .68304     .66864     .65403     .63924     .62426     .60912     .59382
     .57840     .56286     .54723     .53153     .51577     .50000

    1.00000     .99119     .98226     .97321     .96410     .95489     .94553
     .93607     .92638     .91659     .90659     .89640     .88599     .87528
     .86445     .85339     .84208     .83053     .81873     .80666     .79436
     .78179     .76882     .75576     .74242     .72883     .71498     .70089
     .68655     .67197     .65716     .64215     .62692     .61151     .59593
     .58020     .56435     .54840     .53235     .51610     .50000

    1.00000     .99149     .98289     .97417     .96540     .95650     .94750
     .93829     .92893     .91936     .90960     .89956     .88935     .87891
     .86823     .85729     .84609     .83462     .82278     .81078     .79852
     .78597     .77314     .76001     .74662     .73293     .71896     .70471
     .69019     .67541     .66037     .64510     .62960     .61377     .59788
     .58184     .56565     .54934     .53294     .51648     .50000

    1.00000     .99184     .98357     .97526     .96685     .95832     .94961
     .94074     .93166     .92231     .91280     .90305     .89304     .88279
     .87226     .86146     .85032     .83897     .82732     .81539     .80315
     .79061     .77776     .76460     .75113     .73734     .72324     .70884
     .69404     .67906     .66381     .64828     .63250     .61650     .60028
     .58387     .56730     .55059     .53379     .51693     .50000

    1.00000     .99223     .98435     .97645     .96842     .96023     .95188
     .94332     .93450     .92548     .91622     .90670     .89690     .88677
     .87643     .86579     .85487     .84362     .83207     .82020     .80801
     .79546     .78260     .76940     .75579     .74191     .72770     .71316
     .69829     .68309     .66758     .65178     .63570     .61936     .60276
     .58598     .56901     .55190     .53464     .51734     .50000

    1.00000     .99262     .98518     .97768     .97004     .96224     .95420
     .94596     .93748     .92873     .91973     .91039     .90083     .89097
     .88081     .87034     .85954     .84841     .83695     .82516     .81293
     .80044     .78757     .77435     .76076     .74680     .73246     .71776
     .70271     .68728     .67153     .65545     .63903     .62235     .60540
     .58822     .57084     .55329     .53557     .51781     .50000

    1.00000     .99305     .98605     .97897     .97172     .96429     .95660
     .94868     .94048     .93201     .92324     .91421     .90487     .89521
     .88525     .87493     .86428     .85328     .84188     .83016     .81808
     .80561     .79275     .77949     .76585     .75179     .73735     .72251
     .70725     .69162     .67562     .65926     .64252     .62548     .60816
     .59057     .57275     .55474     .53659     .51830     .50000

    1.00000     .99348     .98692     .98025     .97340     .96630     .95898
     .95136     .94344     .93528     .92680     .91801     .90888     .89944
     .88966     .87948     .86898     .85812     .84689     .83524     .82322
     .81078     .79794     .78466     .77096     .75684     .74229     .72730
     .71186     .69603     .67978     .66313     .64609     .62870     .61095
     .59294     .57467     .55619     .53756     .51880     .50000

    1.00000     .99392     .98780     .98153     .97504     .96832     .96131
     .95400     .94640     .93851     .93029     .92175     .91285     .90359
     .89399     .88404     .87370     .86297     .85184     .84029     .82835
     .81594     .80312     .78985     .77612     .76192     .74727     .73215
     .71657     .70053     .68400     .66707     .64972     .63198     .61387
     .59543     .57671     .55776     .53858     .51932     .50000

    1.00000     .99435     .98866     .98278     .97666     .97027     .96357
     .95658     .94929     .94166     .93369     .92536     .91669     .90768
     .89826     .88848     .87829     .86770     .85668     .84525     .83337
     .82102     .80824     .79496     .78120     .76696     .75219     .73695
     .72121     .70497     .68824     .67102     .65336     .63523     .61673
     .59787     .57870     .55926     .53962     .51985     .50000

    1.00000     .99477     .98948     .98399     .97822     .97213     .96577
     .95907     .95205     .94468     .93694     .92887     .92043     .91161
     .90240     .89278     .88276     .87231     .86143     .85007     .83828
     .82600     .81324     .79996     .78619     .77189     .75707     .74171
     .72582     .70936     .69241     .67494     .65696     .63852     .61964
     .60036     .58073     .56081     .54067     .52037     .50000


# ************muon tab*********************** 
#     This table  has been made by using ../../Data/BaseM/Al 
#     with nuclear interaction formula: 1
#     Tue Apr 20 20:14:29 GMT+0900 1999 by KASAHARA using 
#      version epics.uv5.00  
# 
-------------------------------------------
constant used in muon pair creation sampling
  1.000000000000000E-004  .100000000000000  .200000000000000  12.6827011144161  80022.4341598797  1.000000000000000E-002  101  20  39  80022.4341598797

Al      
Muon pair cre. total X-sec. table (Prob./X0) upto E=  80022.4341598798 GeV
  12.6827  5.741210E-03
  15.9666  6.882553E-03
  20.1007  8.165129E-03
  25.3053  9.568896E-03
  31.8575  1.104443E-02
  40.1062  1.256676E-02
  50.4907  1.411664E-02
  63.5641  1.567814E-02
  80.0224  1.723739E-02
  100.742  1.878207E-02
  126.827  2.030102E-02
  159.666  2.178412E-02
  201.007  2.322215E-02
  253.053  2.460686E-02
  318.575  2.593092E-02
  401.062  2.718801E-02
  504.907  2.837289E-02
  635.641  2.948150E-02
  800.224  3.051095E-02
  1007.42  3.145964E-02
  1268.27  3.232722E-02
  1596.66  3.311461E-02
  2010.07  3.382384E-02
  2530.53  3.445801E-02
  3185.75  3.502106E-02
  4010.62  3.551760E-02
  5049.07  3.595271E-02
  6356.41  3.633170E-02
  8002.24  3.665999E-02
  10074.2  3.694288E-02
  12682.7  3.718549E-02
  15966.6  3.739261E-02
  20100.7  3.756870E-02
  25305.3  3.771780E-02
  31857.5  3.784359E-02
  40106.2  3.794931E-02
  50490.7  3.803785E-02
  63564.1  3.811172E-02
  80022.4  3.817314E-02

Al      
dE/dx(v<vmin)/Emu (/(g/cm2))by muon pair cre.
  12.6827  .000000
  15.9666  .000000
  20.1007  .000000
  25.3053  1.101281E-10
  31.8575  5.078875E-10
  40.1062  1.242347E-09
  50.4907  2.325282E-09
  63.5641  3.748140E-09
  80.0224  5.490825E-09
  100.742  7.526724E-09
  126.827  9.825803E-09
  159.666  1.235654E-08
  201.007  1.508711E-08
  253.053  1.798605E-08
  318.575  2.102266E-08
  401.062  2.416706E-08
  504.907  2.739022E-08
  635.641  3.066391E-08
  800.224  3.396063E-08
  1007.42  3.725366E-08
  1268.27  4.051713E-08
  1596.66  4.372625E-08
  2010.07  4.685766E-08
  2530.53  4.988983E-08
  3185.75  5.280352E-08
  4010.62  5.558219E-08
  5049.07  5.821238E-08
  6356.41  6.068388E-08
  8002.24  6.298986E-08
  10074.2  6.512676E-08
  12682.7  6.709406E-08
  15966.6  6.889397E-08
  20100.7  7.053109E-08
  25305.3  7.201184E-08
  31857.5  7.334417E-08
  40106.2  7.453707E-08
  50490.7  7.560018E-08
  63564.1  7.654352E-08
  80022.4  7.737714E-08

Al      
dE/dx(v<vmax)/Emu (/(g/cm2))by muon pair cre.
  12.6827  9.218080E-07
  15.9666  1.018760E-06
  20.1007  1.116595E-06
  25.3053  1.214615E-06
  31.8575  1.312138E-06
  40.1062  1.408508E-06
  50.4907  1.503056E-06
  63.5641  1.595158E-06
  80.0224  1.684205E-06
  100.742  1.769659E-06
  126.827  1.851031E-06
  159.666  1.927930E-06
  201.007  2.000042E-06
  253.053  2.067162E-06
  318.575  2.129176E-06
  401.062  2.186068E-06
  504.907  2.237901E-06
  635.641  2.284818E-06
  800.224  2.327017E-06
  1007.42  2.364747E-06
  1268.27  2.398291E-06
  1596.66  2.427952E-06
  2010.07  2.454048E-06
  2530.53  2.476900E-06
  3185.75  2.496821E-06
  4010.62  2.514117E-06
  5049.07  2.529077E-06
  6356.41  2.541970E-06
  8002.24  2.553046E-06
  10074.2  2.562533E-06
  12682.7  2.570636E-06
  15966.6  2.577539E-06
  20100.7  2.583406E-06
  25305.3  2.588382E-06
  31857.5  2.592593E-06
  40106.2  2.596150E-06
  50490.7  2.599149E-06
  63564.1  2.601674E-06
  80022.4  2.603796E-06

constant used in muon Brems sampling
  1.000000000000000E-004  .100000000000000  .200000000000000  18.1181444491658  72129.6322233696  1.000000000000000E-002  101  19  38  90805.8269493675

Al      
Muon brems total X-sec. table (Prob./X0) upto E=  90805.8269493677 GeV
  18.1181  4.449986E-04
  22.8094  4.511312E-04
  28.7153  4.569208E-04
  36.1505  4.623716E-04
  45.5107  4.674923E-04
  57.2946  4.722923E-04
  72.1296  4.767725E-04
  90.8058  4.809407E-04
  114.318  4.848056E-04
  143.918  4.883769E-04
  181.181  4.916652E-04
  228.094  4.946817E-04
  287.153  4.974385E-04
  361.505  4.999484E-04
  455.107  5.022245E-04
  572.946  5.042807E-04
  721.296  5.061306E-04
  908.058  5.077886E-04
  1143.18  5.092687E-04
  1439.18  5.105847E-04
  1811.81  5.117503E-04
  2280.94  5.127788E-04
  2871.53  5.136827E-04
  3615.05  5.144743E-04
  4551.07  5.151650E-04
  5729.46  5.157654E-04
  7212.96  5.162856E-04
  9080.58  5.167347E-04
  11431.8  5.171211E-04
  14391.8  5.174526E-04
  18118.1  5.177360E-04
  22809.4  5.179776E-04
  28715.3  5.181830E-04
  36150.4  5.183570E-04
  45510.7  5.185042E-04
  57294.6  5.186283E-04
  72129.6  5.187326E-04
  90805.8  5.188202E-04

Al      
dE/dx(v<vmin)/Emu (/(g/cm2))by muon brems
  18.1181  2.517875E-10
  22.8094  2.518118E-10
  28.7153  2.518312E-10
  36.1505  2.518466E-10
  45.5107  2.518588E-10
  57.2946  2.518686E-10
  72.1296  2.518763E-10
  90.8058  2.518824E-10
  114.318  2.518873E-10
  143.918  2.518912E-10
  181.181  2.518943E-10
  228.094  2.518967E-10
  287.153  2.518987E-10
  361.505  2.519002E-10
  455.107  2.519014E-10
  572.946  2.519024E-10
  721.296  2.519032E-10
  908.058  2.519038E-10
  1143.18  2.519043E-10
  1439.18  2.519047E-10
  1811.81  2.519050E-10
  2280.94  2.519052E-10
  2871.53  2.519054E-10
  3615.05  2.519056E-10
  4551.07  2.519057E-10
  5729.46  2.519058E-10
  7212.96  2.519059E-10
  9080.58  2.519059E-10
  11431.8  2.519060E-10
  14391.8  2.519060E-10
  18118.1  2.519061E-10
  22809.4  2.519061E-10
  28715.3  2.519061E-10
  36150.4  2.519061E-10
  45510.7  2.519061E-10
  57294.6  2.519061E-10
  72129.6  2.519061E-10
  90805.8  2.519061E-10

Al      
dE/dx(v<vmax)/Emu (/(g/cm2))by muon brems
  18.1181  9.367383E-07
  22.8094  9.843684E-07
  28.7153  1.031562E-06
  36.1505  1.078222E-06
  45.5107  1.124635E-06
  57.2946  1.170432E-06
  72.1296  1.215424E-06
  90.8058  1.259500E-06
  114.318  1.302547E-06
  143.918  1.344450E-06
  181.181  1.385093E-06
  228.094  1.424365E-06
  287.153  1.462158E-06
  361.505  1.498371E-06
  455.107  1.532911E-06
  572.946  1.565701E-06
  721.296  1.596674E-06
  908.058  1.625781E-06
  1143.18  1.652990E-06
  1439.18  1.678286E-06
  1811.81  1.701676E-06
  2280.94  1.723183E-06
  2871.53  1.742847E-06
  3615.05  1.760727E-06
  4551.07  1.776893E-06
  5729.46  1.791430E-06
  7212.96  1.804430E-06
  9080.58  1.815995E-06
  11431.8  1.826230E-06
  14391.8  1.835241E-06
  18118.1  1.843137E-06
  22809.4  1.850023E-06
  28715.3  1.856002E-06
  36150.4  1.861170E-06
  45510.7  1.865619E-06
  57294.6  1.869435E-06
  72129.6  1.872694E-06
  90805.8  1.875469E-06

constant used in muon Nuc. int. sampling
  1.000000000000000E-004  .100000000000000  .200000000000000  33.3782087205047  83842.2695931305  1.000000000000000E-002  101  18  35  83842.2695931305

Al      
Muon Nuc. Int. total X-sec. table (Prob./X0) upto E=  83842.2695931306 GeV
  33.3782  7.557227E-05
  42.0207  8.358211E-05
  52.9009  9.193638E-05
  66.5983  1.009768E-04
  83.8423  1.094327E-04
  105.551  1.198642E-04
  132.881  1.287001E-04
  167.287  1.386106E-04
  210.602  1.488918E-04
  265.133  1.595150E-04
  333.782  1.709918E-04
  420.207  1.816115E-04
  529.009  1.947567E-04
  665.983  2.058614E-04
  838.423  2.182349E-04
  1055.51  2.310922E-04
  1328.81  2.443112E-04
  1672.87  2.585468E-04
  2106.02  2.716922E-04
  2651.33  2.878675E-04
  3337.82  3.016223E-04
  4202.07  3.167892E-04
  5290.09  3.325560E-04
  6659.83  3.486846E-04
  8384.23  3.554351E-04
  10555.1  3.488569E-04
  13288.1  3.451210E-04
  16728.7  3.444712E-04
  21060.2  3.439835E-04
  26513.3  3.437578E-04
  33378.2  3.438959E-04
  42020.7  3.443966E-04
  52900.9  3.452932E-04
  66598.3  3.465003E-04
  83842.3  3.481630E-04

  1.797315362025090E-002 = power of energy dependence at higher energies
Al      
dE/dx(v<vmin)/Emu (/(g/cm2))by muon Nuc. int
  33.3782  .000000
  42.0207  .000000
  52.9009  .000000
  66.5983  .000000
  83.8423  .000000
  105.551  .000000
  132.881  .000000
  167.287  .000000
  210.602  .000000
  265.133  .000000
  333.782  .000000
  420.207  .000000
  529.009  .000000
  665.983  .000000
  838.423  .000000
  1055.51  .000000
  1328.81  .000000
  1672.87  .000000
  2106.02  .000000
  2651.33  .000000
  3337.82  .000000
  4202.07  .000000
  5290.09  .000000
  6659.83  .000000
  8384.23  3.945782E-11
  10555.1  1.196092E-10
  13288.1  1.724819E-10
  16728.7  2.048614E-10
  21060.2  2.308013E-10
  26513.3  2.510570E-10
  33378.2  2.667285E-10
  42020.7  2.781694E-10
  52900.9  2.866907E-10
  66598.3  2.926799E-10
  83842.3  2.965441E-10

  7.337834887736812E-002 = power of energy dependence at higher energies
Al      
dE/dx(v<vmax)/Emu (/(g/cm2))by muon Nuc. int
  33.3782  3.865017E-07
  42.0207  3.879348E-07
  52.9009  3.885017E-07
  66.5983  3.884503E-07
  83.8423  3.882043E-07
  105.551  3.880212E-07
  132.881  3.880681E-07
  167.287  3.885002E-07
  210.602  3.894626E-07
  265.133  3.910590E-07
  333.782  3.932719E-07
  420.207  3.960682E-07
  529.009  3.994054E-07
  665.983  4.032374E-07
  838.423  4.074919E-07
  1055.51  4.121209E-07
  1328.81  4.170645E-07
  1672.87  4.222831E-07
  2106.02  4.277249E-07
  2651.33  4.333496E-07
  3337.82  4.391219E-07
  4202.07  4.450114E-07
  5290.09  4.509919E-07
  6659.83  4.570416E-07
  8384.23  4.631418E-07
  10555.1  4.692770E-07
  13288.1  4.754344E-07
  16728.7  4.816033E-07
  21060.2  4.877747E-07
  26513.3  4.939417E-07
  33378.2  5.000984E-07
  42020.7  5.062399E-07
  52900.9  5.123624E-07
  66598.3  5.184630E-07
  83842.3  5.245392E-07

  5.100331263626254E-002 = power of energy dependence at higher energies
muon nuc. int.  sampling table
   -1.63810   -1.37813   -1.18640   -1.05503    -.95715    -.88020    -.81755
    -.76524    -.72058    -.68179    -.64761    -.61714    -.58970    -.56479
    -.54200    -.52103    -.50161    -.48354    -.46666    -.45082    -.43591
    -.42182    -.40848    -.39585    -.38388    -.37251    -.36168    -.35134
    -.34147    -.33201    -.32295    -.31424    -.30587    -.29781    -.29004
    -.28254    -.27529    -.26828    -.26149    -.25492    -.24854    -.24234
    -.23633    -.23047    -.22478    -.21923    -.21383    -.20856    -.20341
    -.19839    -.19348    -.18868    -.18398    -.17939    -.17488    -.17047
    -.16614    -.16190    -.15773    -.15364    -.14961    -.14566    -.14177
    -.13794    -.13417    -.13045    -.12679    -.12318    -.11961    -.11609
    -.11261    -.10917    -.10577    -.10240    -.09907    -.09576    -.09248
    -.08923    -.08600    -.08278    -.07958    -.07639    -.07322    -.07004
    -.06687    -.06369    -.06051    -.05731    -.05409    -.05084    -.04756
    -.04421    -.04081    -.03731    -.03367    -.02995    -.02555    -.02116
    -.01725    -.01195    -.00138

   -1.83810   -1.54223   -1.32924   -1.18295   -1.07379    -.98817    -.91861
    -.86043    -.81067    -.76735    -.72906    -.69483    -.66389    -.63569
    -.60979    -.58598    -.56403    -.54370    -.52478    -.50709    -.49051
    -.47492    -.46020    -.44627    -.43306    -.42050    -.40854    -.39712
    -.38619    -.37573    -.36569    -.35604    -.34675    -.33781    -.32917
    -.32083    -.31277    -.30496    -.29740    -.29006    -.28294    -.27602
    -.26928    -.26273    -.25635    -.25013    -.24406    -.23814    -.23235
    -.22670    -.22116    -.21575    -.21045    -.20526    -.20017    -.19517
    -.19027    -.18546    -.18073    -.17608    -.17151    -.16701    -.16258
    -.15822    -.15392    -.14968    -.14550    -.14137    -.13729    -.13326
    -.12928    -.12534    -.12144    -.11758    -.11375    -.10995    -.10618
    -.10244    -.09872    -.09502    -.09134    -.08767    -.08401    -.08035
    -.07669    -.07303    -.06936    -.06567    -.06196    -.05821    -.05442
    -.05057    -.04664    -.04262    -.03848    -.03411    -.02959    -.02399
    -.01903    -.01354    -.00087

   -2.03810   -1.70667   -1.47211   -1.31056   -1.18998   -1.09555   -1.01864
    -.95408    -.89864    -.85014    -.80705    -.76864    -.73422    -.70311
    -.67478    -.64881    -.62487    -.60270    -.58205    -.56277    -.54467
    -.52765    -.51158    -.49637    -.48193    -.46820    -.45512    -.44262
    -.43066    -.41919    -.40818    -.39759    -.38740    -.37757    -.36807
    -.35889    -.35001    -.34141    -.33306    -.32496    -.31708    -.30942
    -.30197    -.29471    -.28763    -.28072    -.27397    -.26738    -.26093
    -.25462    -.24845    -.24240    -.23647    -.23065    -.22494    -.21933
    -.21382    -.20841    -.20308    -.19784    -.19269    -.18761    -.18261
    -.17769    -.17284    -.16805    -.16333    -.15867    -.15406    -.14951
    -.14501    -.14056    -.13615    -.13179    -.12746    -.12317    -.11892
    -.11469    -.11049    -.10631    -.10215    -.09800    -.09387    -.08974
    -.08562    -.08149    -.07735    -.07319    -.06901    -.06479    -.06053
    -.05620    -.05179    -.04728    -.04263    -.03781    -.03268    -.02702
    -.02055    -.01478    -.00055

   -2.23810   -1.87127   -1.61475   -1.43746   -1.30531   -1.20145   -1.11639
   -1.04455    -.98254    -.92886    -.88182    -.84010    -.80272    -.76893
    -.73816    -.70995    -.68394    -.65984    -.63740    -.61641    -.59673
    -.57819    -.56068    -.54410    -.52835    -.51336    -.49906    -.48539
    -.47229    -.45973    -.44765    -.43603    -.42482    -.41400    -.40354
    -.39342    -.38364    -.37415    -.36496    -.35605    -.34738    -.33896
    -.33077    -.32279    -.31501    -.30743    -.30003    -.29280    -.28573
    -.27882    -.27205    -.26543    -.25893    -.25257    -.24633    -.24020
    -.23418    -.22827    -.22245    -.21673    -.21110    -.20556    -.20010
    -.19472    -.18941    -.18418    -.17901    -.17391    -.16886    -.16388
    -.15894    -.15406    -.14923    -.14444    -.13969    -.13498    -.13031
    -.12566    -.12105    -.11645    -.11188    -.10732    -.10278    -.09824
    -.09370    -.08916    -.08461    -.08003    -.07543    -.07080    -.06611
    -.06135    -.05651    -.05156    -.04645    -.04115    -.03555    -.02960
    -.02212    -.01582    -.00035

   -2.43810   -2.03585   -1.75692   -1.56354   -1.41911   -1.30481   -1.21037
   -1.13099   -1.06365   -1.00549    -.95452    -.90931    -.86877    -.83212
    -.79872    -.76808    -.73981    -.71358    -.68914    -.66627    -.64478
    -.62453    -.60537    -.58722    -.57001    -.55366    -.53808    -.52322
    -.50901    -.49539    -.48233    -.46978    -.45769    -.44605    -.43481
    -.42395    -.41345    -.40328    -.39342    -.38384    -.37455    -.36551
    -.35671    -.34814    -.33979    -.33164    -.32369    -.31591    -.30832
    -.30089    -.29361    -.28648    -.27950    -.27265    -.26593    -.25933
    -.25285    -.24648    -.24021    -.23404    -.22798    -.22200    -.21611
    -.21030    -.20457    -.19892    -.19334    -.18782    -.18237    -.17698
    -.17165    -.16637    -.16114    -.15596    -.15082    -.14572    -.14066
    -.13563    -.13063    -.12565    -.12070    -.11576    -.11084    -.10592
    -.10100    -.09608    -.09115    -.08619    -.08121    -.07619    -.07111
    -.06596    -.06072    -.05537    -.04985    -.04413    -.03813    -.03165
    -.02372    -.01664    -.00022

   -2.63810   -2.20021   -1.89823   -1.68828   -1.53047   -1.40423   -1.30084
   -1.21505   -1.14223   -1.07929   -1.02408    -.97504    -.93104    -.89119
    -.85482    -.82141    -.79053    -.76195    -.73541    -.71065    -.68746
    -.66569    -.64516    -.62577    -.60739    -.58993    -.57331    -.55745
    -.54229    -.52777    -.51385    -.50047    -.48760    -.47519    -.46322
    -.45166    -.44047    -.42964    -.41914    -.40895    -.39906    -.38944
    -.38007    -.37096    -.36207    -.35340    -.34494    -.33667    -.32859
    -.32068    -.31294    -.30536    -.29793    -.29064    -.28349    -.27646
    -.26957    -.26279    -.25612    -.24956    -.24310    -.23674    -.23047
    -.22429    -.21819    -.21217    -.20623    -.20036    -.19456    -.18882
    -.18314    -.17752    -.17195    -.16642    -.16095    -.15551    -.15011
    -.14474    -.13941    -.13410    -.12881    -.12354    -.11827    -.11302
    -.10776    -.10250    -.09723    -.09193    -.08660    -.08123    -.07580
    -.07030    -.06469    -.05897    -.05307    -.04696    -.04053    -.03362
    -.02547    -.01737    -.00014

   -2.83810   -2.36422   -2.03844   -1.81116   -1.63841   -1.50036   -1.38889
   -1.29627   -1.21754   -1.14937   -1.08946   -1.03613    -.98817    -.94487
    -.90558    -.86969    -.83670    -.80623    -.77795    -.75159    -.72692
    -.70377    -.68197    -.66138    -.64188    -.62337    -.60576    -.58896
    -.57292    -.55757    -.54285    -.52871    -.51512    -.50203    -.48941
    -.47722    -.46543    -.45403    -.44298    -.43226    -.42185    -.41174
    -.40191    -.39233    -.38300    -.37390    -.36502    -.35634    -.34785
    -.33955    -.33142    -.32345    -.31565    -.30799    -.30047    -.29309
    -.28583    -.27870    -.27168    -.26477    -.25796    -.25126    -.24465
    -.23813    -.23169    -.22533    -.21905    -.21285    -.20671    -.20063
    -.19462    -.18866    -.18276    -.17690    -.17109    -.16532    -.15959
    -.15389    -.14822    -.14258    -.13696    -.13135    -.12575    -.12016
    -.11457    -.10896    -.10335    -.09770    -.09203    -.08630    -.08052
    -.07465    -.06868    -.06257    -.05629    -.04978    -.04294    -.03560
    -.02740    -.01806    -.00009

   -3.03810   -2.52774   -2.17751   -1.93161   -1.74260   -1.59408   -1.47401
   -1.37401   -1.28877   -1.21475   -1.14969   -1.09225   -1.04102    -.99493
    -.95314    -.91502    -.88002    -.84773    -.81780    -.78993    -.76389
    -.73947    -.71651    -.69484    -.67434    -.65491    -.63645    -.61886
    -.60208    -.58603    -.57066    -.55590    -.54171    -.52804    -.51487
    -.50214    -.48984    -.47794    -.46640    -.45521    -.44434    -.43377
    -.42349    -.41347    -.40371    -.39418    -.38489    -.37580    -.36691
    -.35822    -.34970    -.34136    -.33317    -.32515    -.31726    -.30952
    -.30191    -.29442    -.28705    -.27979    -.27264    -.26560    -.25865
    -.25179    -.24502    -.23833    -.23172    -.22518    -.21871    -.21231
    -.20597    -.19969    -.19345    -.18727    -.18114    -.17504    -.16899
    -.16296    -.15697    -.15099    -.14504    -.13911    -.13318    -.12725
    -.12133    -.11539    -.10943    -.10345    -.09742    -.09135    -.08521
    -.07898    -.07264    -.06616    -.05950    -.05259    -.04533    -.03759
    -.02905    -.01874    -.00005

   -3.23810   -2.69067   -2.31521   -2.04897   -1.84450   -1.68502   -1.55567
   -1.44756   -1.35519   -1.27572   -1.20651   -1.14552   -1.09121   -1.04243
    -.99829    -.95808    -.92125    -.88732    -.85593    -.82676    -.79956
    -.77409    -.75014    -.72757    -.70622    -.68598    -.66675    -.64842
    -.63093    -.61420    -.59817    -.58278    -.56798    -.55374    -.54000
    -.52674    -.51392    -.50150    -.48947    -.47780    -.46646    -.45544
    -.44472    -.43427    -.42409    -.41415    -.40445    -.39496    -.38569
    -.37661    -.36772    -.35900    -.35045    -.34206    -.33382    -.32573
    -.31777    -.30994    -.30223    -.29463    -.28715    -.27977    -.27249
    -.26530    -.25821    -.25119    -.24426    -.23740    -.23061    -.22389
    -.21722    -.21062    -.20407    -.19757    -.19112    -.18470    -.17832
    -.17198    -.16566    -.15937    -.15309    -.14683    -.14057    -.13432
    -.12806    -.12179    -.11550    -.10917    -.10280    -.09638    -.08989
    -.08330    -.07660    -.06974    -.06269    -.05539    -.04773    -.03954
    -.03050    -.01943    -.00003

   -3.43810   -2.85292   -2.45130   -2.16287   -1.94398   -1.77278   -1.63330
   -1.51670   -1.41841   -1.33418   -1.26098   -1.19661   -1.13945   -1.08824
   -1.04202   -1.00004    -.96165    -.92633    -.89366    -.86330    -.83497
    -.80843    -.78350    -.75999    -.73776    -.71669    -.69667    -.67760
    -.65939    -.64198    -.62530    -.60929    -.59390    -.57908    -.56479
    -.55100    -.53766    -.52474    -.51223    -.50009    -.48829    -.47683
    -.46567    -.45480    -.44420    -.43386    -.42376    -.41388    -.40423
    -.39477    -.38551    -.37643    -.36753    -.35878    -.35020    -.34176
    -.33346    -.32529    -.31725    -.30932    -.30151    -.29381    -.28620
    -.27870    -.27128    -.26395    -.25670    -.24952    -.24242    -.23538
    -.22841    -.22149    -.21463    -.20781    -.20104    -.19431    -.18762
    -.18096    -.17433    -.16771    -.16112    -.15453    -.14796    -.14138
    -.13479    -.12818    -.12156    -.11489    -.10818    -.10141    -.09457
    -.08762    -.08055    -.07332    -.06589    -.05819    -.05011    -.04148
    -.03196    -.02016    -.00002

   -3.63810   -3.01445   -2.58552   -2.27465   -2.04077   -1.85692   -1.70695
   -1.58334   -1.47947   -1.39072   -1.31385   -1.24648   -1.18687   -1.13358
   -1.08551   -1.04182   -1.00185    -.96508    -.93108    -.89949    -.87003
    -.84243    -.81650    -.79207    -.76897    -.74707    -.72626    -.70645
    -.68754    -.66946    -.65214    -.63551    -.61953    -.60414    -.58930
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