{VERSION 5 0 "SUN SPARC SOLARIS" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 23 "Courier" 1 10 0 0 0 0 0 0 0 0 0 0 3 0 0 1 }{CSTYLE " " -1 257 "" 1 18 0 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "termi nal" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "helvetica" 1 10 0 0 0 0 0 0 0 0 0 0 3 0 0 1 }{CSTYLE "" -1 261 "courier" 1 10 0 0 0 0 0 0 0 0 0 0 3 0 0 1 }{CSTYLE "" -1 262 "fixed" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "fixed" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 271 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 282 "fixed" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 285 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 287 "" 1 18 0 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 288 "" 1 18 0 0 0 0 1 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 289 "" 1 18 0 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 " " 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 3 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }{XPPEDIT 18 0 "pi^o;" "6#)%#piG%\"oG" }{TEXT -1 0 "" }{TEXT 257 23 " Decay,Maple Worksheet " }{TEXT 287 5 " for " }{TEXT 288 1 "e" }{TEXT 289 23 " Detector's Lin e Shape " }}{PARA 0 "" 0 "" {TEXT -1 47 "This worksheet explores the \+ response function " }}{PARA 258 "" 0 "" {XPPEDIT 18 0 "R(E) = A*exp((E -Eo)/a)*(1-erf((E-Eo)/b));" "6#/-%\"RG6#%\"EG*(%\"AG\"\"\"-%$expG6#*&, &F'F*%#EoG!\"\"F*%\"aGF1F*,&F*F*-%$erfG6#*&,&F'F*F0F1F*%\"bGF1F1F*" }} {PARA 0 "" 0 "" {TEXT -1 175 "that simulates a detector's output at en ergy E when an electron of energy Eo MeV enters the detector. The par ameters we use here are the same as those in the Fortran program " } {TEXT 258 12 "Iteration.f:" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 29 "P(1) == Normalization of the " }{XPPEDIT 18 0 "pi^o;" "6#)%#piG%\" oG" }{TEXT -1 6 "-box, " }{TEXT 260 5 "3.5E5" }{TEXT -1 41 " \+ P(9) == 129-Peak position, " }{TEXT 23 4 "0.85" }{TEXT -1 14 " \+ " }}{PARA 0 "" 0 "" {TEXT -1 25 "P(2) == Left edge of the " }{XPPEDIT 18 0 "pi^o;" "6#)%#piG%\"oG" }{TEXT -1 6 "-box, " }{TEXT 261 2 "1." }{TEXT -1 73 " P(10)== Width param eter of higher energy tail, " }{TEXT 23 3 "2.5" }{TEXT -1 33 " \+ " }}{PARA 0 "" 0 "" {TEXT -1 26 "P(3) == Righ t edge of the " }{XPPEDIT 18 0 "pi^o;" "6#)%#piG%\"oG" }{TEXT -1 6 "-b ox, " }{TEXT 23 2 "1." }{TEXT -1 70 " P(11)== W idth parameter of lower energy tail, " }{TEXT 23 3 "13." }{TEXT -1 51 " \nP(4) == Width of high energy tail, " }{TEXT 23 3 "4. 5" }{TEXT -1 68 " P(12)== Normalization of the ex p. background, " }{TEXT 23 5 "2.5E5" }{TEXT -1 4 " " }}{PARA 0 "" 0 "" {TEXT -1 37 "P(5) == Width of low energy tail, " }{TEXT 23 4 " 14.0" }{TEXT -1 46 " P(13)== Pedestal position, " } {TEXT 23 3 "0.0" }}{PARA 0 "" 0 "" {TEXT -1 35 "P(6) == Energy depende nce of P(4), " }{TEXT 23 4 "0.03" }{TEXT -1 65 " P(14 )== Exponential decay parameter of noise, " }{TEXT 23 3 "38." }{TEXT -1 38 " \nP(7) == Energy dependence of P(5), " }{TEXT 23 4 "0.02" } {TEXT -1 48 " P(15)== Constant background, " }{TEXT 23 3 "0.0" }{TEXT -1 23 " " }}{PARA 0 "" 0 "" {TEXT -1 35 "P(8) == Normalization of 129-peak, " }{TEXT 23 5 "7.0E6" }{TEXT -1 154 " \+ \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 23 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "The parameters " }{TEXT 270 1 " a" }{TEXT -1 5 " and " }{TEXT 271 1 "b" }{TEXT -1 4 " in " }{TEXT 272 5 "R(E) " }{TEXT -1 66 " are functions of electron energy, that we des cribe empirically as" }}{PARA 259 "" 0 "" {XPPEDIT 18 0 "a = P(4)*Eo^P (6);" "6#/%\"aG*&-%\"PG6#\"\"%\"\"\")%#EoG-F'6#\"\"'F*" }}{PARA 260 " " 0 "" {XPPEDIT 18 0 "b = P(5)*Eo^P(7);" "6#/%\"bG*&-%\"PG6#\"\"&\"\" \")%#EoG-F'6#\"\"(F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "p4:=4.5;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%#p4G$\"#X!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "p5:=14 .;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p5G$\"#9\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "p6:=0.03;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p6G$\"\"$!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "p7:=0.02;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p7G$\"\"#!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "a:=(Eo)->p4*Eo^p6;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aGf*6#%#EoG6\"6$%)operatorG%&arrow GF(*&%#p4G\"\"\")9$%#p6GF.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "b:=(Eo)->p5*Eo^p7;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"bGf*6#%#EoG6\"6$%)operatorG%&arrowGF(*&%#p5G\"\"\")9$%#p7GF.F(F(F (" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "Eo:=50.;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#EoG$\"#]\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Try different values of the incident electron energy " } {TEXT 273 3 "Eo " }{TEXT -1 40 "and note how resolution function chang es" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "R:=(Xb)->exp(Xb/b(Eo))*(1-erf(Xb/a(Eo)));" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RGf*6#%#XbG6\"6$%)operatorG%&arrowGF(*&- %$expG6#*&9$\"\"\"-%\"bG6#%#EoG!\"\"F2,&F2F2-%$erfG6#*&F1F2-%\"aGF5F7F 7F2F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "plot(R(Xb),Xb= -111...39,title=`R(E) vs Channel Number`);" }}{PARA 13 "" 1 "" {GLPLOT2D 336 252 252 {PLOTDATA 2 "6&-%'CURVESG6$7jo7$$!$6\"\"\"!$\"3% )onzL-o38!#?7$$!31++voUIx5!#:$\"37N#)[.&\\Ti\"F-7$$!3$**\\7y)e&)[5F1$ \"3q_-dZ=!*f>F-7$$!3)***\\73F'o,\"F1$\"3#pe\"zjE4@CF-7$$!3P++voXdY)*!# ;$\"3g(p)oC-+&*HF-7$$!3k+]i:F0E&*FA$\"3t61APc?,PF-7$$!3V+]7Gz))G#*FA$ \"3^b!eXO0R]%F-7$$!3&***\\7.5>@*)FA$\"3L$pYGs^*=bF-7$$!3<**\\7./(Hg)FA $\"38C)*)3VK*4oF-7$$!3i**\\iS.x&G)FA$\"39l[\")zRB(R)F-7$$!3l****\\(3\" \\fzFA$\"3)GAMyqz;/\"!#>7$$!39***\\P9/@n(FA$\"3/8C=bPVf7F\\o7$$!3S**** \\7Xd[tFA$\"3Q81qxo\\f:F\\o7$$!3>****\\PkrBqFA$\"3AVNQdfuK>F\\o7$$!30+ +]([b1r'FA$\"3vxl[TbtwBF\\o7$$!3U**\\7`hOEkFA$\"3(48fN&ypnGF\\o7$$!36+ +]P'=$)3'FA$\"3%zmXPB\\^e$F\\o7$$!3-+++]![>!eFA$\"3q%e[UR%oJVF\\o7$$!3 $)**\\7y4$)oaFA$\"3_]8l@Pz(R&F\\o7$$!3E+++Df'R<&FA$\"3vEcWh6ZelF\\o7$$ !3s**\\7GAX][FA$\"3l?'3:Ad47)F\\o7$$!3'*)*\\P%o!RUXFA$\"3;=?]skd`**F\\ o7$$!3j***\\7yg4A%FA$\"3iIbY&y&zI7!#=7$$!3=+]i!z(yDRFA$\"3C&yl))pbd\\ \"Fir7$$!3w++vVQS2OFA$\"3fp;%ojQe%=Fir7$$!3%***\\7.CpwKFA$\"3M)Q5%*Q#[ 'H#Fir7$$!3&***\\(=72)))HFA$\"3K%[cp2cux#Fir7$$!3J++DJJ)yn#FA$\"3'fvO \"eWn5MFir7$$!3&******\\AomN#FA$\"3y+j%*HO#o@%Fir7$$!3)4+]i5AC/#FA$\"3 9uw)Fir7$$!3U,++DRV(4\"FA$\"3!=:L! 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" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 23 "Note that the variable " }{TEXT 274 4 "Xb, " }{TEXT -1 3 "the" }{TEXT 285 16 " \+ channel number " }{TEXT -1 15 "defined in the " }{TEXT 282 6 "Blur.f" }{TEXT -1 18 "., corresponds to " }{TEXT 275 5 "E-Eo." }{TEXT -1 80 " \+ In an ideal world, the response would be a line or delta function cen tered at " }{TEXT 278 6 "Xb=0. " }{TEXT -1 88 " We see here that the d etector's output has a finite width and is bent towards negative " } {TEXT 281 2 "Xb" }{TEXT -1 117 "'s (the center of the peak is at a low er energy because some of the electron's energy is lost to low energy \+ photons)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 145 "For our experiment, 1 MeV of energy occupied three channels, that is, a peak of width 21 channels corresponds to a width or resolution \+ of 7 MeV. " }}}}{MARK "0 2 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }