CERN Program Library Long Writeup W5013 - CERNLIB ...

Geant 3.16 GEANT User’s Guide PHYS320
Origin : R.Brun, M.Hansroul Submitted: 17.06.85
Revision : F.Carminati, G.R.Lynch Revised: 16.12.93
Documentation : M.Hansroul, G.R.Lynch
1 Subroutines
Gaussian multiple scattering
CALL GMGAUS
(BETA2,DIN*)
BETA2 (REAL) β 2 ;
DIN
(REAL) array of 3 containing the direction of the scattered particle with respect to the
incoming direction.
This routine is called by GTELEC, GTHADR, GTMUON and GTHION via GMULTS when the variable IMULS,
controlled by the data record MULS is equal to 3.
2 Method
2.1 Approximations in use
A charged particle traversing a medium is deflected by many scatters, mostly at small angle. These scatters
are due to the interaction with the Coulomb field of the nuclei, and to a lesser degree, to the electron field,
hence the name of Coulomb scattering. For hadronic projectiles, however, the strong interaction contributes
to multiple scattering. Multiple scattering is well described by Molière theory [37]. Molière multiple
scattering theory is used by default in GEANT (see [PHYS325]). We define θ 0 = θplane rms = θrms space/ √ 2 as
the r.m.s. of the angle between the directions projected on a plane of a particle before and after traversing
a thickness t of absorber. In this case a simple form for the multiple Coulomb scattering of singly charged
particles which is widely used is:
θ 0 ≈ 15MeV
Eβ 2
√
t
X 0
where X 0 is the radiation length of the absorber. This form was proposed by [38], [39]. It can introduce
large errors because it ignores significant dependences from pathlength and Z. To compensate for this, a
similar formula was proposed [40], [41]:
θ 0 ≈ 14.1MeV
Eβ 2
√ [
( )]
t
t
1+0.038 log
X 0 X 0
(1)
A form taking into account the β and z dependence of the particle has been proposed by [42]:
θ 0 = S √ [
( )]
2 t
tZ
2
Eβ 2 1+ɛ log inc
X 10
0 X 0 β 2
(2)
The problem with the formulae (1) and (2) is that if √the distance t in the absorber is travelled in two steps
t = t 1 + t 2 , the r.m.s. angle θ 0 (t) =θ 0 (t 1 + t 2 ) ≠ θ0 2(t 1)+θ0 2(t 2), limiting their use in a MonteCarlo
like GEANT.
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