CERN Program Library Long Writeup W5013 - CERNLIB ...

where,
(a − 1) 1
f(ν) = ( )
1
νc
a−1 − 1 a−1
ν a (5)
ν max
is the normalised distribution in the interval [ν c ,ν max ] and
[
g(ν) = 1 − ν ] 1/2
min
(6)
ν
is the rejection function.
2. r 1 and r 2 being two uniformly distributed random numbers in the interval [0, 1]:
−
Sample ν from the distribution f(ν) as:
( ) 1
1 − r1 r 1 1−a
ν =
ν a−1 c
ν a−1 max
− Accept ν if r 2 ≤ g(ν) (8)
(7)
3. Then compute
ρ max (ν) =
[
1 − 6M 2 ] [
E 2 1 − 4m ] 1/2
(9)
(1 − ν) νE
and generate ρ uniformly in the range [−ρ max , +ρ max ].
After the successful sampling of (ν, ρ), GPAIRM generates the polar angles of the radiated e + e − -pair with
respect to an axis defined along the parent muon’s momentum. Θ is assigned the approximate average value:
Θ= M E
(10)
φ + is generated isotropically and φ − = φ + + π
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