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Geant 3.16 GEANT User’s Guide PHYS325 Origin : M.S. Dixit Submitted: 17.06.85 Revision : G.Lynch Revised: 16.12.93 Documentation : F.Carminati 1 Subroutines 1.1 Initialisation Molière scattering CALL GMULOF GMULOF calculates the table of maximum steps corresponding to the energies in the array ELOW for electrons and muons. It is called during initialisation by GPHYSI. For hadrons and ions the computation is performed during tracking in the routines GTHADR and GTHION. CALL GMOLI (AC,ZC,WMAT,NLM,DENS,OMC*,CHC*) AC REAL array of dimenstion NLM containing the mass numbers; ZC REAL array of dimenstion NLM containing the atomic numbers; WMAT REAL array containing the proportions by weight of the component of a mixture/compound. 1 in case of a single component; NLM INTEGER number of the elements in the mixture/compound; DENS REAL density in g cm −3 ; OMC REAL b c constant of Molière theory; CHC REAL χ cc constant of Molière theory. GMOLI calculates the two material-dependent constants (OMC and CHC). These are needed during initialisation by GMULOF and during tracking to sample the scattering angle, as explained below. It is called at initialisation time by the routine GPROBI which initialises some material constants and computes the probabilities for various processes. 1.2 Sampling of the multiple scattering angle CALL GMULTS GMULTS is the steering routine for the sampling of the multiple scattering angle when the variable IMULTS in common /GCPHYS/ is 1 or 2. This variable can be controlled by the MULT data record. The routine decides if the material-dependent constant OMC computed by GMOLI during initialisation has to be corrected due to its dependence on β and Z inc , and selects Molière theory (GMOLIE) or single Coulomb scattering (GMCOUL). It updates the direction of the particle in the array VECT (COMMON GCTRAK). It is called by the tracking routines GTELEC, GTHADR, GTHION and GTMUON. CALL GMOLIO (AC,ZC,WMAT,NLM,DENS,BETA2,CHARG2,OMC*) BETA2 CHARG2 REAL β 2 of the particle; REAL charge squared of the particle in electron charge unit (Zinc 2 in the following). All the other arguments are routine GMOLI. GMOLIO re-evaluates the material-dependent constant OMC. Itis called by GMULTS, if needed. 242 PHYS325 – 1
CALL GMOLIE (OMEGA,BETA2,DIN*) OMEGA BETA2 DIN REAL Ω 0 of the Molière theory; REAL β 2 of the particle; REAL array of dimension 3 containing the new direction cosines with respect to the original direction of the particle. GMOLIE samples the multiple scattering angle according to Molière theory, as explained in the next section. It is called by the multiple scattering steering routine GMULTS, CALL GMOL4 (Y*,X,VAL,ARG,EPS,IER*) Y X VAL ARG EPS IER REAL value of the interpolated function; REAL value at which the function should be interpolated; REAL array of four values of the function to interpolate; REAL array of four values of the argument of the function to which the values contained in VAL correspond; REAL required precision for the interpolation; INTEGER error flag; GMOL4 inverts the integral of Molière distribution function using four-points continued-fraction interpolation. It is called by GMOLIE. 2 Method 2.1 Introduction When traversing ordinary matter, elementary particles undergo deflection from their originary trajectory due to the interaction with the atoms. This effect is rather large for charged particles, which are deflected by the electric field of nuclei and electrons via a large number of small elastic collisions. To simulate precisely the transport of particles in matter, it is important to provide a precise description of this effect. Considerable effort has gone over the years into the formulation of a theory of Coulomb multiple scattering. In GEANT we follow the theory originally formulated by Molière [43] [44] and then elaborated by Bethe [37]. A review of this theory can be found in [45]. It should be noted that this is not the only theory which describes multiple Coulomb scattering, and a thorough analysis of the problem has been performed by Goudsmit and Saunderson [46] [47]. A complete account of the Molière theory is outside the scope of this manual. For more information the interested reader could refer to the works cited above and to the EGS4 manual [15], from which the notation used in the present chapter has been derived. The principal limitations of Molière theory are the following: 1. the angular deflection is small. Effectively this constraint provides the upper limit for the step-size; 2. the theory is a multiple scattering theory; that is, many atomic collisions participate in causing the incident particle to be deflected. In some implementations, this constraints provides a lower limit on the step size. In GEANT, when the number of scatters is below the limit of applicability of Molière single Coulomb scatterings are simulated, so that there is no effective minimum step size below which multiple scattering is switched off; 3. the theory applies only in semi-infinite homogeneous media. This constraint calls for a very careful handling of particles near to a medium’s boundary; PHYS325 – 2 243
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CERN Program Library Long Writeup W
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Chapter 1: Catalog of Geant section
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