CERN Program Library Long Writeup W5013 - CERNLIB ...

where we have set Θ=θ/χ α . To sample from this distribution we calculate the inverse of the distribution
function:
∫ Θ
2tdt
η =
(1 + t 2 ) 2 =1− 1
√
1
1+Θ 2 ⇒ Θ=
1 − η − 1
0
where η is a number uniformly distributed between 0 and 1. If we observe that also 1 − η is uniformly
distributed between 0 and 1 and we remember the definition of Θ, we obtain:
θ =
√
χ 2 α
( 1
η − 1 )
To calculate χ 2 α we observe that:
Ω 0 = χ2 c
kχ 2 α
χ 2 α = χ2 c
kΩ 0
= χ2 ccZ 2 inc t/E2 β 4
kb c Z 2 inc t/β2 = χ2 cc
kb c p 2 c 2
where we have used the notations of [PHYS325] and k =1.167.
PHYS328 – 2 251