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ADAS Subroutine cxcrdg

      SUBROUTINE CXCRDG ( MXNSHL , MXJSHL , IZ0    , IZ1    ,
     &                    NI     , LI     ,  NJ    , LJ     ,
     &                    TEV    , DENS   , ZP     , TPV    ,
     &                    EMP    , TBLF   , GAE    , GAP    ,
     &                    QEP    , QEM    , QIP    , QIM
     &                  )
C
C
C-----------------------------------------------------------------------
C
C  ****************** FORTRAN77 SUBROUTINE: CXCRDG *********************
C
C  PURPOSE:  CALCULATES ELECTRON AND +VE ION COLLISIONAL RATE
C            COEFFICIENTS BETWEEN NEARLY DEGENERATE LEVELS FOR
C            HYDROGEN-LIKE, LITHIUM-LIKE AND SODIUM-LIKE IONS.
C
C            RATES ARE CALCULATED FOR BOTH TERM AVERAGED AND
C            SEPARATE NLJ->NL+1J' AND NLJ->NL-1J' STATES.
C            
C
C  CALLING PROGRAM: C6TBQM , C8TBQM
C
C  INPUT : (I*4)  MXNSHL  = MAXIMUM NUMBER OF N SHELLS.
C  INPUT : (I*4)  MXJSHL  = MAXIMUM NUMBER OF J SUB-SHELLS.
C  INPUT : (I*4)  IZ0     = TARGET NUCLEAR CHARGE.
C  INPUT : (I*4)  IZ1     = ION CHARGE.
C  INPUT : (I*4)  NI      = VALENCE ELECTRON PRINCIPAL QUANTUM NUMBER
C                           IN STATE I.
C  INPUT : (I*4)  LI      = VALENCE ELECTRON ORBITAL QUANTUM NUMBER IN
C                           STATE I.
C  INPUT : (I*4)  NJ      = VALENCE ELECTRON PRINCIPAL QUANTUM NUMBER
C                           IN STATE J.
C  INPUT : (I*4)  LJ      = VALENCE ELECTRON ORBITAL QUANTUM NUMBER IN
C                           STATE J.
C  INPUT : (R*8)  TEV     = TEMPERATURE (ELECTRON DISTRIBUTION).
C                           UNITS: EV
C  INPUT : (R*8)  DENS    = ELECTRON DENSITY.
C                           UNITS: CM-3
C  INPUT : (R*8)  ZP      = CHARGE OF COLLIDING POSITIVE ION.
C  INPUT : (R*8)  TPV     = TEMPERATURE (COLLIDING POSITIVE ION
C                           DISTRIBUTION).
C                           UNITS: EV
C  INPUT : (R*8)  EMP     = REDUCED MASS FOR COLLIDING POSITIVE ION.
C                           UNITS: ELECTRON MASSES
C  INPUT : (R*8)  TBLF()  = TABLE OF RADIATIVE LIFETIMES.
C                           UNITS: SECS
C                           DIMENSION: REFERENCED BY FUNC I4IDFL(N,L).
C
C  OUTPUT: (R*8)  GAE     = TERM AVERAGED GAMA RATE PARAMETER FOR
C                           ELECTRON COLLISIONS.
C  OUTPUT: (R*8)  GAP     = TERM AVERAGED GAMA RATE PARAMETER FOR
C                           POSITIVE ION COLLISIONS.
C  OUTPUT: (R*8)  QEP()   = ELECTRON RATE COEFFT. FOR NLJ->NL+1J'
C                           DIMENSION: J->J' TRANSITION INDEX.
C  OUTPUT: (R*8)  QEM()   = ELECTRON RATE COEFFT. FOR NLJ->NL-1J'
C                           DIMENSION: J->J' TRANSITION INDEX.
C  OUTPUT: (R*8)  QIP()   = POSITIVE ION RATE COEFFT. FOR NLJ->NL+1J'
C                           DIMENSION: J->J' TRANSITION INDEX.
C  OUTPUT: (R*8)  QIM()   = POSITIVE ION RATE COEFFT. FOR NLJ->NL-1J'
C                           DIMENSION: J->J' TRANSITION INDEX.
C
C  PARAM : (I*4)  MXTEMP  = MAXIMUM NUMBER OF TEMPERATURES.
C  PARAM : (I*4)  MXCOLL  = MAXIMUM NUMBER OF COLLISION STRENGTHS.
C  PARAM : (I*4)  MXTERM  = 2.
C  PARAM : (R*8)  P1      =
C
C          (I*4)  IZ      = IZ1-1.
C          (I*4)  NTEMP   = NUMBER OF TABULATED TEMPERATURES.
C          (I*4)  NCOLL   = NUMBER OF TABULATED COLLISION STRENGTHS.
C          (I*4)  ICI     =
C          (I*4)  ICJ     =
C          (I*4)  IZC     = INTEGER BELOW CHARGE OF POSITIVE ION.
C          (I*4)  I       = LOOP INDEX.
C          (I*4)  J       = LOOP INDEX.
C
C          (R*8)  WI      = STATISTICAL WEIGHT OF STATE I.
C          (R*8)  WJ      = STATISTICAL WEIGHT OF STATE J.
C          (R*8)  EI      = BINDING ENERGY OF STATE I.
C                           UNITS: RYD
C          (R*8)  EJ      = BINDING ENERGY OF STATE I.
C                           UNITS: RYD
C          (R*8)  TE      = TEMPERATURE (ELECTRON DISTRIBUTION).
C                           UNITS:
C          (R*8)  TP      = TEMPERATURE (COLLIDING POSITIVE ION
C                           DISTRIBUTION).
C                           UNITS:
C          (R*8)  Z1      = REAL VALUE = IZ1.
C          (R*8)  XNI     = REAL VALUE = NI.
C          (R*8)  XLI     = REAL VALUE = LI.
C          (R*8)  XLJ     = REAL VALUE = LJ.
C          (R*8)  XLG     =
C          (R*8)  EI0     = BINDING ENERGY FOR STATE I.
C          (R*8)  EJ0     = BINDING ENERGY FOR STATE J.
C          (R*8)  ZEFFI   = EFFECTIVE ION CHARGE FOR STATE I.
C          (R*8)  ZEFFJ   = EFFECTIVE ION CHARGE FOR STATE J.
C          (R*8)  TAU     =
C          (R*8)  W       =
C          (R*8)  T1      =
C          (R*8)  T2      =
C          (R*8)  XXLI    =
C          (R*8)  XXLJ    =
C          (R*8)  XS      =
C          (R*8)  XXJI    =
C          (R*8)  XXJJ    =
C          (R*8)  DE      =
C          (R*8)  PHI     =
C          (R*8)  ZC      =
C          (R*8)  EMM     =
C          (R*8)  QI1     = COLLISIONAL EXCITATION RATE COEFFICIENT FROM
C                           PENGELLY AND SEATON.
C                           UNITS: CM3 SEC-1
C          (R*8)  QIJ     = COLLISIONAL DEEXCITATION RATE COEFFICIENT
C                           FROM PENGELLY AND SEATON.
C                           UNITS: CM3 SEC-1
C          (R*8)  G1      = GAMMA RATE PARAMETER FROM PENGELLY AND
C                           SEATON.
C                           UNITS:
C          (R*8)  RAT     =
C          (R*8)  SCF     = SCALING FACTOR.
C
C          (R*8)  EPS()   = INCIDENT ELECTRON ENERGIES.
C                           UNITS: RYD
C                           DIMENSION: COLLISION INDEX.
C          (R*8)  OMEG()  = COLLISION STRENGTHS.
C                           DIMENSION: COLLISION INDEX.
C          (R*8)  TA()    = TEMPERATURES (INCIDENT POSITIVE ION
C                           DISTRIBUTION).
C                           UNITS: EV
C                           DIMENSION: TEMPERATURE INDEX.
C          (R*8)  QI()    = COLLISIONAL EXCITATION RATE COEFFICIENTS
C                           FROM IMPACT PARAMETER APPROXIMATION.
C                           UNITS: CM3 SEC-1
C                           DIMENSION: TEMPERATURE INDEX.
C          (R*8)  QJ()    = COLLISIONAL DEEXCITATION RATE COEFFICIENTS
C                           FROM IMPACT PARAMETER APPROXIMATION.
C                           UNITS: CM3 SEC-1
C                           DIMENSION: TEMPERATURE INDEX.
C          (R*8)  GA()    = GAMMA RATE PARAMETERS FROM IMPACT PARAMETER
C                           APPROXIMATION.
C                           UNITS:
C                           DIMENSION: TEMPERATURE INDEX.
C          (R*8)  XSJ()   =
C                           DIMENSION: 2
C          (R*8)  XJJ()   =
C                           DIMENSION: 2
C          (R*8)  XEJ()   =
C                           DIMENSION: 2
C          (R*8)  XSI()   =
C                           DIMENSION: 2
C          (R*8)  XJI()   =
C                           DIMENSION: 2
C          (R*8)  XEI()   =
C                           DIMENSION: 2
C
C ROUTINES:
C          ROUTINE    SOURCE    BRIEF DESCRIPTION
C          -------------------------------------------------------------
C          I4UNIT     ADAS      RETURNS UNIT NO. FOR OUTPUT OF MESSAGES.
C          I4IDFL     ADAS      RETURNS UNIQUE INDEX GIVEN QUANTUM
C                               NUMBERS N AND L.
C          R8ZETA     ADAS
C          R8WIG6     ADAS
C          CXHYDE     ADAS      CALCULATES BINDING ENERGY FOR H-LIKE
C                               ION.
C          CXLTHE     ADAS      CALCULATES BINDING ENERGY FOR LI-LIKE
C                               ION.
C          CXSODE     ADAS      CALCULATES BINDING ENERGY FOR NA-LIKE
C                               ION.
C          CXCRPS     ADAS      CALCULATES COLLISON RATE COEFFICIENTS
C                               FROM PENGELLY AND SEATON.
C          CXCRIP     ADAS      CALCULATES COLLISON RATE COEFFICIENTS
C                               FROM IMPACT PARAMETER APPROXIMATION.
C
C NOTES:
C       1) THE J->J' TRANSITION INDEX IS AS FOLLOWS:
C              1 : J=L+0.5 -> J'=L'+0.5
C              2 : J=L+0.5 -> J'=L'-0.5
C              3 : J=L-0.5 -> J'=L'+0.5
C              4 : J=L-0.5 -> J'=L'-0.5
C
C       2) THE SCALING FACTOR 'SCF' USED IN CALCULATING THE POSITIVE ION
C          RATES IS NEEDED BECAUSE THE CROSS-SECTION ROUTINES REQUIRE AN
C          INTEGER VALUE FOR THE ION CHARGE. THE ADJACENT LOWER INTEGER
C          VALUE IS USED AND THE RESULTS SCALED BY 'SCF'.
C
C AUTHOR:  JONATHAN NASH (TESSELLA SUPPORT SERVICES PLC)
C          K1/0/81
C          JET EXT. 5183
C
C DATE:    08/10/93
C
C UPDATE:  01/11/93 - J NASH    - ADAS91:
C          UPDATED TO MORE GENERAL FORM TO ALLOW USE BY EITHER ADAS306
C          OR ADAS308. NOW HANDLES H-, LI-, OR NA-LIKE IONS, AND
C          RETURNS EXPLICIT RATES FOR J-RESOLVED TRANSITIONS.
C
C
C VERSION : 1.2  
C DATE    : 28-09-2005
C MODIFIED: Martin O'Mullane
C               - Scale the gamma (GAP) in addition to the rates
C                 since 308 and 309 use this and ignore QIP and QIM.
C
C VERSION : 1.3 
C DATE    : 17-05-2007
C MODIFIED: Allan Whiteford
C               - Updated comments as part of subroutine documentation
C                 procedure.
C
C-----------------------------------------------------------------------
C
C-----------------------------------------------------------------------
      INTEGER             IZ0,         IZ1,         LI,          LJ
      INTEGER             MXJSHL,      MXNSHL,      NI,          NJ
      REAL*8              DENS,        EMP,         GAE,         GAP
      REAL*8              QEM(2*MXJSHL),            QEP(2*MXJSHL)
      REAL*8              QIM(2*MXJSHL),            QIP(2*MXJSHL)
      REAL*8              TBLF((MXNSHL*(MXNSHL+1))/2),           TEV
      REAL*8              TPV,         ZP
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