ADAS Subroutine qvain

       FUNCTION QVAIN(Z1,N1,N2,VION,PHI,ZP)               
C
       IMPLICIT REAL*8(A-H,O-Z)                          
C
C-----------------------------------------------------------------------
C
C  ****************** FORTRAN77 FUNCTION: QVAIN ************************
C
C  PURPOSE: CALCULATES ION COLLISION CROSS-SECTIONS FOR TRANSITIONS
C           BETWEEN PRINCIPAL QUANTUM SHELLS IN HYDROGEN AND
C           HYDROGENIC IONS.                
C
C  INPUT                                                          
C      Z1   = TARGET ION CHARGE +1                               
C      N1   = INITIAL PRINCIPAL QUANTUM NUMBER                  
C      N2   = FINAL PRINCIPAL QUANTUM NUMBER                   
C      VION = VELOCITY OF INCIDENT ION (CM/SEC)               
C      ZP   = PROJECTILE CHARGE                              
C  OUTPUT                                                   
C      QVAIN=CROSS-SECTION IN PI*A0**2 UNITS               
C
C NOTES: THIS ROUTINE IS NOT YET PROPERLY ANNOTATED
C
C UNIX-IDL PORT:
C
C VERSION: 1.1                          DATE: 16-1-96
C MODIFIED: TIM HAMMOND (TESSELLA SUPPORT SERVICES PLC)
C               - FIRST VERSION
C
C VERSION: 1.2                          DATE: 16-05-07
C MODIFIED: Allan Whiteford
C             - Updated comments as part of subroutine documentation
C               procedure.
C-----------------------------------------------------------------------
C
       ZZ1=Z1*Z1                                                    
       ZZP=ZP*ZP                                                   
       EN1=N1                                                     
       EN2=N2                                                    
       EIJRH=DABS(1/(EN1*EN1) - 1/(EN2*EN2))                    
       ALFA=1.0/137.036                                        
       CLIG=2.998D+10                                         
       CFAC=(CLIG/VION)**2                                            
       BETA=0.5*ALFA*ALFA*CFAC*DSQRT(PHI)*EIJRH*ZP                   
       XFAC1=2*ALFA*ALFA*CFAC*PHI*ZP*ZP                             
       QVAIN=XFAC1*DEXP(-2*DSQRT(BETA))*RIFAC(BETA)                
       RETURN                                                     
       END                                                       
C                                                               
       FUNCTION RIFAC(BETAIN)                                  
       IMPLICIT REAL*8(A-H,O-Z)                               
      INTEGER             N1,          N2
      REAL*8              PHI,         VION,        Z1,          ZP
      REAL*8              BETAIN