CERN Program Library Long Writeup W5013 - CERNLIB ...

where:
x = log
(C T )
Z 2 (T in GeV)
C = 7.5221 × 10 6
a 1 = 0.415
a 3 = 0.0021
a 5 = 0.00054
This e − /e + energy loss difference is not a pure low-energy phenomenon (at least for high Z), as it can be
seen from Tables 1.2, 1.3 and 1.4.
T
Z 2 (GeV ) T η
( )
rad. loss
total loss e −
10 −9 ∼ 7keV ∼ 0.1 ∼ 0%
10 −8 67keV ∼ 0.2 ∼ 1%
2 × 10 −7 1.35MeV ∼ 0.5 ∼ 15%
2 × 10 −6 13.5MeV ∼ 0.8 ∼ 60%
2 × 10 −5 135.MeV ∼ 0.95 > 90%
Table 1.2: ratio of the e − /e + radiative energy loss in lead (Z=82).
The scaling holds for the ratio of the total radiative energy losses, but it is significantly broken for the
photon spectrum in the screened case. In case of a point Coulomb charge the scaling would hold also for
the spectrum. The scaling can be expressed by:
Φ + ( ) T
dσ +
Φ − = η dk
Z 2
dσ −
dk
= does not scale
If we consider the photon spectrum from bremsstrahlung reported in [77] we see that:
dσ ±
dk
= S± ( k
T
)
S + (k)
S − (k) ≤ 1 S+ (1) = 0 S − (1) > 0
We further assume that:
dσ +
dk
= f(ɛ)dσ− dk
ɛ = k T
(9)
In order to satisfy approximately the scaling law for the ratio of the total radiative energy loss, we require
for f(ɛ):
∫ 1
0
f(ɛ)dɛ = η (10)
From the photon spectra we require:
280 PHYS340 – 5