CERN Program Library Long Writeup W5013 - CERNLIB ...

100 E+ dep − E− dep
√ (%)
σ+ 2 + σ−
2
Depth C Pb
(X 0 units) No e ± diff e ± diff No e ± diff e ± diff
0.5 -11.7 -13.0 -0.8 -3.9
1.0 -5.3 -4.9 -1.0 -4.1
1.5 +7.3 +8.0 -1.4 -3.5
2.0 +7.1 +5.3 -0.7 -0.0
2.5 +4.9 +4.3 +1.7 +3.6
3.0 +4.8 +4.1 +1.1 +4.3
3.5 +3.3 +2.7 +2.7 +3.1
4.0 +3.6 +5.3 +2.9 +3.0
4.5 +1.7 +2.8 +0.5 +2.3
5.0 +3.4 +3.5 -1.9 +1.8
Table 1.5: Difference in the shower development for e − /e + in Carbon and Lead. No diff refers to the value
without the correction for the difference e − /e + .
We have defined weight factors F l and F σ for the positron continuous energy loss and discrete bremsstrahlung
cross section:
F l = 1 ɛ 0
∫ ɛ0
0
f(ɛ)dɛ F σ = 1 ∫ 1
f(ɛ)dɛ (13)
1 − ɛ 0 ɛ 0
where ɛ 0 = kc
T
and k c is the photon cut BCUTE. In this scheme the positron energy loss and discrete bremsstrahlung
can be calculated as:
(
− dE
dx
) +
= F l
(
− dE
dx
) −
σ + brems = F σσ − brems
As in this approximation the photon spectra are identical, the same SUBROUTINE is used for generating
e − /e + bremsstrahlung. The following relations hold:
F σ = η(1 − ɛ 0 ) 1 η −1 η 1 − (1 − ɛ 0)
ɛ 0
= η ⇒
{
Fl >η
F σ