THE EGS5 CODE SYSTEM

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[75] H. Hirayama, W. R. Nelson, A. Del Guerra, T. Mulera, and V. Perez-Mendez. Monte Carlo studies for the design of a lead glass drift calorimeter. Nucl. Instrum. Methods, 220:327, 1984. [76] H. Hirayama and D. K. Trubey. Effects of incoherent and coherent scattering on the exposure buildup factors of low-energy gamma rays. Nucl. Sci. Eng., 99:145–156, 1988. [77] J. H. Hubbell and I. Øverbø. Relativistic atomic form factors and photon coherent scattering cross sections. J. Phys. Chem. Ref. Data, 8:69–105, 1979. [78] J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, and R J Howerton. Atomic form factors, incoherent scattering functions, and photon scattering cross sections. J. Phys. Chem. Ref. Data, 4:471–538, 1975. [79] ICRU. Stopping powers for electrons and positrons. ICRU Report 37, International Commission on Radiation Units and Measurements, Washington, D.C., 1984. [80] C. Jakoby, H. Genz, and A. Richter. J. Phys. (Paris) Colloq., C9:487, 1987. [81] F. James. A review of pseudorandom number generators. Report DD/88/22, CERN-Data Handling Division, 1988. [82] F. James. RANLUX: A FORTRAN implementation of the high-quality pseudorandom number generator of Lüscher. Comput. Phys. Commun., 79:111–114, 1994. [83] J. M. Jauch and F. Rohrlich. The Theory of Photons and Electrons. Addison-Wesley, Reading, MA, 1955. [84] P. C. Johns and M. J. Yaffe. Coherent scatter in diagnostic radiology. Med. Phys., 10:40, 1983. [85] H. Kahn. Applications of Monte Carlo. USAEC Report AECU-3259, The Rand Corporation, 1954. [86] P. P. Kane, R. H. Pratt L. Kissel, and S. C. Roy. Elastic scattering of gamma-rays and x-rays by atoms. Phys. Rep., 140:75–159, 1986. [87] K. R. Kase and W. R. Nelson. Concepts of Radiation Dosimetry. Pergamon Press, New York, 1979. [88] I. Kawrakow and A. F. Bielajew. On the condensed history technique for electron transport. Nucl. Instrum. Meth. B, 142:253–280, 1998. [89] J. F. C. Kingman and S. J. Taylor. Introduction to Measure and Probability. Cambridge University Press, 1966. [90] O. Klein and Y. Nishina. Über die Streuung von Strahlung durch freie Electronen nach der Neuen Relativistischen Quantum Dynamic von Dirac. Z. für Physik, 52:853, 1929. [91] H. W. Koch and J. W. Motz. Bremsstrahlung cross-section formulas and related data. Rev. Mod. Phys., 31:920–955, 1959. 414
[92] H. Kolbenstvedt. Simple theory for K-ionization by relativistic electrons. J. Appl. Phys., 38:4785–4787, 1967. [93] T. Kotseroglou, V. Bharadwaj, J. Clendenin, S. Ecklund, J. Frisch, P. Krejcik, A. Kulikov, J. Liu, T. Maruyama, K. K. Millage, G. Mulhollan, W. R. Nelson, D. C. Schultz, J. C. Sheppard, J. Turner, K. VanBibber, K. Flöttmann, and Y. Namito. Recent developments on the design of the NLC positron source. In Proceedings of the 1999 Particle Accelerator Conference (PAC’99), 1999. [94] L. Landau and I. J. Pomeranchuk. Electron-cascade processes at ultra-high energies. Dokl. Akad. Nauk. SSSR, 92:735–738, 1953. [95] L. Landau and I. J. Pomeranchuk. The limits of applicability of the theory of bremsstrahlung by electrons and of creation of pairs at large energies. Dokl. Akad. Nauk. SSSR, 92:535–536, 1953. [96] E. W. Larsen. A theoretical derivation of the condensed history algorithm. Ann. Nucl. Energy, 19:701–714, 1992. [97] H. W. Lewis. Multiple scattering in an infinite medium. Phys. Rev., 78:526–529, 1950. [98] J. C. Liu, T. Kotseroglou, W. R. Nelson, and D. C. Schultz. Polarization study for NLC positron source using EGS4. In Proceedings of the Second International Workshop on EGS4, Japan, 2000. (KEK Proceedings 2000-20). [99] M. Loeve. Probability Theory. Van Nostrand Reinhold Co., New York, 1950. [100] G. A. Loew and Juwen Wang (SLAC). Private communication. [101] C. Malamut, D. W. O. Rogers, and A. F. Bielajew. Calculation of water/air stopping-power ratios using EGS4 with explicit treatment of electron—positron differences. Med. Phys., 18:1222–1228, 1991. [102] E. J. McGuire. Atomic L-shell Coster Kronig, Auger, and radiative rates and fluorescence yields for Na-Th. Phys. Rev. A, 3:587–594, 1971. [103] H. Messel and D. F. Crawford. Electron-Photon Shower Distribution Function. Pergamon Press, Oxford, 1970. [104] H. Messel, A. D. Smirnov, A. A. Varfolomeev, D. F. Crawford, and J. C. Butcher. Radial and angular distributions of electrons in electron-photon showers in lead and in emulsion absorbers. Nucl. Phys., 39:1–88, 1962. [105] L. M. Middleman, R. L. Ford, and R. Hofstadter. Measurement of cross sections for x-ray production by high-energy electrons. Phys. Rev., 2:1429–1443, 1970. [106] A. B. Migdal. Bremsstrahlung and pair production in condensed media at high energies. Phys. Rev., 103:1811, 1956. [107] G. Z. Molière. Theorie der Streuung schneller geladener Teilchen. I. Einzelstreuung am abgeschirmten Coulomb-Field. Z. Naturforsch, 2a:133–145, 1947. 415
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THE EGS5 CODE SYSTEM 1 Hideo Hiraya
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Contents 1 INTRODUCTION 1 1.1 Inten
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2.15.6 Electron Step-Size Selection
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B.4.9 Output of Results (Step 9) .
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List of Figures 2.1 Program flow an
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C.4 Subprogram relationships in PEG
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B.5 Variable descriptions for COMMO
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PREFACE In the nineteen years since
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Chapter 1 INTRODUCTION 1.1 Intent o
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“shower book”. For various reas
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1.2.2 EGS1 About this time Nelson b
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MSCAT. These versions of EGS, PEGS,
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ten for energies less than 100 MeV
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- Molière multiple scattering (i.e
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EGS5. The primary advantages of thi
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ICRU37-compliant using the NIST dat
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high Z materials. Del Guerra et al.
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One of these six cross sections is
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at low energies. The latter, couple
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If E 1 and E 2 are expressions invo
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The result of this algorithm is tha
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2.4 Particle Transport Simulation T
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from appropriate distribution funct
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parameters which may be needed. The
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arrived at their values in a very m
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Math FORTRAN Program Table 2.1 (con
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Figure 2.2: Feynman diagrams for br
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defined by δ ij = 1 if i = j, 0 ot
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Davies, Bethe and Maximon[49] (e.g.
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cross section given in Equation 2.4
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and use this as the variable to be
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we have Now define δ ′ = ∆ C
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This agrees with formula (10) of Bu
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That is, using Equations 2.122 and
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d˘Σ P air, Run−time dE = [ 2 3
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Angular distribution formulas The f
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at either x = 0, x = (πE 0 ) 2 (i.
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The following table, derived from t
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Figure 2.3: Feynman diagrams for tw
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where X 0 = radiation length (cm),
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where α ′ 1 = α ′ 2 = k 0 ′
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+ 1 E 2 ′ − 1 E 1 ′ − C 2 l
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PEGS functions BHABDM, BHABRM, and
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To find the limits of E, we first c
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Figure 2.5: Feynman diagram for sin
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Ī adj = average adjusted mean ioni
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Table 2.2 (cont.) Z Symbol Atomic D
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Table 2.3 (cont.) LABEL a m s x 0 x
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(c) If 10.5 ≤ −C < 11.0 then x
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obtain the real scattering angle. E
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ρ = material mass density (g/cm 3
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Hence, so that ln [1.13 + 3.76(αZ
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g 3 (θ) = θ4 ( ) λf (0) (θ) + f
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Actually, b = 0 does not correspond
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Assume that an electron starts off
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At small path lengths t, a very lar
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x Final Direction φ Θ ∆x t Init
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shown that this version of the rand
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and as we noted earlier, they are d
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Final Direction x Energy Hinges φ
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Transport Steps, ∆ E = E x ESTEPE
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tranport step 1 DEINITIAL1 DERESID1
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= ∆E ( ∣ ∣∣∣ dE −1 ∣
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Since the CSDA range is uniquely de
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short steps accurate, but slow step
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Table 2.4: Materials used in refere
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Average Lateral Displacement (cm) 0
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100 MeV Electrons 0.01 0.001 Li C L
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actions involving photons with ener
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Cu 40 keV Counts (/keV/sr/source) 1
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Table 2.6: Data sources for general
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2.16.2 Photoelectron Angular Distri
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where r 0 is the classical electron
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second term on the right-hand side
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Z θ k Y O φ e 0 X k 0 Figure 2.23
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Note the similarities and differenc
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X Z ω k 0 O e 0 Y Figure 2.25: Dir
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W = Atomic, molecular and mixture w
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In order to use EGS5 to answer the
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write(6,100) 100 FORMAT(’ PEGS5-c
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! plate is 1 mm thick !------------
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implicit none include ’include/eg
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0.989 MeV kinetic energy Brem photo
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! locally (in fact EDEP = particles
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inmax=max(binmax,ebin(j)) end do wr
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0.40 0.0058 * 0.60 0.0054 * 0.80 0.
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!----------------------------------
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endif if(loop.lt.3) then write(6,12
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180 FORMAT(/’ Knock-on electrons
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common/score/escore(3), iscore(3) r
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Brem photons can be created and any
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in any combination of 31 well speci
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end do end do ! nmed and dunit defa
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! ------------------------------ cl
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if (iarg.eq.17) then ! A Compton sc
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! the general purpose geometry subr
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eturn end !------------------------
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open(UNIT= 6,FILE=’egs5job.out’
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write(6,130) 130 format(/’ Start
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icol= * int(dlog10(ebin(j)*10000.0/
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0.0300 0.0000* 0.0320 0.0001* 0.034
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0.0780 0.0014 * 0.0800 0.0012 * 0.0
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The main purpose of this section, h
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4.1.3 Leading Particle Biasing The
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• Sum the weighted energy deposit
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4 z 6 Vac 11 5 Pb 6 5 Air 7 4 9 10
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Figure 4.3: UCBEND simulation at 3.
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necessary geometry input. The follo
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Appendix A EGS5 FLOW DIAGRAMS Hideo
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subroutine annih Version 051219-143
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¡ eq 1 anormr = 1./sqrt(anorm2) si
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1 br = max(br,0.D0) ekse2 = br*ekin
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1 2 3 br = br*p esg = eie*br yes es
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¤ ne ¤ ne subroutine collis (lele
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¦ ne ¦ ne call ausgab(iarg) 6 iq(
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subroutine compt Version 051219-143
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3 4 5 6 icprof(medium) .eq. 3 no ye
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subroutine counters_out Version 051
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1 2 3 4 5 6 7 no ii .ne. jj yes no
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© ne 1 2 3 neispl = (2*neispl + 1)
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subroutine electr(ircode) ielectr =
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7 8 9 10 11 12 13 detot = e(np)-ecu
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2324 25 26 27 28 29 30 ustep .gt. d
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4142 43 44 45 46 47 48 49 ecut(irne
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5859 60 61 62 63 64 tmscat .eq. 0.0
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73 74 75 76 no edep .lt. e(np) yes
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subroutine hardx (charge,kEnergy,ke
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1 2 3 4 5 iz = izz iz .eq. 0 no xsi
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13 14 15 16 17 sint .ne. 0. yes rde
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19 im=1 im=im+1 im >nmed no yes no
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22 23 write(kmpo,1610) read(kmpi,12
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26 27 28 iprofm(im) .ne. 1 no yes w
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30 31 32 33 34 esig0(i,im) = esig0(
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36 37 38 no iedgfl(ii).ne.0 .or. ia
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no kaug .eq. 6 call lshell(3) kaug.
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subroutine kxray Version 051219-143
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1 2 3 dfl3aug(5,iz) .eq. 0. no naug
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1 2 3 4 rnnow .le. omegal2(iz) + f2
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1 2 dflx3(6,iz) .eq. 0. no nxray=nx
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1 impacr(ir(np)).eq.1 .and. iedgfl(
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1 2 fject = (ktot - k1grd(iprt,ik1)
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5 6 7 8 9 thr = 1./eta "Central cor
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1 2 3 delta = delcm(medium)*del "Re
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8 9 10 11 12 galpha .ge. 0.0 yes no
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subroutine photo Version 051219-143
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4 5 6 7 8 rnnow .le. pbran(i) no ye
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12 13 14 beta = sqrt((eelec - RM)*(
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subroutine photon Version 051219-14
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6 7 8 9 10 idisc .gt. 0 yes no edep
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17 18 19 20 21 iausfl(iarg+1) ne 0
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27 28 iausfl(iarg+1) ne 0 no ircod
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subroutine rk1 Version 060313-0945
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4 5 6 j=1 j=j+1 j>neke-1 no yes j .
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18 19 20 21 22 23 elkeold = elke k1
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1 2 "end of file; go to 13" read(17
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4 5 "go to 30" no abs(k1mine-k1grd(
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7 8 read(17,'(72a1)') buffer read(1
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subroutine shower (iqi,ei,xi,yi,zi,
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subroutine uphi(ientry,lvl) Version
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subroutine randomset(rndum) Version
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subroutine rluxinit Version 051219-
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1 i=1 i=i+1 i>24 no yes seeds(i) =
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subroutine rluxin Version 051219-14
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Appendix B EGS5 USER MANUAL Hideo H
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Table B.1: Variable descriptions fo
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Table B.12: Variable descriptions f
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Optional parameter modifications Th
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the call to PEGS5 may be skipped if
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egions. Execution of EGS5 is termin
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of the transport in the walls of el
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call rluxinit after specifying LUXL
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END OF FILE ON UNIT 12 PROGRAM STOP
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do i=1,ncases uf(1)=ufi vf(1)=vfi w
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crossed, then USTEP should be set t
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subroutine howfar implicit none inc
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Table B.18: IARG values program sta
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As an example of how to write an AU
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!**********************************
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nreg=3 do i=2,nreg ecut(i)=100.0 pc
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nlines=0 nwrite=15 !---------------
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if (nlines.lt.nwrite) then write(6,
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Appendix C PEGS USER MANUAL Hideo H
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is entered. On each pass through th
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(from previous figure) (to previous
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(from previous figure) | | + ------
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+------+ |BREMTR| +------+ | V +---
Page 379 and 380: +------+ |PAIRTR| +------+ | V +---
Page 381 and 382: Name DCSLOAD DCSSTOR DCSTAB ELASTIN
Page 383 and 384: Name AFFACT AINTP ALKE ALKEI ALIN A
Page 385 and 386: Table C.5: Functions in PEGS, part
Page 387 and 388: +------+ +------+ +------+ +------+
Page 389 and 390: Table C.8: ELEM option input data l
Page 391 and 392: Table C.10: MIXT option input data
Page 393 and 394: Table C.12: PWLF option input data
Page 395 and 396: Table C.17: PLTN option input data
Page 397 and 398: ICPROF is set to 3, the user must c
Page 399 and 400: Column Line 12345678911234567892123
Page 401 and 402: interiors of the intervals. If FEXA
Page 403 and 404: C.3.6 The TEST Option The TEST opti
Page 405 and 406: C.3.9 The HPLT Option The Histogram
Page 407 and 408: Appendix D EGS5 INSTALLATION GUIDE
Page 409 and 410: egs5 directory (preferably using th
Page 411 and 412: 6. The user is then asked to key-in
Page 413 and 414: * User code tutor1.f has been compi
Page 415 and 416: Appendix E CONTENTS OF THE EGS5 DIS
Page 417 and 418: All of the actual FORTRAN source co
Page 419 and 420: aprime.data Data for empirical brem
Page 421 and 422: eryllium iron silicon bismuth krypt
Page 423 and 424: The tutorial problems and advanced
Page 425 and 426: Bibliography [1] R. G. Alsmiller Jr
Page 427 and 428: [28] A. F. Bielajew. HOWFAR and HOW
Page 429: [59] K. Flöttmann. Investigations
Page 433 and 434: [123] Y. Namito, H. Hirayama, A. Ta
Page 435 and 436: [156] Y. A. Shreider, editor. The M
Page 437 and 438: Index “shower book”, 37 AE, 28,
Page 439 and 440: Klein-Nishina formula, 62 Landau di
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