CERN Program Library Long Writeup W5013 - CERNLIB ...

Much of the difficulty in approximating multiple Coulomb scattering in terms of the radiation length is that
the number of radiation lengths is a poor measure of the scattering. A better expression, which is used in
GEANT has been proposed by [42]:
θ 2 0 =
[ ]
χ2 c 1+ν
1+F 2 log(1 + ν) − 1
ν
(3)
where
ν =
Ω 0
2(1 − F )
F = fraction of the tracks in the sample
Ω 0 =
χ 2 c
1.167χ 2 α
is the mean number of scatters
χ 2 c and χ 2 α are parameters of the Molière theory, for which the reader is invited to see [PHYS325], and
1.167 ≈ exp(2γ − 1) where γ is the Euler’s constant =0.57721 .... This form, which is the result of
empirical fits, is derived from the screened Rutherford cross section, which has the form 2χ 2 α/(χ 2 α + θ0 2).
For F anywhere from 0.9 to 0.995 this expression represents Molière scattering to better than 2% for 10 <
Ω 0 < 10 8 , which covers singly charged relativistic particles (β ≈ 1) in the range 10 −3