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ADAS Subroutine r8fdip2

C
       REAL*8 FUNCTION R8FDIP2(E1,L1,E2,L2)                             
       IMPLICIT REAL*8(A-H,O-Z)                                         
C-----------------------------------------------------------------------
C
C  ****************** FORTRAN77 FUNCTION: R8FDIP2 **********************
C
C PURPOSE: CALCULATES THE DIPOLE INTEGRAL I(KAPPA1,L1,KAPPA2,L2,1) FOR 
C          WHERE MIN(E1,E2)/EMAX(E1,E2) > 0.03
C
C NOTE: CREATED BY  ALAN BURGESS FOR USE IN THE DIPOLE INTEGRAL 
C       I(KAPPA1,L1,KAPPA2,L2,1) EVALUATION AS DEFINED IN PHIL. 
C       TRANS. ROY. SOC. A226,255,1970, WHERE E1=KAPPA1**2 AND 
C       E2=KAPPA2**2. APPLIES TO POSITIVE ELECTRON ENERGIES, .  
c       THAT IS THE FREE-FREE CASE.                                              
C
C CALLING PROGRAMS: R8FDIP
C
C INPUT:  (R*8)  E1      = KAPPA1**2 WHERE KAPPA1 IS SCALED INITIAL
C                          ELECTRON WAVE NUMBER 
C INPUT:  (I*4)  L1      = ORBITAL ANGULAR OMENTUM OF INITIAL ELECTRON 
C INPUT:  (R*8)  E2      = KAPPA2**2 WHERE KAPPA2 IS SCALED INITIAL
C                          ELECTRON WAVE NUMBER 
C INPUT:  (I*4)  L2      = ORBITAL ANGULAR OMENTUM OF FINAL ELECTRON 
C
C OUTPUT: (R*8)  R8FDIP2 = I(KAPPA1,L1,KAPPA2,L2,1) 
C
C ROUTINES:
C          ROUTINE    SOURCE   BRIEF DESCRIPTION
C          -------------------------------------------------------------
C          ARGAM      ADAS     CALCULATES ARGGAMMA(L+1+I*A)
C
C UNIX-IDL PORT:
C
C VERSION: 1.1                          DATE: 17-04-07
C MODIFIED: HUGH SUMMERS
C               - FIRST FULLY COMMENTED RELEASE
C
C-----------------------------------------------------------------------
       WMAX=200.0D0                                                     
       ETA1=1.0D0/DSQRT(E1)                                             
       ETA2=1.0D0/DSQRT(E2)                                             
       W1=ETA2-ETA1                                                     
       PI=3.141592653589793D0                                           
       A=DABS(W1)                                                       
       B=PI*A                                                           
       IF(B-0.01D0)1,1,2                                                
    1  C=3.0D0/(3.0D0-B*(3.0D0-B*(2.0D0-B)))                            
       C=DSQRT(C)                                                       
       GO TO 5                                                          
    2  IF(B-14.0D0)4,3,3                                                
    3  C=DSQRT(B+B)                                                     
       GO TO 5                                                          
    4  B=B+B                                                            
       C1=1.0D0-DEXP(-B)                                                
       C=DSQRT(B/C1)                                                    
    5  C=0.5D0*C/DSQRT(ETA1*ETA2)                                       
       C2=ETA1+ETA2                                                     
       C1=4.0D0*ETA1*ETA2/(C2*C2)                                       
       L=L1                                                             
       IF(L2-L1)6,6,7                                                   
    6  L=L2                                                             
       T1=ETA1                                                          
       ETA1=ETA2                                                        
       ETA2=T1                                                          
       W1=-W1                                                           
    7  C=C*C1**(L+1)                                                    
       U0=L+1                                                           
       U1=ETA1                                                          
       V0=U0                                                            
       V1=-ETA2                                                         
       W0=1.0D0                                                         
       X0=W1/(C2*C2)                                                    
       Y2=-ETA2-ETA2                                                    
       Y0=-U0*W1+Y2                                                     
       Y1=ETA2*W1                                                       
       T1=X0/(1.0D0+W1*W1)                                              
       Z0=U0*T1                                                         
       Z1=U1*T1                                                         
       T=Z0-Z1*W1                                                       
       Z1=Z0*W1+Z1                                                      
       Z0=T                                                             
       Q0=-1.0D0+Z0*Y0-Z1*Y1                                            
       Q1=Z0*Y1+Z1*Y0                                                   
       X=W1*X0                                                          
    8  U0=U0+1.0D0                                                      
       V0=V0+1.0D0                                                      
       W0=W0+1.0D0                                                      
       IF(W0-WMAX)21,21,20                                              
   20  R8FDIP2=0.0D0                                                    
       RETURN                                                           
   21  CONTINUE                                                         
       Y0=Y0+Y2                                                         
       T=Z0*U0-Z1*U1                                                    
       Z1=Z0*U1+Z1*U0                                                   
       Z0=T                                                             
       T=Z0*V0-Z1*V1                                                    
       Z1=Z0*V1+Z1*V0                                                   
       Z0=T                                                             
       T=Z0*W0-Z1*W1                                                    
       Z1=Z0*W1+Z1*W0                                                   
       Z0=T                                                             
       X0=X/(W0*(W0*W0+W1*W1))                                          
       Z0=Z0*X0                                                         
       Z1=Z1*X0                                                         
       T0=Z0*Y0-Z1*Y1                                                   
       T1=Z0*Y1+Z1*Y0                                                   
       Q0=Q0+T0                                                         
       Q1=Q1+T1                                                         
       T1=T0*T0+T1*T1                                                   
       T0=Q0*Q0+Q1*Q1                                                   
       IF(T0-1.0D24*T1)8,8,9                                            
    9  J1=0                                                             
       J2=L+1                                                           
       P=ARGAM(J1,W1)+ARGAM(L,ETA1)-ARGAM(J2,ETA2)                      
       IW0=W0                                                           
       IF(A-1.0D-40)11,11,10                                            
   10  P=P+W1*DLOG(C2/A)                                                
   11  P0=DCOS(P)                                                       
       P1=DSIN(P)                                                       
       T=P0*Q0-P1*Q1                                                    
       Q1=P0*Q1+P1*Q0                                                   
       Q0=T                                                             
       R8FDIP2=C*Q1                                                     
       RETURN                                                           
      END                                                               
      INTEGER             L1,          L2
      REAL*8              E1,          E2
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