CERN Program Library Long Writeup W5013 - CERNLIB ...

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Geant 3.16 GEANT User’s Guide PHYS340 Origin : L. Urbán Submitted: 28.05.86 Revision : Revised: 16.12.93 Documentation : 1 Subroutines Total cross-section and energy loss for bremsstrahlung by e-e+ CALL GBRELA GBRELA fills the tables for the energy loss of electrons, positrons and muons due to bremsstrahlung at initialisation time for different materials. The energy binning is set within the array ELOW (common /CGMULO/)in the routine GPHYSI. In the tables, the dE/dx due to bremsstrahlung is summed with that due to the ionisation. For energy loss of electrons and positrons, GBRELA calls the function GBRELE. Following pointers are used: JMA = LQ(JMATE-I) pointer to the I th material; JEL1 = LQ(JMA-1) pointer to dE/dx for e − ; JEL1+NEK1 pointer to dE/dx for e + . GBRELA is called at initialisation time by GPHYSI. VALUE = GBRELE (ZZ,T,BCUT) GBRELE calculates the energy loss due to bremsstrahlung of an electron with kinetic energy T in material with atomic number ZZ. It is called by GBRELA and for energies below the cut BCUT it adds the contribution of bremsstrahlung to. Above this cut, the bremsstrahlung process is simulated explicitly (see [PHYS341]) and tabulation of these continuous losses is not needed. GBRELE is called by GBRELA. VALUE = GBFLOS (T,C) GBFLOS calculates a weight factor for the positron continuous bremsstrahlung energy loss. T is the kinetic energy in GeV of the positron and C is the energy cut for bremsstrahlung (BCUTE). The value is the ratio of the energy loss due to bremsstrahlung of the positron to that of the electron so that: = GBFLOS × . GBFLOS is called by GBRELA. CALL GBRSGA GBRSGA calculates the total cross-section for bremsstrahlung in all materials. It tabulates the mean free path, λ = 1 Σ (in cm) as a function of medium and energy. The energy binning is set within the array ELOW (common /CGMULO/) in the routine GPHYSI. The following pointers are used: JMA = LQ(JMATE-I) JBREM = LQ(JMA-9) JBREM pointer to the I th material pointer to bremsstrahlung cross-sections pointer for e − JBREM+NEK1 pointer for e + JBREM+2*NEK1 pointer for µ + /µ − GBRSGA is called at initialisation time by GPHYSI. VALUE = GBRSGE (ZZ,T,BCUT) GBRSGE calculates the total cross-section of bremsstrahlung of an electron with kinetic energy T in material with atomic number ZZ. It is called by GBRSGA. For kinetic energies which are below the cut BCUT or for which bremsstrahlung process is not simulated explicitly (see [PHYS341]) it returns 0. 276 PHYS340 – 1
VALUE = GBFSIG (T,C) GBFSIG calculates a weight factor for the positron discrete (hard) bremsstrahlung cross section. T is the kinetic energy in GeV of the positron and C is the energy cut for bremsstrahlung (BCUTE). The value returned is the ratio of the positron bremsstrahlung cross-section to that of the electron so that: ¡positron crosssection¿ = GBFSIG × ¡electron cross-section¿. GBFSIG is called by GBRSGA. 2 Method Let’s call dσ(Z, T, k)/dk the differential cross-section for production of a photon of energy k by an electron of kinetic energy T in the field of an atom of charge Z, and k c the energy cut-off below which the soft photons are treated as continuous energy loss (BCUTE in the program). Then the mean value of the energy lost by the electron due to soft photons is ∫ kc ELoss brem dσ(Z, T, k) (Z, T, k c )= k dk (1) 0 dk whereas the total cross-section for the emission of a photon of energy larger than k c is ∫ T dσ(Z, T, k) σ brem (Z, T, k c )= dk (2) k c dk Many theories of the bremsstrahlung process exist, each with its own limitations and regions of applicability. Perhaps the best synthesis of these theories can be found in the paper of S.M. Seltzer and M.J. Berger [75]. The authors give a tabulation of the bremsstrahlung cross-section dσ/dk differential in the photon energy k, for electrons with kinetic energies T from 1 keV to 10 GeV. For electron energies above 10 GeV the screened Bethe-Heitler differential cross-section can be used [12, 35] together with the Midgal corrections [54, 76]. The first of the two Migdal corrections is important for very high electron energies only (T ≥ 1 TeV) and has the effect of reducing the cross-section. The second Migdal correction is effective even at “ordinary” energies (100 MeV – 1 GeV) and it decreases the differential cross-section at photon energies below a certain fraction of the incident electron energy (dσ/dk decreases significantly if k/T ≤ 10 −4 .) 2.1 Parameterisation of energy loss and total cross-section Using the tabulated cross-section values of Seltzer and Berger together with the Migdal corrected Bethe- Heitler formula we have computed σ(Z, T, k c ) and we have used these computed values as “data points” in the fitting procedure. Calculating the “low energy” (T ≤ 10 GeV) data we have applied the second Midgal correction to the results of Seltzer and Berger. We have chosen the parameterisations: σ(Z, T, k c )= Z(Z + ξ σ)(T + m) 2 [ln(T/k c )] α F σ (Z, X, Y ) T (T +2m) (barn) (3) and ELoss brem (Z, T, k c )= Z(Z + ξ l)(T + m) 2 [ ] kc C β M F l (Z, X, Y ) (T +2m) T (GeV barn) (4) where m is the mass of the electron, X =ln(E/m), Y =ln(v σ E/k c ) for the total cross-section σ X =ln(T/m), Y =ln(k c /v l E) for the energy loss ELoss brem with E = T + m. The constants ξ σ ,ξ l ,α,β,v σ ,v l are parameters to be fitted. C M = 1 1+ nr 0λ −2 (T + m) 2 πk 2 c is the Midgal correction factor, with PHYS340 – 2 277
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CERN Program Library Long Writeup W
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Chapter 1: Catalog of Geant section
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IOPA500 KINE001 KINE100 KINE199 KIN
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Geant 3.21 GEANT User’s Guide AAA
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The routines made available for GEA
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GUDIGI GUOUT GTRIGC UGLAST GLAST GU
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Particles JPART Materials JMATE/JTM
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3 Summary of GEANT data records 3.1
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3.4 User applications KEY N I VAR S
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SUBROUTINE UGEOM + (’TGT ’,2,
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LQ(JHEAD-1) user link IQ(JHEAD+1) I
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CALL GDOPEN(3) CALL GDRAWC(’ALEF
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VECT,SNEXT,SAFETY Compute distance
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VECT,SNEXT,SAFETY Compute distance
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VECT,SNEXT,SAFETY Compute SFIELD,SM
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SUBROUTINE GUSTEP +SEQ,GCKING,GCVOL
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CALL GRKUTA (CHARGE,STEP,VECT,VOUT*
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Clicking then on the right button o
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CHUSET C “User set identifier”
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