CERN Program Library Long Writeup W5013 - CERNLIB ...

The energy lost due to the soft δ-rays is tabulated during initialisation as a function of the medium and of
the energy by routine GDRELA
The tables are filled with the quantity dE/dx in GeV cm −1 (formula (4) above). For a molecule or a mixture
the following formula is used:
dE
dx = ρ ∑ i
( ) dE
p i
dX i
where x is in cm, X in g cm −2 and p i is the proportion by weight of the I th element.
The energy loss of all charged particles other than electrons, positrons and muons is obtained from that of
protons by calculating the kinetic energy of a proton with the same β, and using this value to interpolate the
tables:
T proton = M p
M T (7)
2.2 Total cross-section
The integration of formula (1) gives the total cross-section :
(6)
⎧
⎪⎨
σ(Z, E, T cut )=
⎪⎩
2πr 2 0 m Z β 2 1 − Y + β 2 Y ln Y
T cut
2πr 2 0 m Z β 2 (
1 − Y + β 2 Y ln Y
T cut
+ T )
max − T cut
2E 2
for spin-0 particles
for spin- 1 2 particles (8)
The mean free path is tabulated during initialisation as a function of the medium and of the energy by the
routine GDRSGA for leptons only.
The cross-section (8) is strongly dependent on the mass of the incident particle, and cannot be tabulated
in a general way for any charged hadrons. Therefore, for such particles, the cross-section is computed at
tracking time in the routine GTHADR.
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