Method

This set of routines generates the interactions of muons with the nuclei of the tracking material. The code is a straight translation into the GEANT style of the corresponding code from the GHEISHA Monte Carlo Program. The GHEISHA routines CASMU and CALIM have been used [].

The information contained in this chapter is mainly taken from the GHEISHA manual to which the user is referred. The muon-nucleus inelastic cross-section is taken as 0.0003 mb for a nucleon when the energy of the incoming muon is E<30 GeV, and slowly increases for E>30 GeV according to the law:

The energy and angle of final state muon is generated according to the ``free quark parton model''. If E is the energy of the incoming muon and $\Omega$ and W the angle and the energy of the outgoing muon, the differential cross-section can be written as:

$\{d\; \sigma d\; \Omega dW\}=\gamma (\; \sigma$_T+ εσ_S)

where:

$\Gamma$	$=$	$\{k\; \alpha 2\; \pi \}\{WE\}\{11-\; \epsilon \}$
$\epsilon$	$=$	$[\; 1+2\; \{Q2+\; \nu 2Q2\}tan2\theta 2]$

$Q2$ and $\nu$ are the normal scaling variables expressed by:

$Q2=\; -q2=\; 2(EW-|p||p\text{'}|cos\theta -m$_-μ²)&quad;and&quad;ν= E-W

here $\sigma$_T and $\sigma$_S are the photo-absorption cross-sections for transverse and longitudinal photons respectively for which the relation used is:

$\sigma$_S= 0.3 ( 1- {11.868}Q²ν) σ_T

and $\sigma$_T is assumed to be constant $\sigma$_T= 0.12 mb. For the incident flux K of the photons Gillman's convention is used:

$K\; =\; \nu +\; Q2/2\nu$

A three-dimensional importance sampling in the variables E, W and $\theta$ is performed each time an interaction has to occur.

This set of routines only works if GUPHAD calls GPGHEI and GUHADR calls GHEISH. The hadrons are generated in an approximate way. The virtual photon is replaced by a real pion of random charge with the same kinetic energy. Then the GUHADR routine is called to generate a $\pi$ -nucleus inelastic scattering. While the final state generated this way gives a good approximation for calorimetric purposes, the kinematics of the final state may be a rather poor approximation of reality. The muon-nucleus interactions are activated by the MUNU data record of GEANT. After a muon-nucleus interaction the muon will still be the current particle. If MUNU 1 has been specified, secondaries coming from the interaction of the virtual photon with the nucleus will be in the GEANT temporary stack. If MUNU 2 has been specified, then the secondary particles will not be generated and the energy lost by the muon will be added to DESTEP. For each material a table of muon-nucleus cross-sections is stored at initialisation time. See material bank structure for details.

F. Carminati PHYS510