Sampling

Apart from the normalisation, the cross-section can be written as

$\{d\sigma d\epsilon \}=f(\epsilon )\; g(\epsilon ),$

where, for $e-e-$ scattering,

$f(\epsilon )$	$=$	$\{1\epsilon 2\}\{\epsilon$01- 2ε0}
$g(\epsilon )$	$=$	$\{49\gamma 2-\; 10\; \gamma +\; 5\}[(\gamma -1)2\epsilon 2-\; (2\; \gamma 2+2\gamma -1)\; \{\epsilon 1-\; \epsilon \}+\{\gamma 2(1-\; \epsilon )2\}]$

and for $e+e-$ scattering

$f(\epsilon )$	$=$	$\{1\epsilon 2\}\{\epsilon$01- ε0}
$g(\epsilon )$	$=$	$\{B$0-B1ε+B2ε2-B3ε3+B4ε4B0-B1ε0+B2ε02-B3ε03+B4ε04}

Here $B$₀=γ²/(γ²-1) and all the other quantities have been defined above. For the other charged particles:

GDRAY samples the variable $\epsilon$ by:

1. sample $\epsilon$ from $f(\epsilon )$

2. calculate the rejection function $g(\epsilon )$ and accept the sampled $\epsilon$ with a probability of $g(\epsilon )$ .

After the successful sampling of $\epsilon$ , GDRAY generates the polar angles of the scattered electron with respect to the direction of the incident particle. The azimuthal angle $\phi$ is generated isotropically; the polar angle $\theta$ is calculated from the energy momentum conservation. This information is used to calculate the energy and momentum of both scattered particles and to transform them into the GEANT coordinate system.

F.Carminati, K.Lassila-Perini

PHYS332