| fe4da5cc |
1 | |
| 2 | C*********************************************************************** |
| 3 | |
| 4 | SUBROUTINE PYI3AU(EPS,RAT,Y3RE,Y3IM) |
| 5 | |
| 6 | C...Calculates real and imaginary parts of the auxiliary function I3; |
| 7 | C...see R. K. Ellis, I. Hinchliffe, M. Soldate and J. J. van der Bij, |
| 8 | C...Nucl. Phys. B297 (1988) 221. |
| 9 | COMMON/LUDAT1/MSTU(200),PARU(200),MSTJ(200),PARJ(200) |
| 10 | SAVE /LUDAT1/ |
| 11 | |
| 12 | BE=0.5*(1.+SQRT(1.+RAT*EPS)) |
| 13 | IF(EPS.LT.1.) GA=0.5*(1.+SQRT(1.-EPS)) |
| 14 | |
| 15 | IF(EPS.LT.0.) THEN |
| 16 | IF(ABS(EPS).LT.1.E-4.AND.ABS(RAT*EPS).LT.1.E-4) THEN |
| 17 | F3RE=PYSPEN(-0.25*EPS/(1.+0.25*(RAT-1.)*EPS),0.,1)- |
| 18 | & PYSPEN((1.-0.25*EPS)/(1.+0.25*(RAT-1.)*EPS),0.,1)+ |
| 19 | & PYSPEN(0.25*(RAT+1.)*EPS/(1.+0.25*RAT*EPS),0.,1)- |
| 20 | & PYSPEN((RAT+1.)/RAT,0.,1)+0.5*(LOG(1.+0.25*RAT*EPS)**2- |
| 21 | & LOG(0.25*RAT*EPS)**2)+LOG(1.-0.25*EPS)* |
| 22 | & LOG((1.+0.25*(RAT-1.)*EPS)/(1.+0.25*RAT*EPS))+ |
| 23 | & LOG(-0.25*EPS)*LOG(0.25*RAT*EPS/(1.+0.25*(RAT-1.)*EPS)) |
| 24 | ELSEIF(ABS(EPS).LT.1.E-4.AND.ABS(RAT*EPS).GE.1.E-4) THEN |
| 25 | F3RE=PYSPEN(-0.25*EPS/(BE-0.25*EPS),0.,1)- |
| 26 | & PYSPEN((1.-0.25*EPS)/(BE-0.25*EPS),0.,1)+ |
| 27 | & PYSPEN((BE-1.+0.25*EPS)/BE,0.,1)- |
| 28 | & PYSPEN((BE-1.+0.25*EPS)/(BE-1.),0.,1)+ |
| 29 | & 0.5*(LOG(BE)**2-LOG(BE-1.)**2)+ |
| 30 | & LOG(1.-0.25*EPS)*LOG((BE-0.25*EPS)/BE)+ |
| 31 | & LOG(-0.25*EPS)*LOG((BE-1.)/(BE-0.25*EPS)) |
| 32 | ELSEIF(ABS(EPS).GE.1.E-4.AND.ABS(RAT*EPS).LT.1.E-4) THEN |
| 33 | F3RE=PYSPEN((GA-1.)/(GA+0.25*RAT*EPS),0.,1)- |
| 34 | & PYSPEN(GA/(GA+0.25*RAT*EPS),0.,1)+ |
| 35 | & PYSPEN((1.+0.25*RAT*EPS-GA)/(1.+0.25*RAT*EPS),0.,1)- |
| 36 | & PYSPEN((1.+0.25*RAT*EPS-GA)/(0.25*RAT*EPS),0.,1)+ |
| 37 | & 0.5*(LOG(1.+0.25*RAT*EPS)**2-LOG(0.25*RAT*EPS)**2)+ |
| 38 | & LOG(GA)*LOG((GA+0.25*RAT*EPS)/(1.+0.25*RAT*EPS))+ |
| 39 | & LOG(GA-1.)*LOG(0.25*RAT*EPS/(GA+0.25*RAT*EPS)) |
| 40 | ELSE |
| 41 | F3RE=PYSPEN((GA-1.)/(GA+BE-1.),0.,1)- |
| 42 | & PYSPEN(GA/(GA+BE-1.),0.,1)+PYSPEN((BE-GA)/BE,0.,1)- |
| 43 | & PYSPEN((BE-GA)/(BE-1.),0.,1)+0.5*(LOG(BE)**2-LOG(BE-1.)**2)+ |
| 44 | & LOG(GA)*LOG((GA+BE-1.)/BE)+LOG(GA-1.)*LOG((BE-1.)/(GA+BE-1.)) |
| 45 | ENDIF |
| 46 | F3IM=0. |
| 47 | ELSEIF(EPS.LT.1.) THEN |
| 48 | IF(ABS(EPS).LT.1.E-4.AND.ABS(RAT*EPS).LT.1.E-4) THEN |
| 49 | F3RE=PYSPEN(-0.25*EPS/(1.+0.25*(RAT-1.)*EPS),0.,1)- |
| 50 | & PYSPEN((1.-0.25*EPS)/(1.+0.25*(RAT-1.)*EPS),0.,1)+ |
| 51 | & PYSPEN((1.-0.25*EPS)/(-0.25*(RAT+1.)*EPS),0.,1)- |
| 52 | & PYSPEN(1./(RAT+1.),0.,1)+LOG((1.-0.25*EPS)/(0.25*EPS))* |
| 53 | & LOG((1.+0.25*(RAT-1.)*EPS)/(0.25*(RAT+1.)*EPS)) |
| 54 | F3IM=-PARU(1)*LOG((1.+0.25*(RAT-1.)*EPS)/(0.25*(RAT+1.)*EPS)) |
| 55 | ELSEIF(ABS(EPS).LT.1.E-4.AND.ABS(RAT*EPS).GE.1.E-4) THEN |
| 56 | F3RE=PYSPEN(-0.25*EPS/(BE-0.25*EPS),0.,1)- |
| 57 | & PYSPEN((1.-0.25*EPS)/(BE-0.25*EPS),0.,1)+ |
| 58 | & PYSPEN((1.-0.25*EPS)/(1.-0.25*EPS-BE),0.,1)- |
| 59 | & PYSPEN(-0.25*EPS/(1.-0.25*EPS-BE),0.,1)+ |
| 60 | & LOG((1.-0.25*EPS)/(0.25*EPS))* |
| 61 | & LOG((BE-0.25*EPS)/(BE-1.+0.25*EPS)) |
| 62 | F3IM=-PARU(1)*LOG((BE-0.25*EPS)/(BE-1.+0.25*EPS)) |
| 63 | ELSEIF(ABS(EPS).GE.1.E-4.AND.ABS(RAT*EPS).LT.1.E-4) THEN |
| 64 | F3RE=PYSPEN((GA-1.)/(GA+0.25*RAT*EPS),0.,1)- |
| 65 | & PYSPEN(GA/(GA+0.25*RAT*EPS),0.,1)+ |
| 66 | & PYSPEN(GA/(GA-1.-0.25*RAT*EPS),0.,1)- |
| 67 | & PYSPEN((GA-1.)/(GA-1.-0.25*RAT*EPS),0.,1)+ |
| 68 | & LOG(GA/(1.-GA))*LOG((GA+0.25*RAT*EPS)/(1.+0.25*RAT*EPS-GA)) |
| 69 | F3IM=-PARU(1)*LOG((GA+0.25*RAT*EPS)/(1.+0.25*RAT*EPS-GA)) |
| 70 | ELSE |
| 71 | F3RE=PYSPEN((GA-1.)/(GA+BE-1.),0.,1)- |
| 72 | & PYSPEN(GA/(GA+BE-1.),0.,1)+PYSPEN(GA/(GA-BE),0.,1)- |
| 73 | & PYSPEN((GA-1.)/(GA-BE),0.,1)+LOG(GA/(1.-GA))* |
| 74 | & LOG((GA+BE-1.)/(BE-GA)) |
| 75 | F3IM=-PARU(1)*LOG((GA+BE-1.)/(BE-GA)) |
| 76 | ENDIF |
| 77 | ELSE |
| 78 | RSQ=EPS/(EPS-1.+(2.*BE-1.)**2) |
| 79 | RCTHE=RSQ*(1.-2.*BE/EPS) |
| 80 | RSTHE=SQRT(MAX(0.,RSQ-RCTHE**2)) |
| 81 | RCPHI=RSQ*(1.+2.*(BE-1.)/EPS) |
| 82 | RSPHI=SQRT(MAX(0.,RSQ-RCPHI**2)) |
| 83 | R=SQRT(RSQ) |
| 84 | THE=ACOS(MAX(-0.999999,MIN(0.999999,RCTHE/R))) |
| 85 | PHI=ACOS(MAX(-0.999999,MIN(0.999999,RCPHI/R))) |
| 86 | F3RE=PYSPEN(RCTHE,RSTHE,1)+PYSPEN(RCTHE,-RSTHE,1)- |
| 87 | & PYSPEN(RCPHI,RSPHI,1)-PYSPEN(RCPHI,-RSPHI,1)+ |
| 88 | & (PHI-THE)*(PHI+THE-PARU(1)) |
| 89 | F3IM=PYSPEN(RCTHE,RSTHE,2)+PYSPEN(RCTHE,-RSTHE,2)- |
| 90 | & PYSPEN(RCPHI,RSPHI,2)-PYSPEN(RCPHI,-RSPHI,2) |
| 91 | ENDIF |
| 92 | |
| 93 | Y3RE=2./(2.*BE-1.)*F3RE |
| 94 | Y3IM=2./(2.*BE-1.)*F3IM |
| 95 | |
| 96 | RETURN |
| 97 | END |
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