This is a code to follow individual particle down to
Ekine=1MeV while calculating  A.S size (Ne) by a hybrid
method. You can verify that the hybrid method and
full M.C results  agrees quite well (except for shower tail)
if particle tracking is done by 1 dimensional mode. However, if
individual particle traking is done by 3-D mode, 
many low energy particles are scattered away, thus
the particle number at a give horizontal  depth  
becomes  different from the one by 1-D mode.  As a
result, 3-D showers develop rapider than those of the
hybrid mode (the hybrid mode  has no difference
between 1-D and 3-D modes, becuase the hybrid mode
replaces  high energy electrons by a formula (
so called B-approximation of shower theory ) and
for such high energy particles scattering can be neglected.

The shower max values become less than the hybrid
mode by a factor of 20~30 %.
The shower tail of 3-D showers becomes 
little bit larger than the hybrid mode. This last fact 
is due to the difference of cross-sections;
The B-approximation dose not include the Compton scattering
while the constant pair creation cross-section is assumed,
and thus makes the rapider attenuation of showers.



