CERN Program Library Long Writeup W5013 - CERNLIB ...

∆σ
σ
=
{
12 − 15% for T ≤ 1MeV
≤ 5 − 6% for 1MeV < T ≤ 10TeV
∆E brem
Loss
E brem
Loss
=
⎧
⎪⎨
⎪⎩
10 − 15% for T ≤ 1MeV
5 − 6% for 1MeV < T ≤ 100GeV
10% for 100GeV < T ≤ 10TeV
We have performed a fit to the “data” without the Midgal corrections, too. In this case we used the data of
Seltzer and Berger without any correction for T ≤ 10 GeV and we used the Bethe-Heitler cross-section for
T ≥ 10 GeV. The parameterised forms of the cross-section and energy loss are the same as they were in
the first fit (i.e. (3) and (4)), only the numerical values of the parameters have changed. These values are
in DATA statements in the functions GBRSGE and GBRELE and this second kind of parameterisation can be
activated using the PATCHY switch +USE,BETHE. (The two parameterisations give different results for high
electron energy.)
The energy loss due to soft photon bremsstrahlung is tabulated at initialisation time as a function of the
medium and of the energy by routine GBRELA (see JMATE data structure).
The mean free path for discrete bremsstrahlung is tabuled at initialisation time as a function of the medium
and of the energy by routine GBRSGA (see JMATE data structure).
2.2 Corrections for e − /e + differences
The radiative energy loss for electrons or positrons is:
− 1 ( ) dE ±
= N Avαre
2
ρ dx rad A (T + m)Z2 Φ ± rad (Z, T )
∫
Φ ± rad (Z, T ) = 1
T
αre 2 k dσ±
Z2 (T + m) dk dk
0
Reference [77] says that:
“The differences between the radiative loss of positrons and electrons are considerable and cannot be disregarded.
[...] The ratio of the radiative energy loss for positrons to that for electrons obeys a simple scaling law, [...]
is a function only of the quantity T/Z 2 ”
In other words:
η = Φ+ rad (Z, T )
Φ − rad (Z, T ) = η ( T
Z 2 )
The authors have calculated this function in the range 10 −7 ≤ T Z 2 ≤ 0.5 (here the kinetic energy T is
expressed in MeV). Their data can be fairly accurately reproduced using a parametrisation:
η =
⎧
⎪⎨
⎪⎩
0 if x ≤−8
1
2 + 1 π arctan ( a 1 x + a 3 x 3 + a 5 x 5) if −8