THE EGS5 CODE SYSTEM

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wt(np)=wt(np)/lspltdo isplt=1,nspltx(np+isplt)=x(np)y(np+isplt)=y(np)z(np+isplt)=z(np)u(np+isplt)=u(np)v(np+isplt)=v(np)w(np+isplt)=w(np)ir(np+isplt)=ir(np)wt(np+isplt)=wt(np)dnear(np+isplt)=dnear(np)latch(np+isplt)=latch(np)e(np+isplt)=e(np)iq(np+isplt)=iq(np)k1step(np+isplt)=0.d0k1rsd(np+isplt)=0.d0k1init(np+isplt)=0.d0end donp=np+nspltend ifend ifwhere IRL is a local variable (IR(NP)= region of interest), IRSPLT(IRL) is a flag telling us thatsplitting is “turned on”, and IRL.NE.IRLOLD provides us with a way of doing the splitting onlywhen the photon (IQ(NP)=0) first enters the region.Most of the variables above are associated with the current (ı.e. NP) particle on the “stack” (ı.e.COMMON/STACK/), and with the number of splits (LSPLT=10 in UCCYL).For convenience, the commoncommon/passit/irsplt(66),lsplt,nsplt,nreginteger irsplt,lsplt,nsplt,nregwas also included in the user code (NSPLT=LSPLT-1).The result of this effort was an increase in the number of energy deposition events in theimportant region of interest and, as a result, a decrease in the variance (as judged by batch-runstatistics.190
4.1.3 Leading Particle BiasingThe second application of importance sampling that we will discuss primarily concerns the depositionof energy in an electromagnetic shower initiated by a high energy electron (or photon).The analog approach that is used throughout <strong>EGS5</strong>, in which each and every particle is generallyfollowed to completion (ı.e. energy cutoff guarantees that high energy shower calculations will takelots of time. For the most energetic particle energies under consideration at present day accelerators(> 50 GeV), one can barely manage to simulate showers in this fashion because of computertime limitations (Recall that execution time per incident particle grows linearly with energy). Fortunately,a certain class of problems involving the calculation of energy deposition is well-suitedfor a non-analog treatment known as leading particle biasing[175]. Examples of such problems areradiobiological dose, heating effects, and radiation damage, although some care must be taken innot being too general with this statement (more on this later).As a rule, variance reduction techniques of this type should only be used when there is someprior knowledge of the physical processes that are the most (or least) important to the answer oneis looking for. Leading particle biasing is a classic example of this. The most important processes inthe development of an EM shower, at least in terms of total energy deposition, are bremsstrahlungand pair production. Furthermore, after every one of these interactions the particle with the higherof the two energies is expected to contribute most to the total energy deposition.Leading particle biasing is very easily implemented within the framework of <strong>EGS5</strong> by means ofthe following statements:if (iarg.eq.7) then ! Apply Leading Particle Biasing for brems.eks=e(np)+e(np-1)-RM ! Kinetic energy before brems.ekenp=e(np)if(iq(np).ne.0) ekenp=e(np)-RMcall randomset(rnnolp)if (rnnolp.lt.ekenp/eks) then ! Follow npe(np-1)=e(np)iq(np-1)=iq(np)u(np-1)=u(np)v(np-1)=v(np)w(np-1)=w(np)end ifekenp=e(np-1)if (iq(np-1).ne.0) ekenp=e(np-1)-RMwt(np-1)=wt(np-1)*eks/ekenpnp=np-1end ifif (iarg.eq.16) then ! Apply Leading Particle Biasing for pair.eks=e(np)+e(np-1)-2.0*RM191
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THE EGS5 CODE SYSTEM 1Hideo Hirayam
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4.1 UCCYL - Cylinder-Slab Geometry
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E CONTENTS OF THE EGS5 DISTRIBUTION
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2.17 Convergence of energy depositi
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List of Tables2.1 Symbols used in E
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C.2 Goudsmit-Saunderson-related sub
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With the release of the EGS4 versio
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“shower book”.For various reaso
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1.2.2 EGS1About this time Nelson be
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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 SimulationTh
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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 ProgramTable 2.1 (cont
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Figure 2.2: Feynman diagrams for br
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defined byδ ij = 1 if i = j,0 othe
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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 haveNow defineδ ′ = ∆ 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−timedE=[23 − 1
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Angular distribution formulasThe fo
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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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whereX 0 = radiation length (cm),n
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whereα ′ 1 =α ′ 2 =k 0′k 0
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+ 1 E 2′ − 1 E 1′− C 2 ln E
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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 De
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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 thatln [1.13 + 3.76(αZ i
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g 3 (θ) =θ4 ()λf (0) (θ) + f (1
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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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xFinalDirectionφΘ∆xtInitialDire
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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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FinalDirectionxEnergy HingesφΘt(
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Transport Steps,∆ E = E x ESTEPEt
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tranport step 1DEINITIAL1 DERESID1t
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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 slowstep
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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 Electrons0.010.001LiCLWAlST
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actions involving photons with ener
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Cu 40 keVCounts (/keV/sr/source)10
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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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ZθkYOφe0Xk0Figure 2.23: Photon sc
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Note the similarities and differenc
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XZωk0Oe0YFigure 2.25: Direction of
Page 155 and 156: W = Atomic, molecular and mixture w
Page 157 and 158: In order to use EGS5 to answer the
Page 159 and 160: write(6,100)100 FORMAT(’ PEGS5-ca
Page 161 and 162: ! plate is 1 mm thick!-------------
Page 163 and 164: implicit noneinclude ’include/egs
Page 165 and 166: 0.989 MeV kinetic energyBrem photon
Page 167 and 168: ! locally (in fact EDEP = particles
Page 169 and 170: inmax=max(binmax,ebin(j))end dowrit
Page 171 and 172: 0.40 0.0058 *0.60 0.0054 *0.80 0.00
Page 173 and 174: !----------------------------------
Page 175 and 176: endifif(loop.lt.3) thenwrite(6,120)
Page 177 and 178: 180 FORMAT(/’ Knock-on electrons
Page 179 and 180: common/score/escore(3), iscore(3)re
Page 181 and 182: Brem photons can be created and any
Page 183 and 184: in any combination of 31 well speci
Page 185 and 186: end doend do! nmed and dunit defaul
Page 187 and 188: ! ------------------------------clo
Page 189 and 190: if (iarg.eq.17) then! A Compton sca
Page 191 and 192: ! the general purpose geometry subr
Page 193 and 194: eturnend!--------------------------
Page 195 and 196: open(UNIT= 6,FILE=’egs5job.out’
Page 197 and 198: write(6,130)130 format(/’ Start t
Page 199 and 200: icol=* int(dlog10(ebin(j)*10000.0/f
Page 201 and 202: 0.0300 0.0000*0.0320 0.0001*0.0340
Page 203 and 204: 0.0780 0.0014 *0.0800 0.0012 *0.082
Page 205: The main purpose of this section, h
Page 209 and 210: • Sum the weighted energy deposit
Page 211 and 212: 4z6Vac115Pb65Air749 1012AirAir8Vac
Page 213 and 214: Figure 4.3: UCBEND simulation at 3.
Page 215 and 216: necessary geometry input. The follo
Page 217 and 218: Appendix AEGS5 FLOW DIAGRAMSHideo H
Page 219 and 220: subroutineannihVersion051219-1435ia
Page 221 and 222: ¡eq1anormr = 1./sqrt(anorm2)sineta
Page 223 and 224: 1br = max(br,0.D0)ekse2 = br*ekines
Page 225 and 226: 12 3br = br*pesg = eie*bryesesg.lt.
Page 227 and 228: ¤ne¤nesubroutinecollis(lelec,irl,
Page 229 and 230: ¦ne¦necallausgab(iarg)6iq(np).eq.
Page 231 and 232: subroutinecomptVersion051219-1435ic
Page 233 and 234: 3456icprof(medium).eq.3noyescallran
Page 235 and 236: subroutinecounters_outVersion051227
Page 237 and 238: 1234567noii.ne.jjyesnoledgb(ii,medi
Page 239 and 240: ©ne1 2 3neispl = (2*neispl + 1)/3f
Page 241 and 242: subroutineelectr(ircode)ielectr = i
Page 243 and 244: 7 8 9 10 11 12 13detot = e(np)-ecut
Page 245 and 246: 2324 25 26 27 282930ustep.gt.dnear(
Page 247 and 248: 4142 43 44 45 4647 48 49ecut(irnew)
Page 249 and 250: 5859 60 61 6263 64tmscat.eq.0.0noye
Page 251 and 252: 73 7475 76noedep.lt.e(np)yescallran
Page 253 and 254: subroutinehardx(charge,kEnergy,keIn
Page 255 and 256: 1 2 3 4 5iz = izziz.eq.0noxsi = zer
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13 14 15 16 17sint.ne.0.yesrdev = m
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19im=1im=im+1im >nmednoyesnoiprofm(
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2223write(kmpo,1610)read(kmpi,1260)
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26 27 28iprofm(im).ne.1noyeswrite(6
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30 31 32 33 34esig0(i,im) = esig0(i
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36 37 38noiedgfl(ii).ne.0.or.iauger
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nokaug.eq.6calllshell(3)kaug.eq.7ka
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subroutinekxrayVersion051219-1435ik
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123dfl3aug(5,iz).eq.0.nonauger = na
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12 3 4rnnow.le.omegal2(iz) + f23(iz
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1 2dflx3(6,iz).eq.0.nonxray=nxray+1
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1impacr(ir(np)).eq.1.and.iedgfl(ir(
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12fject = (ktot - k1grd(iprt,ik1))
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56789thr = 1./eta"Central correctio
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1 2 3delta = delcm(medium)*del"Reje
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89101112galpha.ge.0.0yesnoximid = 0
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subroutinephotoVersion051219-1435"C
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4 5 6 7 8rnnow.le.pbran(i)noyesiz =
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121314beta = sqrt((eelec - RM)*(eel
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subroutinephotonVersion051219-1435i
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678910idisc.gt.0yesnoedep = 0.iarg
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1718192021iausfl(iarg+1)ne0nocallpa
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2728iausfl(iarg+1)ne0noircode = 2np
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subroutinerk1Version060313-0945open
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4 5 6j=1j=j+1j>neke-1noyesj.eq.1noj
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18 19 20 21 22 23elkeold = elkek1ol
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1 2"end of file; go to 13"read(17,*
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4 5"go to 30"noabs(k1mine-k1grd(1,1
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7 8read(17,'(72a1)') bufferread(17,
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subroutine shower(iqi,ei,xi,yi,zi,u
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subroutineuphi(ientry,lvl)Version05
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subroutinerandomset(rndum)Version05
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subroutinerluxinitVersion051219-143
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1i=1i=i+1i>24noyesseeds(i) = real(i
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subroutinerluxinVersion051219-1435w
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Appendix BEGS5 USER MANUALHideo Hir
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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 modificationsThe
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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 rluxinitafter specifying LUXLE
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END OF FILE ON UNIT 12PROGRAM STOPP
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do i=1,ncasesuf(1)=ufivf(1)=vfiwf(1
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crossed, then USTEP should be set t
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subroutine howfarimplicit noneinclu
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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=3do i=2,nregecut(i)=100.0pcut(
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nlines=0nwrite=15!-----------------
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if (nlines.lt.nwrite) thenwrite(6,1
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Appendix CPEGS USER MANUALHideo Hir
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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+------+|
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+------+|PAIRTR|+------+|V+------+|
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NameDCSLOADDCSSTORDCSTABELASTINOELI
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NameAFFACTAINTPALKEALKEIALINALINIAD
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Table C.5: Functions in PEGS, part
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+------+ +------+ +------+ +------+
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Table C.8: ELEM option input data l
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Table C.10: MIXT option input data
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Table C.12: PWLF option input data
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Table C.17: PLTN option input data
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ICPROF is set to 3, the user must c
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ColumnLine 123456789112345678921234
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interiors of the intervals. If FEXA
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C.3.6The TEST OptionThe TEST option
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C.3.9The HPLT OptionThe Histogram P
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Appendix DEGS5 INSTALLATION GUIDEHi
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egs5 directory (preferably using th
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6. The user is then asked to key-in
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* User code tutor1.f has been compi
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Appendix ECONTENTS OF THE EGS5DISTR
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All of the actual FORTRAN source co
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aprime.data Data for empirical brem
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ismuth krypton silverboron lanthanu
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The tutorial problems and advanced
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Bibliography[1] R. G. Alsmiller Jr.
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[28] A. F. Bielajew. HOWFAR and HOW
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[59] K. Flöttmann. Investigations
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[92] H. Kolbenstvedt. Simple theory
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[123] Y. Namito, H. Hirayama, A. Ta
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[156] Y. A. Shreider, editor. The M
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Index“shower book”, 37AE, 28, 3
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Klein-Nishina formula, 62Landau dis
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