c From leif.axelsson@fy.chalmers.se Wed Oct 6 10:26:27 1999 c Date: Tue, 05 Oct 1999 11:36:29 +0200 c From: Leif Axelsson c To: Karin Markenroth c Subject: Re: R-matrix program c> Date: Tue, 5 Oct 1999 11:02:00 +1000 (EST) c> From: Frederick Barker c> X-Sender: fcb105@delta.anu.edu.au c> To: leif.axelsson@fy.chalmers.se c> Subject: Re: R-matrix program c> c> Dear Leif, c> c> I was pleased to hear from you again, and to know that work is c> continuing on 11N. c> c> I am enclosing a copy of the FORTRAN program that I used for fitting c> your data. This consists of the main program and a sub-program (FUNVAL) c> that calculates the cross section for given parameter values. Two other c> sub-programs are used: one (FIT77) varies the parameters to get a c> least-squares fit of the data, the other (HACOOL) calculates Coulomb c>functions (penetration factor, shift factor, hard-sphere phase shift). c> I use locally-written programs, but you presumably have programs that c> are equivalent. I also enclose an input file (INFILE) and the resulting c> output file (RESULTS.DAT); these are for the fit given in my FAX to you c> of 17 October 1997, with the corresponding parameter values given in the c> table of my e-mail of 15 October 1997. I hope that the notation, etc. is c> clear, but please let me know if there are any problems. c> c> Best wishes c> Fred Barker c> c> C FIT TO AXELSSON ET AL. EXCITATION FUNCTION C SUBS HACOOL,FIT77,FUNVAL C PAR LABELS C 1/2+ 1/2- 5/2+ C E gs phi0/R0 E gs phi0/R0 E gs phi0/R0 C 1 2 3 4 5 6 7 8 9 EXTERNAL FUNVAL COMMON E(150),SIGX(150),ERR(150),ND,AK(150),ET(150),CPH(3,150), 1P(3,150),S0(3,150),PHI(3,150),LL,LU,PAR(9),STEP(9),SIGC(150), 2CT(3,150),NCH(3) DIMENSION CR(3),BC(3),COOL(100),WORK(126),KEEP(9),DELTA(3), 1BETA(3),DSF(3) COMPLEX CT 501 FORMAT (8F10.4) 502 FORMAT (6I4,6X,5F10.4) 503 FORMAT (10F8.4) 601 FORMAT ('FIT TO AXELSSON ET AL. EXCITATION FUNCTION FROM',F6.3, 1' TO',F6.3,' MeV'/' '/13X,'1/2+',11X,'1/2-',11X,'5/2+'/'CR', 23F15.3/'BC',F16.4,2F15.4/'NCH',I12,2I14/' '/'STARTING VALUES') 602 FORMAT (17X,'1/2+',24X,'1/2-',24X,'5/2+'/'PAR',3X,3(2F8.4,F10.4, 12X)/'STEP',2X,3(2F8.4,F10.4,2X)) 603 FORMAT (' '/'CHISQ =',F15.4/' '/'FINAL VALUES') 604 FORMAT (' '/'FIT TO EXCITATION FUNCTION'/3X,'E',4X,'SIGC',3X, 1'SIGX',4X,'ERR',5X,'CHI',22X,'AMPLITUDES T'/44X,'1/2+',13X, 2'1/2-',13X,'5/2+') 605 FORMAT (F6.3,3F7.1,F9.4,3(2X,F7.4,',',F7.4)) 606 FORMAT (' '/'COULOMB DATA'/3X,'E',9X,'P',9X,'S0',5X,'PHI',5X, 1'CPH') 607 FORMAT (F6.3,E12.4,F9.4,F8.3) 608 FORMAT (E18.4,F9.4,2F8.3) 609 FORMAT (' '/'VALUES OF DELTA,BETA,DENSITY-OF-STATES FUNCTION'/ 13X,'E',15X,'1/2+',22X,'1/2-',22X,'5/2+'/5X,3(6X,'DELTA',3X, 2'BETA',5X,'DSF')) 610 FORMAT (F6.3,3(F10.2,F8.2,F8.4)) OPEN (UNIT=15,FILE='INFILE',STATUS='UNKNOWN') OPEN (UNIT=16,FILE='RESULTS.DAT',STATUS='UNKNOWN') C LOAD EXCITATION FUNCTION DATA DO 1 J=1,150 READ (15,501) E(J),SIGX(J),ERR(J) IF (E(J)) 2,1,1 1 CONTINUE ND=150 4 READ (15,501) AA IF (AA) 3,4,4 2 ND=J-1 C CALCULATE COULOMB DATA 3 READ (15,501) CR,BC DO 5 J=1,ND AE=SQRT(E(J)) AK(J)=0.20856*AE ETA=0.90091/AE ET(J)=ETA CPH(1,J)=0.0 CPH(2,J)=ATAN(ETA) CPH(3,J)=CPH(2,J)+ATAN(ETA/2.0) C CPH = COULOMB PHASE DO 6 K=1,3 RHO=CR(K)*AK(J) L=K-1 CALL HACOOL(ETA,RHO,L,COOL,+2) P(K,J)=COOL(L+1) S0(K,J)=COOL(L+26)-BC(K) 6 PHI(K,J)=COOL(L+51) 5 CONTINUE C LOAD FITTING INSTRUCTIONS 11 READ (15,502) NPR,LL,LU,LOP,MUM,KONV,SIZE,CHILIM C NPR = 1 FOR PRINTOUT OF COULOMB DATA, 2 OTHERWISE IF (NPR) 3,999,7 7 IF (LU.GT.ND) LU=ND C LOAD STARTING VALUES READ (15,502) NCH C NCH = 1 FOR phi0, 2 FOR R0 READ (15,503) PAR READ (15,503) STEP C WRITE INPUT WRITE (16,601) E(LL),E(LU),CR,BC,NCH WRITE (16,602) PAR,STEP C ADJUST PARAMETERS FOR BEST FIT CHISQ=CHILIM NOUT=KONV CALL FIT77(9,PAR,STEP,WORK,KEEP,SIZE,CHISQ,FUNVAL,LOP,MUM,NOUT) WRITE (16,603) CHISQ WRITE (16,602) PAR,STEP C OUTPUT OF FIT TO DATA WRITE (16,604) DO 8 J=1,ND CHI=(SIGX(J)-SIGC(J))/ERR(J) 8 WRITE (16,605) E(J),SIGC(J),SIGX(J),ERR(J),CHI,(CT(K,J),K=1,3) C CALCULATION OF DELTA,BETA,DENSITY-OF-STATES FUNCTION WRITE (16,609) DO 9 J=1,ND DO 10 K=1,3 IF (NCH(K).EQ.2) GO TO 14 AA=PAR(3*K-1)*P(K,J) AB=PAR(3*K-2)-E(J)-PAR(3*K-1)*S0(K,J) AC=ATAN(AA/AB) IF (AB.LT.0.0) AC=AC+3.141593 BETA(K)=AC*57.29577 DELTA(K)=BETA(K)-PHI(K,J)-PAR(3*K) DSF(K)=SIN(AC)**2/P(K,J) GO TO 10 14 R=PAR(3*K-1)/(PAR(3*K-2)-E(J))+PAR(3*K) AA=P(K,J) AB=1.0/R-S0(K,J) AC=ATAN(AA/AB) IF (AB.LT.0.0) AC=AC+3.141593 BETA(K)=AC*57.29577 DELTA(K)=BETA(K)-PHI(K,J) AA=PAR(3*K-1)*P(K,J) AB=PAR(3*K-2)-E(J)-PAR(3*K-1)*S0(K,J) DSF(K)=AA/(AB**2+AA**2) 10 CONTINUE 9 WRITE (16,610) E(J),(DELTA(K),BETA(K),DSF(K),K=1,3) IF (NPR.NE.1) GO TO 11 C COULOMB DATA WRITE (16,606) DO 12 J=1,ND WRITE (16,607) E(J),P(1,J),S0(1,J),PHI(1,J) DO 13 K=2,3 AA=CPH(K,J)*57.29577 13 WRITE (16,608) P(K,J),S0(K,J),PHI(K,J),AA 12 CONTINUE GO TO 11 999 STOP END FUNCTION FUNVAL(PAS,NP) COMMON E(150),SIGX(150),ERR(150),ND,AK(150),ET(150),CPH(3,150), 1P(3,150),S0(3,150),PHI(3,150),LL,LU,PAR(9),STEP(9),SIGC(150), 2CT(3,150),NCH(3) DIMENSION PAS(9) COMPLEX CA,CB,CC,CT DO 1 J=1,ND DO 2 K=1,3 R=PAR(3*K-1)/(PAR(3*K-2)-E(J)) IF (NCH(K).EQ.2) R=R+PAR(3*K) AA=1.0/R CA=CMPLX(S0(K,J),P(K,J)) CB=AA-CA CC=1.0+(0.0,2.0)*P(K,J)/CB AA=PHI(K,J) IF (NCH(K).EQ.1) AA=AA+PAR(3*K) CA=CMPLX(0.0,-2.0*AA/57.29577) CB=CEXP(CA) CC=1.0-CB*CC CA=CMPLX(0.0,2.0*CPH(K,J)) CB=CEXP(CA) 2 CT(K,J)=CB*CC AA=AIMAG(CT(1,J)-CT(2,J)+3.0*CT(3,J)) AB=REAL(6.0*CONJG(CT(1,J))*CT(3,J)-2.0*CONJG(CT(2,J))*CT(1,J) 1-6.0*CONJG(CT(2,J))*CT(3,J)) AC=CONJG(CT(1,J))*CT(1,J)+CONJG(CT(2,J))*CT(2,J)+9.0* 1CONJG(CT(3,J))*CT(3,J) AD=ET(J)**2+2.0*ET(J)*AA+(AC+AB) 1 SIGC(J)=2.5*AD/AK(J)**2 SUM=0.0 DO 3 J=LL,LU CHI=(SIGX(J)-SIGC(J))/ERR(J) 3 SUM=SUM+CHI**2 FUNVAL=SUM RETURN END 0.6465 393.44 20. 0.6777 320.53 20. 0.7099 276.63 20. 0.7428 246.97 20. 0.7766 158.28 15. 0.8109 129.50 15. 0.8458 115.42 15. 0.8813 101.98 10. 0.9172 112.08 10. 0.9534 58.97 10. 0.9901 39.68 10. 1.0270 49.42 10. 1.0643 35.98 10. 1.1018 53.79 10. 1.1395 49.66 10. 1.1775 70.89 10. 1.2157 85.68 10. 1.2540 77.09 10. 1.2925 93.25 10. 1.3312 106.14 10. 1.3700 94.47 10. 1.4089 80.57 10. 1.4480 102.03 10. 1.4871 85.40 10. 1.5263 96.07 10. 1.5657 107.99 10. 1.6051 103.98 10. 1.6446 143.46 10. 1.6842 120.32 10. 1.7239 104.23 10. 1.7636 93.45 10. 1.8035 105.32 10. 1.8433 93.70 10. 1.8832 124.24 15. 1.9232 112.46 15. 1.9632 130.91 15. 2.0032 136.76 15. 2.0434 141.09 15. 2.0835 152.25 15. 2.1237 159.63 15. 2.1639 181.30 20. 2.2042 183.16 20. 2.2445 223.43 20. 2.2848 217.16 20. 2.3252 234.71 20. 2.3655 280.35 25. 2.4059 264.12 25. 2.4464 277.93 25. 2.4868 304.03 30. 2.5273 318.06 30. 2.5678 271.23 30. 2.6084 309.93 30. 2.6489 287.32 30. 2.6895 360.46 30. 2.7301 333.92 30. 2.7707 324.74 30. 2.8113 333.09 30. 2.8320 333.12 30. 2.8926 348.63 30. 2.9333 359.48 30. 2.9740 345.87 30. 3.0147 385.86 35. 3.0554 422.22 35. 3.0962 423.01 35. 3.1369 405.59 35. 3.1777 487.91 40. 3.2184 434.57 40. 3.2592 502.72 40. 3.3000 526.99 40. 3.3408 588.83 45. 3.3816 584.83 45. 3.4224 619.08 45. 3.4633 624.72 45. 3.5042 661.64 45. 3.5450 700.67 45. 3.5859 700.45 45. 3.6267 661.57 45. 3.6676 664.05 45. 3.7085 569.65 45. 3.7494 470.44 45. 3.7903 491.76 45. 3.8313 388.47 40. 3.8722 283.22 40. 3.9131 387.49 40. 3.9540 436.12 40. 3.9950 287.36 40. -9.9 4.574 4.574 4.574 -0.3308 -0.7434 -1.3437 2 11 82 5 2 10 0.1 0.0 1 1 1 2.25 2.7431 -29.73 2.4871 2.1238 -31.88 3.7819 1.0511 -12.34 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 FIT TO AXELSSON ET AL. EXCITATION FUNCTION FROM 0.990 TO 3.831 MeV 1/2+ 1/2- 5/2+ CR 4.574 4.574 4.574 BC -0.3308 -0.7434 -1.3437 NCH 1 1 1 STARTING VALUES 1/2+ 1/2- 5/2+ PAR 2.2500 2.7431 -29.7300 2.4871 2.1238 -31.8800 3.7819 1.0511 -12.3400 STEP 0.0000 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 CHISQ = 53.5913 FINAL VALUES 1/2+ 1/2- 5/2+ PAR 2.2500 2.7278 -29.6818 2.4840 2.1223 -31.7096 3.7821 1.0547 -12.3437 STEP 0.0000 0.1980 1.4995 0.0449 0.2474 1.5086 0.0309 0.1091 0.4314 FIT TO EXCITATION FUNCTION E SIGC SIGX ERR CHI AMPLITUDES T 1/2+ 1/2- 5/2+ 0.646 56.5 393.4 20.0 16.8479 0.5889,-0.9116 0.8311, 0.6648 0.0935, 0.4173 0.678 50.4 320.5 20.0 13.5088 0.6089,-0.9203 0.8477, 0.6483 0.1116, 0.4129 0.710 45.2 276.6 20.0 11.5724 0.6322,-0.9299 0.8639, 0.6323 0.1290, 0.4079 0.743 41.0 247.0 20.0 10.2979 0.6590,-0.9401 0.8798, 0.6169 0.1458, 0.4023 0.777 37.8 158.3 15.0 8.0306 0.6900,-0.9507 0.8955, 0.6022 0.1619, 0.3961 0.811 35.7 129.5 15.0 6.2564 0.7250,-0.9614 0.9110, 0.5886 0.1773, 0.3896 0.846 34.5 115.4 15.0 5.3945 0.7646,-0.9719 0.9263, 0.5759 0.1919, 0.3827 0.881 34.4 102.0 10.0 6.7602 0.8089,-0.9816 0.9416, 0.5643 0.2058, 0.3755 0.917 35.3 112.1 10.0 7.6799 0.8581,-0.9899 0.9570, 0.5540 0.2191, 0.3682 0.953 37.2 59.0 10.0 2.1782 0.9119,-0.9961 0.9725, 0.5450 0.2316, 0.3607 0.990 40.1 39.7 10.0 -0.0402 0.9706,-0.9996 0.9882, 0.5375 0.2434, 0.3530 1.027 43.9 49.4 10.0 0.5535 1.0335,-0.9994 1.0043, 0.5317 0.2547, 0.3453 1.064 48.5 36.0 10.0 -1.2552 1.1005,-0.9949 1.0209, 0.5275 0.2653, 0.3375 1.102 53.9 53.8 10.0 -0.0094 1.1706,-0.9853 1.0379, 0.5253 0.2754, 0.3298 1.140 59.8 49.7 10.0 -1.0128 1.2430,-0.9700 1.0556, 0.5251 0.2849, 0.3221 1.178 66.1 70.9 10.0 0.4813 1.3168,-0.9485 1.0740, 0.5272 0.2940, 0.3144 1.216 72.5 85.7 10.0 1.3153 1.3907,-0.9205 1.0932, 0.5317 0.3026, 0.3068 1.254 78.9 77.1 10.0 -0.1810 1.4633,-0.8862 1.1132, 0.5389 0.3108, 0.2992 1.293 85.0 93.3 10.0 0.8262 1.5335,-0.8458 1.1340, 0.5490 0.3186, 0.2918 1.331 90.6 106.1 10.0 1.5557 1.6003,-0.7998 1.1556, 0.5625 0.3260, 0.2845 1.370 95.5 94.5 10.0 -0.1019 1.6625,-0.7491 1.1780, 0.5795 0.3331, 0.2774 1.409 99.6 80.6 10.0 -1.9003 1.7193,-0.6947 1.2009, 0.6006 0.3399, 0.2704 1.448 102.8 102.0 10.0 -0.0731 1.7705,-0.6375 1.2244, 0.6261 0.3464, 0.2635 1.487 105.0 85.4 10.0 -1.9613 1.8154,-0.5789 1.2480, 0.6565 0.3527, 0.2568 1.526 106.4 96.1 10.0 -1.0306 1.8543,-0.5197 1.2713, 0.6922 0.3587, 0.2502 1.566 106.9 108.0 10.0 0.1041 1.8875,-0.4609 1.2939, 0.7339 0.3646, 0.2439 1.605 106.9 104.0 10.0 -0.2903 1.9150,-0.4035 1.3150, 0.7818 0.3704, 0.2377 1.645 106.4 143.5 10.0 3.7070 1.9375,-0.3481 1.3337, 0.8365 0.3760, 0.2317 1.684 105.7 120.3 10.0 1.4595 1.9555,-0.2951 1.3489, 0.8981 0.3815, 0.2259 1.724 105.2 104.2 10.0 -0.0953 1.9695,-0.2450 1.3592, 0.9670 0.3869, 0.2202 1.764 105.1 93.4 10.0 -1.1641 1.9802,-0.1982 1.3632, 1.0427 0.3923, 0.2148 1.804 105.8 105.3 10.0 -0.0475 1.9880,-0.1545 1.3591, 1.1249 0.3977, 0.2095 1.843 107.6 93.7 10.0 -1.3926 1.9934,-0.1144 1.3454, 1.2122 0.4031, 0.2045 1.883 110.9 124.2 15.0 0.8892 1.9970,-0.0776 1.3203, 1.3032 0.4085, 0.1997 1.923 115.9 112.5 15.0 -0.2279 1.9990,-0.0439 1.2825, 1.3959 0.4140, 0.1951 1.963 122.7 130.9 15.0 0.5469 1.9999,-0.0135 1.2313, 1.4875 0.4195, 0.1907 2.003 131.4 136.8 15.0 0.3560 1.9999, 0.0140 1.1667, 1.5748 0.4252, 0.1866 2.043 142.0 141.1 15.0 -0.0592 1.9993, 0.0387 1.0891, 1.6554 0.4311, 0.1827 2.083 154.1 152.3 15.0 -0.1214 1.9982, 0.0606 1.0008, 1.7258 0.4372, 0.1790 2.124 167.4 159.6 15.0 -0.5185 1.9968, 0.0801 0.9037, 1.7841 0.4435, 0.1756 2.164 181.5 181.3 20.0 -0.0118 1.9953, 0.0972 0.8012, 1.8287 0.4500, 0.1724 2.204 196.0 183.2 20.0 -0.6440 1.9937, 0.1123 0.6962, 1.8591 0.4569, 0.1696 2.244 210.5 223.4 20.0 0.6483 1.9921, 0.1253 0.5919, 1.8757 0.4641, 0.1670 2.285 224.4 217.2 20.0 -0.3643 1.9907, 0.1364 0.4911, 1.8795 0.4718, 0.1647 2.325 237.7 234.7 20.0 -0.1520 1.9893, 0.1458 0.3958, 1.8721 0.4799, 0.1628 2.365 250.1 280.4 25.0 1.2083 1.9881, 0.1536 0.3077, 1.8557 0.4884, 0.1613 2.406 261.6 264.1 25.0 0.1005 1.9871, 0.1600 0.2275, 1.8320 0.4976, 0.1601 2.446 272.1 277.9 25.0 0.2316 1.9863, 0.1649 0.1554, 1.8031 0.5073, 0.1593 2.487 281.8 304.0 30.0 0.7426 1.9857, 0.1686 0.0917, 1.7707 0.5178, 0.1591 2.527 290.6 318.1 30.0 0.9154 1.9852, 0.1712 0.0358, 1.7362 0.5290, 0.1593 2.568 298.8 271.2 30.0 -0.9184 1.9850, 0.1726 -0.0128, 1.7008 0.5411, 0.1601 2.608 306.5 309.9 30.0 0.1150 1.9849, 0.1730 -0.0548, 1.6654 0.5542, 0.1616 2.649 313.8 287.3 30.0 -0.8828 1.9850, 0.1725 -0.0906, 1.6308 0.5683, 0.1637 2.690 321.0 360.5 30.0 1.3167 1.9852, 0.1712 -0.1212, 1.5974 0.5836, 0.1667 2.730 328.1 333.9 30.0 0.1947 1.9856, 0.1690 -0.1471, 1.5656 0.6001, 0.1707 2.771 335.3 324.7 30.0 -0.3528 1.9861, 0.1660 -0.1689, 1.5356 0.6181, 0.1758 2.811 342.9 333.1 30.0 -0.3255 1.9867, 0.1623 -0.1871, 1.5075 0.6376, 0.1821 2.832 346.9 333.1 30.0 -0.4578 1.9871, 0.1602 -0.1952, 1.4940 0.6483, 0.1859 2.893 359.4 348.6 30.0 -0.3599 1.9882, 0.1531 -0.2148, 1.4573 0.6822, 0.1996 2.933 368.8 359.5 30.0 -0.3108 1.9891, 0.1476 -0.2250, 1.4352 0.7075, 0.2113 2.974 379.1 345.9 30.0 -1.1088 1.9899, 0.1415 -0.2332, 1.4149 0.7352, 0.2255 3.015 390.6 385.9 35.0 -0.1357 1.9909, 0.1349 -0.2397, 1.3964 0.7653, 0.2428 3.055 403.4 422.2 35.0 0.5367 1.9918, 0.1279 -0.2447, 1.3797 0.7981, 0.2637 3.096 417.9 423.0 35.0 0.1470 1.9927, 0.1204 -0.2484, 1.3646 0.8338, 0.2892 3.137 434.1 405.6 35.0 -0.8133 1.9936, 0.1126 -0.2510, 1.3510 0.8724, 0.3201 3.178 452.3 487.9 40.0 0.8896 1.9945, 0.1043 -0.2525, 1.3389 0.9140, 0.3577 3.218 472.8 434.6 40.0 -0.9562 1.9954, 0.0957 -0.2532, 1.3281 0.9581, 0.4036 3.259 495.8 502.7 40.0 0.1727 1.9962, 0.0867 -0.2532, 1.3186 1.0045, 0.4597 3.300 521.4 527.0 40.0 0.1408 1.9970, 0.0774 -0.2525, 1.3103 1.0519, 0.5282 3.341 549.4 588.8 45.0 0.8768 1.9977, 0.0678 -0.2511, 1.3031 1.0984, 0.6119 3.382 579.4 584.8 45.0 0.1198 1.9983, 0.0579 -0.2493, 1.2968 1.1410, 0.7135 3.422 610.6 619.1 45.0 0.1884 1.9989, 0.0478 -0.2469, 1.2916 1.1748, 0.8357 3.463 641.2 624.7 45.0 -0.3651 1.9993, 0.0374 -0.2441, 1.2872 1.1929, 0.9807 3.504 668.1 661.6 45.0 -0.1434 1.9996, 0.0268 -0.2409, 1.2836 1.1859, 1.1476 3.545 687.2 700.7 45.0 0.3001 1.9999, 0.0160 -0.2374, 1.2808 1.1427, 1.3312 3.586 693.3 700.5 45.0 0.1598 2.0000, 0.0050 -0.2335, 1.2787 1.0525, 1.5216 3.627 681.3 661.6 45.0 -0.4373 2.0000,-0.0062 -0.2294, 1.2773 0.9093, 1.7004 3.668 648.0 664.0 45.0 0.3576 1.9998,-0.0176 -0.2249, 1.2764 0.7153, 1.8467 3.708 594.1 569.7 45.0 -0.5442 1.9996,-0.0291 -0.2202, 1.2761 0.4850, 1.9402 3.749 525.0 470.4 45.0 -1.2115 1.9992,-0.0408 -0.2152, 1.2764 0.2417, 1.9707 3.790 448.4 491.8 45.0 0.9644 1.9986,-0.0526 -0.2100, 1.2771 0.0102, 1.9407 3.831 372.1 388.5 40.0 0.4081 1.9979,-0.0646 -0.2046, 1.2783 -0.1916, 1.8633 3.872 302.6 283.2 40.0 -0.4833 1.9971,-0.0766 -0.1989, 1.2799 -0.3537, 1.7562 3.913 242.4 387.5 40.0 3.6263 1.9961,-0.0888 -0.1931, 1.2819 -0.4762, 1.6354 3.954 192.6 436.1 40.0 6.0890 1.9949,-0.1010 -0.1871, 1.2843 -0.5639, 1.5129 3.995 152.2 287.4 40.0 3.3798 1.9936,-0.1133 -0.1809, 1.2870 -0.6236, 1.3959 VALUES OF DELTA,BETA,DENSITY-OF-STATES FUNCTION E 1/2+ 1/2- 5/2+ DELTA BETA DSF DELTA BETA DSF DELTA BETA DSF 0.646 32.86 5.57 0.1007 32.15 0.74 0.0088 12.35 0.02 0.0001 0.678 33.49 6.57 0.1224 32.25 0.89 0.0109 12.35 0.02 0.0001 0.710 34.21 7.70 0.1481 32.36 1.07 0.0133 12.35 0.02 0.0001 0.743 35.03 8.96 0.1780 32.50 1.28 0.0163 12.35 0.03 0.0001 0.777 35.97 10.38 0.2128 32.66 1.52 0.0198 12.35 0.04 0.0002 0.811 37.02 11.93 0.2526 32.84 1.80 0.0239 12.36 0.04 0.0002 0.846 38.19 13.64 0.2979 33.05 2.11 0.0288 12.36 0.05 0.0003 0.881 39.49 15.51 0.3491 33.29 2.46 0.0345 12.36 0.06 0.0003 0.917 40.92 17.54 0.4060 33.57 2.85 0.0412 12.37 0.08 0.0004 0.953 42.47 19.71 0.4685 33.88 3.29 0.0489 12.37 0.09 0.0004 0.990 44.16 22.03 0.5369 34.23 3.78 0.0578 12.38 0.10 0.0005 1.027 45.96 24.50 0.6101 34.62 4.32 0.0681 12.39 0.12 0.0006 1.064 47.88 27.10 0.6878 35.07 4.93 0.0801 12.40 0.14 0.0007 1.102 49.91 29.83 0.7686 35.57 5.59 0.0938 12.40 0.17 0.0009 1.140 52.03 32.66 0.8513 36.12 6.32 0.1095 12.42 0.19 0.0010 1.178 54.23 35.59 0.9346 36.74 7.13 0.1276 12.43 0.22 0.0012 1.216 56.50 38.59 1.0166 37.43 8.01 0.1484 12.44 0.25 0.0014 1.254 58.80 41.64 1.0954 38.20 8.98 0.1722 12.46 0.28 0.0016 1.293 61.12 44.72 1.1696 39.05 10.04 0.1993 12.47 0.32 0.0018 1.331 63.45 47.82 1.2376 39.99 11.20 0.2305 12.49 0.36 0.0021 1.370 65.74 50.89 1.2980 41.03 12.47 0.2659 12.52 0.41 0.0024 1.409 68.00 53.93 1.3499 42.17 13.85 0.3064 12.54 0.46 0.0028 1.448 70.20 56.91 1.3929 43.44 15.36 0.3524 12.57 0.51 0.0031 1.487 72.31 59.82 1.4266 44.83 17.01 0.4045 12.60 0.57 0.0036 1.526 74.34 62.64 1.4513 46.37 18.80 0.4635 12.63 0.64 0.0040 1.566 76.28 65.37 1.4674 48.05 20.75 0.5302 12.67 0.71 0.0046 1.605 78.10 68.00 1.4756 49.90 22.87 0.6048 12.71 0.78 0.0051 1.645 79.82 70.51 1.4767 51.92 25.16 0.6881 12.76 0.86 0.0058 1.684 81.42 72.92 1.4715 54.12 27.65 0.7803 12.81 0.95 0.0065 1.724 82.91 75.21 1.4609 56.52 30.33 0.8815 12.86 1.05 0.0073 1.764 84.28 77.39 1.4459 59.11 33.22 0.9909 12.92 1.15 0.0082 1.804 85.56 79.46 1.4271 61.90 36.32 1.1081 12.99 1.26 0.0091 1.843 86.72 81.43 1.4054 64.88 39.61 1.2305 13.06 1.38 0.0102 1.883 87.78 83.29 1.3815 68.06 43.09 1.3563 13.14 1.51 0.0114 1.923 88.74 85.05 1.3558 71.41 46.76 1.4821 13.23 1.65 0.0127 1.963 89.61 86.72 1.3290 74.90 50.57 1.6038 13.32 1.79 0.0142 2.003 90.40 88.31 1.3015 78.51 54.51 1.7171 13.43 1.95 0.0158 2.043 91.11 89.81 1.2734 82.22 58.54 1.8183 13.54 2.12 0.0176 2.083 91.74 91.23 1.2452 85.95 62.61 1.9028 13.66 2.31 0.0195 2.124 92.30 92.58 1.2172 89.69 66.68 1.9681 13.80 2.50 0.0217 2.164 92.79 93.86 1.1894 93.37 70.71 2.0123 13.94 2.71 0.0242 2.204 93.22 95.08 1.1619 96.97 74.65 2.0351 14.10 2.94 0.0269 2.244 93.60 96.24 1.1350 100.45 78.47 2.0375 14.28 3.18 0.0299 2.285 93.92 97.34 1.1087 103.76 82.14 2.0214 14.47 3.44 0.0332 2.325 94.19 98.39 1.0831 106.91 85.65 1.9895 14.68 3.72 0.0370 2.365 94.42 99.39 1.0582 109.86 88.95 1.9450 14.90 4.02 0.0411 2.406 94.60 100.34 1.0340 112.62 92.07 1.8906 15.15 4.35 0.0458 2.446 94.75 101.25 1.0105 115.19 95.00 1.8293 15.42 4.70 0.0510 2.487 94.85 102.12 0.9877 117.56 97.73 1.7637 15.71 5.07 0.0568 2.527 94.93 102.96 0.9657 119.74 100.28 1.6957 16.04 5.48 0.0634 2.568 94.97 103.76 0.9445 121.74 102.65 1.6270 16.39 5.92 0.0708 2.608 94.98 104.52 0.9239 123.58 104.86 1.5588 16.78 6.39 0.0792 2.649 94.97 105.26 0.9040 125.25 106.91 1.4923 17.20 6.90 0.0886 2.690 94.93 105.96 0.8848 126.77 108.81 1.4279 17.67 7.46 0.0994 2.730 94.86 106.64 0.8663 128.16 110.58 1.3660 18.18 8.07 0.1116 2.771 94.78 107.30 0.8484 129.43 112.22 1.3071 18.74 8.73 0.1256 2.811 94.67 107.93 0.8311 130.58 113.75 1.2512 19.36 9.45 0.1416 2.832 94.61 108.24 0.8225 131.12 114.48 1.2238 19.71 9.84 0.1506 2.893 94.40 109.12 0.7983 132.56 116.50 1.1483 20.82 11.11 0.1812 2.933 94.24 109.68 0.7827 133.42 117.74 1.1012 21.67 12.06 0.2058 2.974 94.07 110.23 0.7677 134.19 118.90 1.0568 22.61 13.11 0.2344 3.015 93.88 110.76 0.7531 134.89 119.99 1.0152 23.67 14.28 0.2678 3.055 93.67 111.27 0.7391 135.52 121.01 0.9760 24.85 15.57 0.3070 3.096 93.46 111.77 0.7255 136.09 121.97 0.9391 26.19 17.02 0.3532 3.137 93.23 112.25 0.7123 136.60 122.87 0.9045 27.69 18.63 0.4079 3.178 92.99 112.71 0.6996 137.06 123.71 0.8719 29.39 20.45 0.4729 3.218 92.74 113.17 0.6873 137.47 124.51 0.8413 31.32 22.50 0.5503 3.259 92.49 113.61 0.6754 137.83 125.27 0.8124 33.53 24.83 0.6429 3.300 92.22 114.03 0.6638 138.15 125.98 0.7852 36.05 27.48 0.7538 3.341 91.94 114.45 0.6526 138.43 126.66 0.7595 38.95 30.50 0.8863 3.382 91.66 114.85 0.6418 138.68 127.30 0.7353 42.29 33.97 1.0439 3.422 91.37 115.24 0.6312 138.89 127.91 0.7124 46.13 37.93 1.2292 3.463 91.07 115.63 0.6210 139.08 128.49 0.6907 50.55 42.48 1.4439 3.504 90.77 116.00 0.6111 139.23 129.04 0.6702 55.60 47.67 1.6844 3.545 90.46 116.37 0.6015 139.36 129.57 0.6508 61.31 53.51 1.9407 3.586 90.14 116.72 0.5921 139.46 130.07 0.6323 67.68 60.02 2.1957 3.627 89.82 117.07 0.5831 139.55 130.55 0.6148 74.61 67.09 2.4211 3.668 89.50 117.41 0.5743 139.61 131.01 0.5982 81.97 74.58 2.5870 3.708 89.17 117.74 0.5657 139.65 131.45 0.5824 89.49 82.25 2.6674 3.749 88.83 118.06 0.5574 139.67 131.87 0.5673 96.91 89.81 2.6526 3.790 88.49 118.38 0.5492 139.67 132.27 0.5529 103.98 97.02 2.5524 3.831 88.15 118.69 0.5413 139.66 132.66 0.5392 110.52 103.71 2.3896 3.872 87.80 118.99 0.5337 139.64 133.03 0.5262 116.40 109.73 2.1929 3.913 87.45 119.29 0.5262 139.59 133.39 0.5137 121.61 115.09 1.9853 3.954 87.10 119.58 0.5189 139.54 133.73 0.5018 126.17 119.80 1.7831 3.995 86.75 119.86 0.5118 139.47 134.07 0.4903 130.15 123.93 1.5953