CERN Program Library Long Writeup W5013 - CERNLIB ...

VALUE = GBRSGM (Z,T,BCUT)
Z
T
BCUT
(REAL) atomic number of the materian;
(REAL) kinetic energy of the muon;
(REAL) soft bremsstrahlung cut.
GBRSGM calculates the total bremsstrahlung cross-section for muons when the emitted photon has an energy
greater than BCUT, (variable BCUTM in the common /GCCUTS/). It is called by GBRSGA.
2 Method
The mean value of the energy lost by the muon due to bremsstrahlung of photons of energy k c is
σ(Z, T, k c )=
∫ T
dσ(Z, T, k)
k c dk
dk (2)
Accurate cross-section formula for the high energy (T ≥ 1 GeV) muon bremsstrahlung can be found in
[99].
2.1 Parameterisation of energy loss and total cross-section
The cross-sections from [99] have been used to calculate data points for (1) and (2). These have been
parameterised as:
[
σ(Z, T, k c ) = Z[Z + ξ σ (1 + γ ln Z)] ln k ] α
max
F σ (Z, X, Y ) in barn
k c
E brem
loss (Z, T, k c) = Z[Z + ξ l (1 + δ ln Z)]
[
ln k c
E
] β
F l (Z, X, Y ) in GeV barn
k max = E − 0.75 √ em µ Z 1/3 X = ln E m µ
Y = ln k c
E = T + m µ
m µ
where k max is the maximum possible value of the photon energy. The functions F i (Z, X, Y ) (i = σ, l) are
polynomials:
F i (Z, X, Y ) = (C 1 + C 2 X + ···+ C 6 X 5 )+(C 7 + C 8 X + ···+ C 12 X 5 )Y
+ ···+(C 31 + C 32 X + ···+ C 36 X 5 )Y 5
+ Z[(C 37 + C 38 X + ···+ C 40 X 3 )+(C 41 + C 42 X + ···+ C 44 X 3 )Y
+ ···+(C 48 + C 49 X + ···+ C 52 X 3 )Y 3 )] (3)
A least-squares fit has been performed on more than 2000 points for Z =1, 6, 13, 26, 50, 82, 92 and 1 GeV
≤ T ≤ 10 TeV and 10 keV ≤ k c ≤ T . The resulting values of ξ σ,l , γ, α ,C i , ξ l , δ and β can be found in the
DATA statements within the functions GBRSGM and GBRELM which compute formulae (1) and (2) respectively.
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