2 c---------|---------|---------|---------|---------|---------|---------|---------|
3 *-- Author : R.Lednicky 20/01/95
5 C=======================================================================
6 C Calculates final state interaction (FSI) weights
7 C WEIF = weight due to particle - (effective) nucleus FSI (p-N)
8 C WEI = weight due to p-p-N FSI
9 C WEIN = weight due to p-p FSI; note that WEIN=WEI if I3C=0;
10 C note that if I3C=1 the calculation of
11 C WEIN can be skipped by putting J=0
12 C.......................................................................
13 C Correlation Functions:
14 C CF(p-p-N) = sum(WEI)/sum(WEIF)
15 C CF(p-p) = sum(WEIN)/sum(1); here the nucleus is completely
17 C CF(p-p-"N") = sum(WEIN*WEIF')/sum(WEIF'), where WEIN and WEIF'
18 C are not correlated (calculated at different emission
19 C points, e.g., for different events);
20 C thus here the nucleus affects one-particle
21 C spectra but not the correlation
22 C.......................................................................
23 C User must supply data file <fn> on unit NUNIT (e.g. =11) specifying
25 C NS : approximation used to calculate Bethe-Salpeter amplitude
27 C If ITEST=1 then also following parameters are required
28 C ICH : 1(0) Coulomb interaction between the two particles ON (OFF)
29 C IQS : 1(0) quantum statistics for the two particles ON (OFF)
30 C ISI : 1(0) strong interaction between the two particles ON (OFF)
31 C I3C : 1(0) Coulomb interaction with residual nucleus ON (OFF)
32 C This data file can contain other information useful for the user.
33 C It is read by subroutines READINT4 and READREA8(4) (or READ_FILE).
34 C----------------------------------------------------------------------
35 C- LL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
36 C- part. 1: n p n alfa pi+ pi0 pi+ n p pi+ pi+ pi+ pi- K+ K+ K+ K-
37 C- part. 2: n p p alfa pi- pi0 pi+ d d K- K+ p p K- K+ p p
38 C NS=1 y/n: + + + + + - - - - - - - - - - - -
39 C----------------------------------------------------------------------
40 C- LL 18 19 20 21 22 23 24 25 26 27 28
41 C- part. 1: d d t t K0 K0 d p p p n
42 C- part. 2: d alfa t alfa K0 K0b t t alfa lambda lambda
43 C NS=1 y/n: - - - - - - - - - + +
44 C----------------------------------------------------------------------
45 C NS=1 Square well potential,
47 C NS=4 scattered wave approximated by the spherical wave,
48 C NS=2 same as NS=4 but the approx. of equal emission times in PRF
49 C not required (t=0 approx. used in all other cases).
50 C Note: if NS=2,4, the B-S amplitude diverges at zero distance r* in
51 C the two-particle c.m.s.; user can specify a cutoff AA in
52 C SUBROUTINE FSIINI, for example:
53 C IF(NS.EQ.2.OR.NS.EQ.4)AA=5.D0 !! in 1/GeV --> AA=1. fm
54 C---------------------------------------------------------------------
55 C ITEST=1 any values of parameters ICH, IQS, ISI, I3C are allowed
56 C and should be given in data file <fn>
57 C ITEST=0 physical values of these parameters are put automatically
58 C in FSIINI (their values are not required in data file)
59 C=====================================================================
60 C At the beginning of calculation user should call FSIINI,
61 C which reads LL, NS, ITEST (and eventually ICH, IQS, ISI, I3C)
62 C and initializes various parameters.
63 C In particular the constants in
64 C COMMON/FSI_CONS/PI,PI2,SPI,DR,W
65 C may be useful for the user:
66 C W=1/.1973D0 ! from fm to 1/GeV
70 C DR=180.D0/PI ! from radian to degree
71 C _______________________________________________________
72 C !! |Important note: all real quantities are assumed REAL*8 | !!
73 C -------------------------------------------------------
74 C For each event user should fill in the following information
75 C in COMMONs (all COMMONs in FSI calculation start with FSI_):
76 C ...................................................................
77 C COMMON/FSI_POC/AMN,AM1,AM2,CN,C1,C2,AC1,AC2
79 C AMN = mass of the effective nucleus [GeV/c**2]
80 C CN = charge of the effective nucleus [elem. charge units]
82 C ...................................................................
83 C COMMON/FSI_MOM/P1X,P1Y,P1Z,E1,P1, !part. momenta in the rest frame
84 C 1 P2X,P2Y,P2Z,E2,P2 !of effective nucleus (NRF)
87 C in NRF are required.
88 C To make the corresponding Lorentz transformation user can use the
89 C subroutines LTRAN and LTRANB
90 C ...................................................................
91 C COMMON/FSI_COOR/X1,Y1,Z1,T1,R1, ! 4-coord. of emission
92 C 1 X2,Y2,Z2,T2,R2 ! points in NRF
97 C should be given in NRF with the origin assumed at the center
98 C of the effective nucleus. If the effect of residual nucleus is
99 C not calculated within FSIW, the NRF can be any fixed frame.
100 C-----------------------------------------------------------------------
101 C Before calling FSIW the user must call
103 C Besides Lorentz transformation to pair rest frame:
104 C (p1-p2)/2 --> k* it also transforms 4-coordinates of
105 C emission points from fm to 1/GeV and calculates Ei,Pi and Ri.
106 C Note that |k*|=AK in COMMON/FSI_PRF/
107 C-----------------------------------------------------------------------
108 C After making some additional filtering using k* (say k* < k*max)
109 C or direction of vector k*,
110 C user can finally call FSIW to calculate the FSI weights
111 C to be used to construct the correlation function
112 C=======================================================================
114 IMPLICIT REAL*8 (A-H,O-Z)
116 COMMON/FSI_POC/AMN,AM1,AM2,CN,C1,C2,AC1,AC2
117 COMMON/FSI_MOM/P1X,P1Y,P1Z,E1,P1, ! particle momenta in NRF
119 COMMON/FSI_PRF/PPX,PPY,PPZ,AK,AKS, ! k*=(p1-p2)/2 and x1-x2
120 1 X,Y,Z,T,RP,RPS ! in pair rest frame (PRF)
121 COMMON/FSI_COOR/X1,Y1,Z1,T1,R1, !4-coord. of emis. points in NRF
123 COMMON/FSI_NS/LL,NS,ICH,ISI,IQS,I3C,I3S
124 COMMON/FSI_FFPN/FF12,FF21
125 COMMON/LEDWEIGHT/WEIF,WEI,WEIN,ITEST,IRANPOS
127 C------------------------------------------------------------------
128 C==> AC1,2 = "relativistic" Bohr radii for particle-nucleus systems
130 IF(C1N.NE.0.D0)AC1=137.036D0/(C1N*E1) !m1-->E1
132 IF(C2N.NE.0.D0)AC2=137.036D0/(C2N*E2) !m2-->E2
134 C-----------------------------------------------------------
136 CALL FSIPN !weight due to particle-nucleus FSI
138 CALL FSIWF !weight due to particle-particle-nucleus FSI
141 FF12=DCMPLX(1.D0,0.D0)
142 FF21=DCMPLX(1.D0,0.D0)
144 CALL VZ ! weight due to particle-particle FSI
149 C=======================================================================
151 SUBROUTINE LTRAN(P0,P,PS)
152 C==>calculating particle 4-momentum PS={PSX,PSY,PSZ,ES}
153 C in rest frame of a system 0 with 4-momentum P0={P0X,P0Y,P0Z,E0}
154 C from its 4-momentum P={PX,PY,PZ,E}
156 IMPLICIT REAL*8 (A-H,O-Z)
157 DIMENSION P0(4),P(4),PS(4)
158 C-----------------------------------------------------------------------
159 P0S=P0(1)**2+P0(2)**2+P0(3)**2
160 AM0=DSQRT(P0(4)**2-P0S)
162 PP0=P(1)*P0(1)+P(2)*P0(2)+P(3)*P0(3)
167 PS(4)=(P0(4)*P(4)-PP0)/AM0
171 SUBROUTINE LTRANB(P0,PS,P)
172 C==>calculating particle 4-momentum P={PX,PY,PZ,E}
173 C from its 4-momentum PS={PSX,PSY,PSZ,ES}
174 C in rest frame of a system 0 with 4-momentum P0={P0X,P0Y,P0Z,E0}
176 IMPLICIT REAL*8 (A-H,O-Z)
177 DIMENSION P0(4),P(4),PS(4)
178 C-----------------------------------------------------------------------
179 P0S=P0(1)**2+P0(2)**2+P0(3)**2
180 AM0=DSQRT(P0(4)**2-P0S)
182 PSP0=PS(1)*P0(1)+PS(2)*P0(2)+PS(3)*P0(3)
183 HS=(PSP0/EPM+PS(4))/AM0
187 P(4)=(P0(4)*PS(4)+PSP0)/AM0
193 C--- GDD = k*COTG(DELTA), X=k^2
194 C--- J=1,2,3 corresp. to S=0,1,2
195 IMPLICIT REAL*8 (A-H,O-Z)
196 COMMON/FSI_AADD/AADD(20,3)
197 COMMON/FSI_C/C(10),AM,AMS,DM
198 COMMON/FSI_CONS/PI,PI2,SPI,DR,W
203 GDD=ER*(AADD(1,1)*DEXP(-E/AADD(2,1))-AADD(3,1))
204 GDD=GDD/DR ! from degree to radian
206 IF(TAND.EQ.0.D0)TAND=1.D-10
213 GDD=ER*(AADD(1,3)+AADD(2,3)*E)
214 GDD=GDD/DR ! from degree to radian
216 IF(TAND.EQ.0.D0)TAND=1.D-10
224 C calculating particle-nucleus Coulomb Wave functions FFij
225 IMPLICIT REAL*8 (A-H,O-Z)
226 COMMON/FSI_POC/AMN,AM1,AM2,CN,C1,C2,AC1,AC2
227 COMMON/FSI_MOM/P1X,P1Y,P1Z,E1,P1, !part. momenta in NRF
229 COMMON/FSI_COOR/X1,Y1,Z1,T1,R1, ! 4-coord. of emis. points in NRF
231 COMMON/FSI_NS/LL,NS,ICH,ISI,IQS,I3C,I3S
232 COMMON/FSI_ACH/HPR,AC,ACH,ACHR,ISPIN,MSPIN
235 COMMON/FSI_FFPN/FF12,FF21
236 COMMON/LEDWEIGHT/WEIF,WEI,WEIN,ITEST,IRANPOS
238 COMPLEX*16 FF1,FF12,FF21
239 FF12=DCMPLX(1.D0,0.D0)
240 FF21=DCMPLX(1.D0,0.D0)
248 IF(XH.NE.0.D0)ETA=1/XH
250 HS=X1*P1X+Y1*P1Y+Z1*P1Z
251 FF12=FF12*FF1(RHOS,HS)
254 HS=X2*P1X+Y2*P1Y+Z2*P1Z
255 FF21=FF21*FF1(RHOS,HS)
262 IF(XH.NE.0.D0)ETA=1/XH
264 HS=X2*P2X+Y2*P2Y+Z2*P2Z
265 FF12=FF12*FF1(RHOS,HS)
266 CW WRITE(6,41)'AC2 ',AC2,'ACH ',ACH,'ETA ',ETA,'RHOS ',RHOS,'HS ',HS
267 41 FORMAT(5(A5,E11.4))
268 CW WRITE(6,40)'FF12 ',DREAL(FF12),DIMAG(FF12)
271 HS=X1*P2X+Y1*P2Y+Z1*P2Z
272 FF21=FF21*FF1(RHOS,HS)
273 CW WRITE(6,41)'AC1 ',AC1,'ACH ',ACH,'ETA ',ETA,'RHOS ',RHOS,'HS ',HS
274 CW WRITE(6,40)'FF21 ',DREAL(FF21),DIMAG(FF21)
278 C WEIF = the weight due to the Coulomb particle-nucleus interaction
279 WEIF=DREAL(FF12)**2+DIMAG(FF12)**2
280 IF(IQS.EQ.1)WEIF=0.5D0*(WEIF+DREAL(FF21)**2+DIMAG(FF21)**2)
285 C--- GPIPI = k*COTG(DELTA), X=k^2
286 C-- J=1(2) corresponds to isospin=0(2)
287 IMPLICIT REAL*8 (A-H,O-Z)
288 COMMON/FSI_AAPI/AAPI(20,2)
289 COMMON/FSI_C/HELP(20),AM,AMS,DM
293 GPIPI=GPIPI*(1+(AAPI(3,J)-AAPI(1,J)**2)*XX+AAPI(4,J)*XX*XX)
294 GPIPI=GPIPI/(1+(AAPI(3,J)+AAPI(2,J)/AAPI(1,J))*XX)
298 C--- GND = k*COTG(DELTA), X=k^2
299 C--- J=1(2) corresp. to nd(pd), S=1/2,
300 C--- J=3(4) corresp. to nd(pd), S=3/2
301 IMPLICIT REAL*8 (A-H,O-Z)
302 COMMON/FSI_AAND/AAND(20,4)
304 GND=1/AAND(1,J)+.5D0*AAND(2,J)*X
307 1 GND=GND+AAND(I,J)*XX
308 GND=GND/(1+AAND(3,J)*X)
312 SUBROUTINE CKKB ! calculates KK-b scattering amplitude,
313 ! saturated by S*(980) and delta(982) resonances
314 IMPLICIT REAL*8 (A-H,O-Z)
315 COMMON/FSI_PRF/PPX,PPY,PPZ,AK,AKS,
317 COMMON/FSI_AAKK/AAKK(9)
318 COMMON/FSI_C/C(10),AM,AMS,DM
322 AKPIPI=DSQRT(S4-AAKK(2))
323 EETA2=(S+AAKK(3)-AAKK(2))**2/4/S
324 AKPIETA=DSQRT(EETA2-AAKK(3))
325 C(1)=AAKK(6)/2/DCMPLX(AAKK(4)-S,
326 ,-AK*AAKK(6)-AKPIPI*AAKK(7))
327 C(1)=C(1)+AAKK(8)/2/DCMPLX(AAKK(5)-S,
328 ,-AK*AAKK(8)-AKPIETA*AAKK(9))
335 C==> Prepares necessary quantities and call VZ(WEI) to calculate
336 C the weight due to FSI
337 IMPLICIT REAL*8 (A-H,O-Z)
339 COMMON/FSI_MOM/P1X,P1Y,P1Z,E1,P1, !part. momenta in NRF
341 COMMON/FSI_PRF/PPX,PPY,PPZ,AK,AKS,
343 COMMON/FSI_COOR/X1,Y1,Z1,T1,R1, ! 4-coord. of emis. points in NRF
345 COMMON/FSI_POC/AMN,AM1,AM2,CN,C1,C2,AC1,AC2
346 COMMON/FSI_SPIN/RHO(10)
349 COMMON/FSI_ACH/HPR,AC,ACH,ACHR,ISPIN,MSPIN
350 COMMON/FSI_SW/RB(10),EB(10),BK(10),CDK(10),SDK(10),
352 COMMON/FSI_NS/LL,NS,ICH,ISI,IQS,I3C,I3S
354 COMMON/FSI_FD/FD(10),RD(10)
355 COMMON/FSI_C/C(10),AM,AMS,DM
358 COMMON/FSI_SHH/SH,CHH
359 COMMON/FSI_AAPI/AAPI(20,2)/FSI_AAND/AAND(20,4)
360 COMMON/FSI_P12/P12X,P12Y,P12Z,E12,P12,AM12,EPM
361 COMMON/LEDWEIGHT/WEIF,WEI,WEIN,ITEST,IRANPOS
364 C==>calculating relative 4-coordinates of the particles in PRF
365 C- {T,X,Y,Z} from the relative coordinates {TS,XS,YS,ZS} in NRF
370 RS12=XS*P12X+YS*P12Y+ZS*P12Z
371 H1=(RS12/EPM-TS)/AM12
376 c-mlv T=(E12*TS-RS12)/AM12
377 c-mlv RPS=X*X+Y*Y+Z*Z
379 c WRITE(6,38)'RP ',RP,'X ',X,Y,Z,T
380 c38 FORMAT(A7,E11.4,A7,4E11.4)
382 CVK=(P12X*PPX+P12Y*PPY+P12Z*PPZ)/(P12*AK)
390 IF(XH.NE.0.D0)ETA=1/XH
391 C---HCP, HPR needed (e.g. in GST) if ICH=1
393 HPR=HCP+.1544313298D0
398 C---Calc. quantities for the square well potential;
399 C-- for LL > 5 the square well potential is not possible or available
401 BK(JJ)=DSQRT(EB(JJ)**2+AKS)
411 IF(AK.NE.0.D0)SDKK(JJ)=SH/AK
412 IF(ICH.EQ.1)SDK(JJ)=ACH*SDK(JJ)
414 C-----------------------------------------------------------------------
415 C---Calc. the strong s-wave scattering amplitude = C(JJ)
416 C-- divided by Coulomb penetration factor squared (if ICH=1)
418 IF(LL.NE.4)GOTO 230 ! SW scat. amplitude used for alfa-alfa only
420 IF(ICH.EQ.1)AKACH=AK*ACH
421 C(JJ)=1/DCMPLX(GAK,-AKACH) ! amplitude for the SW-potential
423 230 IF(LL.EQ.5.OR.LL.EQ.6.OR.LL.EQ.7)GOTO20 ! pipi
424 IF(LL.EQ.8.OR.LL.EQ.9)GOTO20 ! Nd
425 IF(LL.EQ.14.OR.LL.EQ.17.OR.LL.EQ.23)GOTO27 ! K+K-, K-p, K0K0-b
428 IF(ICH.EQ.1)A2=A2-2*HCP*FD(JJ)/AC
430 IF(ICH.EQ.1)AKF=AKF*ACH
431 C(JJ)=FD(JJ)/DCMPLX(A2,-AKF)
434 C---Calc. scatt. ampl. C(JJ) for pipi and Nd
436 IF(LL.GT.7)GPI2=GND(AKS,JH)
437 IF(LL.LE.7)GPI2=GPIPI(AKS,2)
438 C(JJ)=1.D0/DCMPLX(GPI2,-AK)
441 IF(LL.EQ.5)C(JJ)=.6667D0/DCMPLX(GPI1,-AK)+.3333D0*C(JJ)
442 IF(LL.EQ.6)C(JJ)=.3333D0/DCMPLX(GPI1,-AK)+.6667D0*C(JJ)
444 C---Calc. K+K-, K0K0-b or K-p s-wave scatt. ampl.
445 IF(LL.EQ.14.OR.LL.EQ.23)CALL CKKB
446 IF(LL.EQ.17)C(JJ)=DCMPLX(3.29D0,3.55D0)
447 C---Calc. pi+pi-, pi+pi+, pd, K+K- or K-p s-wave scatt. amplitude
448 C-- divided by Coulomb penetration factor squared (if ICH=1)
452 C(JJ)=1/(1/C(JJ)-HCP2+DCMPLX(0.D0,AK-AAK))
454 C***********************************************************************
460 C==> Calculates the weight WEI due to FSI
461 IMPLICIT REAL*8 (A-H,O-Z)
463 COMMON/FSI_PRF/PPX,PPY,PPZ,AK,AKS,
465 COMMON/FSI_SPIN/RHO(10)
468 COMMON/FSI_FFF/F12,F21
469 COMMON/FSI_ACH/HPR,AC,ACH,ACHR,ISPIN,MSPIN
470 COMMON/FSI_NS/LL,NS,ICH,ISI,IQS,I3C,I3S
471 COMMON/FSI_FD/FD(10),RD(10)
473 COMMON/FSI_C/C(10),AM,AMS,DM
474 COMMON/FSI_COULPH/EIDC
475 COMMON/LEDWEIGHT/WEIF,WEI,WEIN,ITEST,IRANPOS
477 COMPLEX*16 F,C,G,PSI12,PSI21
481 COMMON/FSI_FFPN/FF12,FF21
487 IF(RHOS.LT.15.D0.AND.RHOS+DABS(HS).LT.20.D0)GOTO 2
488 C---Calc. EIDC=exp(i*Coul.Ph.);
489 C-- used in calc. of hypergeom. f-s in SEQA, FAS at k*R > 15, 20
490 Z8=CMPLX(1.,SNGL(ETA))
494 c write(*,*)'Z8 EIDC',Z8,EIDC
498 IF(ISI.EQ.0)GOTO 4 ! the strong interaction ON (OFF) if ISI=1(0)
500 IF(JRAT.NE.1) CALL FIRT
501 IF(IQS.EQ.0)GOTO 5 ! the quantum statistics ON (OFF) if IQS=1(0)
510 1 WEI=WEI+RHO(JJ)*(DREAL(G)**2+DIMAG(G)**2)
515 CW WRITE(6,38)'JJ ',JJ,'F ',DREAL(F(JJ)),DIMAG(F(JJ))
516 CW WRITE(6,38)'JJ ',JJ,'C ',DREAL(C(JJ)),DIMAG(C(JJ))
517 CW WRITE(6,38)'JJ ',JJ,'G ',DREAL(G),DIMAG(G)
518 CW WRITE(6,38)'JJ ',JJ,'F12+G ',DREAL(F12+G),DIMAG(F12+G)
519 CW WRITE(6,38)'JJ ',JJ,'F21+G ',DREAL(F21+G),DIMAG(F21+G)
520 38 FORMAT(A7,I3,A7,2E11.4)
522 6 WEI=WEI+RHO(JJ)*(DREAL(PSI12)**2+DIMAG(PSI12)**2)
525 IF(IQS.EQ.0)GOTO 50 ! the quantum statistics ON (OFF) if IQS=1(0)
531 3 WEI=WEI+RHO(JJ)*(DREAL(G)**2+DIMAG(G)**2)
533 50 WEI=DREAL(PSI12)**2+DIMAG(PSI12)**2
545 C-- F(JJ)*C(JJ)= DEVIATION OF THE BETHE-SALPETER AMPL. FROM PLANE WAVE
546 IMPLICIT REAL*8 (A-H,O-Z)
547 COMMON/FSI_PRF/PPX,PPY,PPZ,AK,AKS,
549 COMMON/FSI_SHH/SH,CHH
551 COMMON/FSI_ACH/HPR,AC,ACH,ACHR,ISPIN,MSPIN
552 COMMON/FSI_C/C(10),AM,AMS,DM
553 COMMON/FSI_SW/RB(10),EB(10),BK(10),CDK(10),SDK(10),
555 COMMON/FSI_NS/LL,NS,ICH,ISI,IQS,I3C,I3S
557 EQUIVALENCE(RSS,RP),(TSS,T)
574 IF(ICH.EQ.1) SHH=ACH*SH
576 C---F= ASYMPTOTIC FORMULA (T= 0 APPROX.); NS= 4
577 6 F(JJ)=DCMPLX(CHH,SHH)
579 C---F INSIDE THE SQUARE-WELL (T= 0 APPROX.); NS= 1
580 IF(RSS.GE.RB(JJ)) GOTO 10
581 IF(AK.NE.0.D0.AND.JJ.EQ.1)SHK=SH/AK
585 F(JJ)=DCMPLX(CDK(JJ),SDK(JJ))*SKR
586 CH1=(SDKK(JJ)*SKR-SHK*SBKRB(JJ))/C(JJ)
587 F(JJ)=(F(JJ)+CH1)/SBKRB(JJ)
590 C---F= ASYMPTOTIC FORMULA (T= 0 NOT REQUIRED); NS= 2
594 IF(DM.NE.0.D0)GOTO 11
620 IF(I.EQ.1)TSSH=TSSA*(1+DM)
621 IF(I.EQ.2)TSSH=TSSA*(1-DM)
623 IF(AK.NE.0.D0)GOTO 12
646 A2=.5D0*(CHH*(A12+A21)+SH*(A12-A21))+SHH
647 A1=.5D0*(CHH*(C12+S12)+SH*(C12-S12))
648 F(JJ)=.3989422D0*DCMPLX(A1,A2)
655 IMPLICIT REAL*8 (A-H,O-Z)
656 IF(X.LT.-15.D0) GO TO 1
663 C---CALC. FUNCTIONS B, P (EQS. (17) OF G-K-L-L);
664 C-- NEEDED TO CALC. THE CONFLUENT HYPERGEOMETRIC FUNCTION GST.
665 IMPLICIT REAL*8 (A-H,O-Z)
667 DIMENSION BH(3),PH(3)
678 BH(3)=(X*BH(2)-HS*BH(1))/((J+1)*(J+2))
679 PH(3)=(X*PH(2)-HS*PH(1)-(2*J+1)*X*BH(2))/(J*(J+1))
682 Z=DABS(BH(2))+DABS(BH(3))+DABS(PH(2))+DABS(PH(3))
691 C---CALC. FUNCTIONS CHH=REAL(GST), SH=IMAG(GST)/ACH, B=SH/H
692 C-- IN THE ASYMPTOTIC REGION H=K*R >> 1.
693 IMPLICIT REAL*8 (A-H,O-Z)
695 COMMON/FSI_SHH/SH,CHH
697 COMMON/FSI_ACH/HPR,AC,ACH,ACHR,ISPIN,MSPIN
698 COMMON/FSI_COULPH/EIDC
701 GST=DCMPLX(DCOS(ARG),DSIN(ARG))
710 C-- F12= FF0* plane wave, FF0=F*ACHR,
711 C---F is the confluent hypergeometric function,
712 C-- ACHR=sqrt(ACH), where ACH is the Coulomb factor
713 IMPLICIT REAL*8 (A-H,O-Z)
714 COMMON/FSI_ACH/HPR,AC,ACH,ACHR,ISPIN,MSPIN
715 COMMON/FSI_NS/LL,NS,ICH,ISI,IQS,I3C,I3S
717 COMMON/FSI_FFF/F12,F21
718 COMPLEX*16 FF0,F12,F21
732 C---F is the confluent hypergeometric function at k*r >> 1
733 C-- ACHR=sqrt(ACH), where ACH is the Coulomb factor
734 IMPLICIT REAL*8 (A-H,O-Z)
735 COMPLEX*16 FAS,EIDC,ZZ1
736 COMMON/FSI_ACH/HPR,AC,ACH,ACHR,ISPIN,MSPIN
738 COMMON/FSI_COULPH/EIDC
741 ZZ1=DCMPLX(DCOS(D1),DSIN(D1))/EIDC
742 FAS=DCMPLX(1.D0,-D2)*ZZ1
743 FAS=FAS-DCMPLX(DCOS(RKS),DSIN(RKS))*ETA/RKS/ZZ1
748 C-- F is the confluent hypergeometric function
749 C-- (Eq. (15) of G-K-L-L), F= 1 at r* << AC
750 C-- ACHR=sqrt(ACH), where ACH is the Coulomb factor
751 IMPLICIT REAL*8 (A-H,O-Z)
752 COMMON/FSI_ACH/HPR,AC,ACH,ACHR,ISPIN,MSPIN
753 COMMON/FSI_NS/LL,NS,ICH,ISI,IQS,I3C,I3S
755 COMPLEX*16 ALF,ALF1,Z,S,A,FF0,FAS
760 CC GOTO 5 ! rejects the approx. calcul. of hyperg. f-ion F
761 IF(RHOP.LT.20.D0)GOTO5
762 FF0=FAS(RHOP) ! approx. calc.
764 5 ALF=DCMPLX(.0D0,-ETA)
774 IF((ZR+ZI).GT.ERR)GOTO3
779 C---HC = h-function of Landau-Lifshitz: h(x)=Re[psi(1-i/x)]+ln(x)
780 C-- psi(x) is the digamma function (the logarithmic derivative of
781 C-- the gamma function)
782 IMPLICIT REAL*8 (A-H,O-Z)
784 DATA BN/.8333333333D-1,.8333333333D-2,.396825396825D-2,
785 1 .4166666667D-2,.7575757576D-2,.2109279609D-1,
786 2 .8333333333D-1,.4432598039D0 ,.305395433D1,
787 3 .2645621212D2, .2814601449D3, .3607510546D4,
788 4 .5482758333D5, .9749368235D6, .200526958D8/
790 IF(X.LT..33D0) GOTO 1
791 CC IF(X.GE.3.5D0) GO TO 2
795 DS=1.D0/N/((N*X)**2+1)
797 IF(DS.GT.0.1D-12) GOTO 3
798 C---Provides 7 digit accuracy
799 HC=S-.5772156649D0+DLOG(X)
801 CC 2 HC=1.2D0/X**2+DLOG(X)-.5772156649 D0
814 C--- ACP = COULOMB PENETRATION FACTOR
815 IMPLICIT REAL*8 (A-H,O-Z)
816 IF(X.LT.0.05D0.AND.X.GE.0.D0) GO TO 1
824 C---CALC. THE CONFL. HYPERGEOM. F-N = CHH+i*SH
825 C-- AND THE COULOMB F-S B, P (CALLS SEQ OR SEQA).
826 IMPLICIT REAL*8 (A-H,O-Z)
827 COMMON/FSI_ACH/HPR,AC,ACH,ACHR,ISPIN,MSPIN
828 COMMON/FSI_NS/LL,NS,ICH,ISI,IQS,I3C,I3S
829 COMMON/FSI_SHH/SH,CHH
839 IF(H.GT.15.D0)GOTO4 ! comment out if you want to reject
840 ! the approximate calculation of hyperg. f-ion G
841 CALL SEQ(X,H) ! exact calculation
843 CHH=P+B*X*(DLOG(DABS(X))+HPR)
850 C---FF1=FF0; used for particle-nucleus system
852 C-- F12 is the confluent hypergeometric function
853 C-- (Eq. (15) of G-K-L-L), F12= 1 at r* << AC
854 C-- ACHR=sqrt(ACH), where ACH is the Coulomb factor
855 IMPLICIT REAL*8 (A-H,O-Z)
856 COMMON/FSI_ACH/HPR,AC,ACH,ACHR,ISPIN,MSPIN
857 COMMON/FSI_NS/LL,NS,ICH,ISI,IQS,I3C,I3S
859 COMMON/FSI_COULPH/EIDC
864 FF1=DCMPLX(1.D0,0.D0)
866 IF(RHO.LT.15.D0.AND.RHO+H.LT.20.D0)GOTO 2
867 C---Calc. EIDC=exp(i*Coul.Ph.);
868 C-- used in calc. of hypergeom. f-s in SEQA, FAS at k*R > 15, 20
869 Z8=CMPLX(1.,SNGL(ETA))
877 C---Used to calculate SW scattering amplitude for alpa-alpha system
878 C---NOTE THAT SCATT. AMPL.= 1/CMPLX(G(AK),-AK*ACH)
879 IMPLICIT REAL*8 (A-H,O-Z)
880 COMMON/FSI_SW/RB(10),EB(10),BK(10),CDK(10),SDK(10),
882 COMMON/FSI_NS/LL,NS,ICH,ISI,IQS,I3C,I3S
883 COMMON/FSI_ACH/HPR,AC,ACH,ACHR,JJ,MSPIN
884 COMMON/FSI_BP/B,P/FSI_DERIV/BPR,PPR/FSI_SHH/SH,CHH
889 HPR=HCP+.1544313298D0
893 BK(JJ)=DSQRT(AKS+EB(JJ)**2) ! kappa=kp
895 H=BK(JJ)*RB(JJ) ! kp*d
898 SBKRB(JJ)=SH ! kp*d*B(kp,d)
900 BRHOP=BPR ! B'(kp,d)= dB(kp,r)/dln(r) at r=d
903 CDK(JJ)=CHH ! ReG(k,d)
908 SDK(JJ)=ACH*SH ! ImG(k,d)
909 IF(AK.EQ.0.D0.AND.AC.LT.0.D0)SDK(JJ)=3.14159*X*B
911 IF(AK.NE.0.D0)SDKK(JJ)=SH/AK ! d*B(k,d)
912 CALL DERIW(X,H) ! PPR=P'(k,d)= dP(k,r)/dln(r) at r=d
914 IF(ICH.EQ.1)ZZ=ZZ+X*(BRHOS+BPR*(DLOG(DABS(X))+HPR))
915 C ZZ= P'(k,d)-P(k,d)+x*{B(k,d)+B'(k,d)*[ln!x!+2*C-1+h(k*ac)]}
916 GG=(BRHOP*CDK(JJ)-BRHO*ZZ)/RB(JJ)
917 C GG= [B'(kp,d)*ReG(k,d)-B(kp,d)*ZZ]/d
918 G=GG/(BRHO*BPR-BRHOP*BRHOS)
919 C G= GG/[B(kp,d)*B'(k,d)-B'(kp,d)*B(k,d)]
922 SUBROUTINE DERIW(X,H)
923 C---CALLED BY F-N G(AK)
924 IMPLICIT REAL*8 (A-H,O-Z)
925 COMMON/FSI_NS/LL,NS,ICH,ISI,IQS,I3C,I3S
926 COMMON/FSI_BP/B,P/FSI_DERIV/BPR,PPR
944 C================================================================
947 c-------------#include "gen/pilot.h"
950 IMPLICIT DOUBLE PRECISION (A-H,O-Z)
952 DIMENSION A(0:16),B(0:15),C1(0:25),C2(0:28)
954 PARAMETER (Z1 = 1, R8 = Z1/8, R32 = Z1/32)
956 DATA C0 /1.25331 41373 15500 3D0/
958 DATA NA,NB,NC1,NC2 /16,15,25,28/
960 DATA A( 0) / 0.76435 13866 41860 002D0/
961 DATA A( 1) /-0.43135 54754 76601 793D0/
962 DATA A( 2) / 0.43288 19997 97266 531D0/
963 DATA A( 3) /-0.26973 31033 83871 110D0/
964 DATA A( 4) / 0.08416 04532 08769 354D0/
965 DATA A( 5) /-0.01546 52448 44613 820D0/
966 DATA A( 6) / 0.00187 85542 34398 220D0/
967 DATA A( 7) /-0.00016 26497 76188 875D0/
968 DATA A( 8) / 0.00001 05739 76563 833D0/
969 DATA A( 9) /-0.00000 05360 93398 892D0/
970 DATA A(10) / 0.00000 00218 16584 549D0/
971 DATA A(11) /-0.00000 00007 29016 212D0/
972 DATA A(12) / 0.00000 00000 20373 325D0/
973 DATA A(13) /-0.00000 00000 00483 440D0/
974 DATA A(14) / 0.00000 00000 00009 865D0/
975 DATA A(15) /-0.00000 00000 00000 175D0/
976 DATA A(16) / 0.00000 00000 00000 003D0/
978 DATA B( 0) / 0.63041 40431 45705 392D0/
979 DATA B( 1) /-0.42344 51140 57053 335D0/
980 DATA B( 2) / 0.37617 17264 33436 566D0/
981 DATA B( 3) /-0.16249 48915 45095 674D0/
982 DATA B( 4) / 0.03822 25577 86330 087D0/
983 DATA B( 5) /-0.00564 56347 71321 909D0/
984 DATA B( 6) / 0.00057 45495 19768 974D0/
985 DATA B( 7) /-0.00004 28707 15321 020D0/
986 DATA B( 8) / 0.00000 24512 07499 233D0/
987 DATA B( 9) /-0.00000 01109 88418 409D0/
988 DATA B(10) / 0.00000 00040 82497 317D0/
989 DATA B(11) /-0.00000 00001 24498 302D0/
990 DATA B(12) / 0.00000 00000 03200 484D0/
991 DATA B(13) /-0.00000 00000 00070 324D0/
992 DATA B(14) / 0.00000 00000 00001 336D0/
993 DATA B(15) /-0.00000 00000 00000 022D0/
995 DATA C1( 0) / 0.99056 04793 73497 549D0/
996 DATA C1( 1) /-0.01218 35098 31478 997D0/
997 DATA C1( 2) /-0.00248 27428 23113 060D0/
998 DATA C1( 3) / 0.00026 60949 52647 247D0/
999 DATA C1( 4) /-0.00000 10790 68987 406D0/
1000 DATA C1( 5) /-0.00000 48836 81753 933D0/
1001 DATA C1( 6) / 0.00000 09990 55266 368D0/
1002 DATA C1( 7) /-0.00000 00750 92717 372D0/
1003 DATA C1( 8) /-0.00000 00190 79487 573D0/
1004 DATA C1( 9) / 0.00000 00090 90797 293D0/
1005 DATA C1(10) /-0.00000 00019 66236 033D0/
1006 DATA C1(11) / 0.00000 00001 64772 911D0/
1007 DATA C1(12) / 0.00000 00000 63079 714D0/
1008 DATA C1(13) /-0.00000 00000 36432 219D0/
1009 DATA C1(14) / 0.00000 00000 10536 930D0/
1010 DATA C1(15) /-0.00000 00000 01716 438D0/
1011 DATA C1(16) /-0.00000 00000 00107 124D0/
1012 DATA C1(17) / 0.00000 00000 00204 099D0/
1013 DATA C1(18) /-0.00000 00000 00090 064D0/
1014 DATA C1(19) / 0.00000 00000 00025 506D0/
1015 DATA C1(20) /-0.00000 00000 00004 036D0/
1016 DATA C1(21) /-0.00000 00000 00000 570D0/
1017 DATA C1(22) / 0.00000 00000 00000 762D0/
1018 DATA C1(23) /-0.00000 00000 00000 363D0/
1019 DATA C1(24) / 0.00000 00000 00000 118D0/
1020 DATA C1(25) /-0.00000 00000 00000 025D0/
1022 DATA C2( 0) / 0.04655 77987 37516 4561D0/
1023 DATA C2( 1) / 0.04499 21302 01239 4140D0/
1024 DATA C2( 2) /-0.00175 42871 39651 4532D0/
1025 DATA C2( 3) /-0.00014 65340 02581 0678D0/
1026 DATA C2( 4) / 0.00003 91330 40863 0159D0/
1027 DATA C2( 5) /-0.00000 34932 28659 7731D0/
1028 DATA C2( 6) /-0.00000 03153 53003 2345D0/
1029 DATA C2( 7) / 0.00000 01876 58200 8529D0/
1030 DATA C2( 8) /-0.00000 00377 55280 4930D0/
1031 DATA C2( 9) / 0.00000 00026 65516 5010D0/
1032 DATA C2(10) / 0.00000 00010 88144 8122D0/
1033 DATA C2(11) /-0.00000 00005 35500 7671D0/
1034 DATA C2(12) / 0.00000 00001 31576 5447D0/
1035 DATA C2(13) /-0.00000 00000 15286 0881D0/
1036 DATA C2(14) /-0.00000 00000 03394 7646D0/
1037 DATA C2(15) / 0.00000 00000 02702 0267D0/
1038 DATA C2(16) /-0.00000 00000 00946 3142D0/
1039 DATA C2(17) / 0.00000 00000 00207 1565D0/
1040 DATA C2(18) /-0.00000 00000 00012 6931D0/
1041 DATA C2(19) /-0.00000 00000 00013 9756D0/
1042 DATA C2(20) / 0.00000 00000 00008 5929D0/
1043 DATA C2(21) /-0.00000 00000 00003 1070D0/
1044 DATA C2(22) / 0.00000 00000 00000 7515D0/
1045 DATA C2(23) /-0.00000 00000 00000 0648D0/
1046 DATA C2(24) /-0.00000 00000 00000 0522D0/
1047 DATA C2(25) / 0.00000 00000 00000 0386D0/
1048 DATA C2(26) /-0.00000 00000 00000 0165D0/
1049 DATA C2(27) / 0.00000 00000 00000 0050D0/
1050 DATA C2(28) /-0.00000 00000 00000 0009D0/
1081 H=C0-SQRT(R)*(S*COS(V)+(B0-H*B2)*SIN(V))
1116 H=C0-SQRT(R)*((B0-H*B2)*COS(V)-S*SIN(V))
1123 c--#include "gen/pilot.h"
1128 COMPLEX*8 Z,U,V,F,H,S
1131 PARAMETER (NAME = 'CGAMMA')
1135 PARAMETER (Z1 = 1, HF = Z1/2)
1137 c--#if defined(CERNLIB_QF2C)
1138 c--#include "gen/gcmpfun.inc"
1141 DATA PI /3.14159 26535 89793 24D0/
1142 DATA C1 /2.50662 82746 31000 50D0/
1144 DATA C( 0) / 41.62443 69164 39068D0/
1145 DATA C( 1) /-51.22424 10223 74774D0/
1146 DATA C( 2) / 11.33875 58134 88977D0/
1147 DATA C( 3) / -0.74773 26877 72388D0/
1148 DATA C( 4) / 0.00878 28774 93061D0/
1149 DATA C( 5) / -0.00000 18990 30264D0/
1150 DATA C( 6) / 0.00000 00019 46335D0/
1151 DATA C( 7) / -0.00000 00001 99345D0/
1152 DATA C( 8) / 0.00000 00000 08433D0/
1153 DATA C( 9) / 0.00000 00000 01486D0/
1154 DATA C(10) / -0.00000 00000 00806D0/
1155 DATA C(11) / 0.00000 00000 00293D0/
1156 DATA C(12) / -0.00000 00000 00102D0/
1157 DATA C(13) / 0.00000 00000 00037D0/
1158 DATA C(14) / -0.00000 00000 00014D0/
1159 DATA C(15) / 0.00000 00000 00006D0/
1161 c----#if !defined(CERNLIB_QF2C)
1162 c----#include "gen/gcmpfun.inc"
1165 COMPLEX*8 GREAL,GIMAG,XARG,YARG
1167 COMPLEX*8 ZARG,GCONJG,GCMPLX
1168 GREAL( ZARG)=REAL( ZARG)
1169 GIMAG( ZARG)=AIMAG(ZARG)
1170 GCONJG(ZARG)=CONJG(ZARG)
1171 c-- GCMPLX(XARG,YARG)= CMPLX(XARG,YARG)
1175 IF(GIMAG(U) .EQ. 0 .AND. -ABS(X) .EQ. INT(X)) THEN
1179 c- CALL MTLPRT(NAME,'C305.1',ERRTXT)
1184 ELSEIF(X .GE. 0) THEN
1194 H=((V-K)/(V+(K-1)))*H
1197 H=C1*EXP((V-HF)*LOG(H)-H)*S
1198 IF(X .LT. 0) H=PI/(SIN(PI*U)*H)
1201 c----#if !defined(CERNLIB_DOUBLE)
1206 101 FORMAT('ARGUMENT EQUALS NON-POSITIVE INTEGER = ',1P,E15.1)