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/* This file is part of Cloudy and is copyright (C)1978-2008 by Gary J. Ferland and
 * others.  For conditions of distribution and use see copyright notice in license.txt */
/*esc_CRDwing_1side fundamental escape probability radiative transfer routine, for complete redistribution */
/*esc_PRD_1side fundamental escape probability radiative transfer routine for incomplete redistribution */
/*RTesc_lya escape prob for hydrogen atom Lya, using Hummer and Kunasz results,
 * called by hydropesc */
/*esc_PRD escape probability radiative transfer for incomplete redistribution */
/*esc_CRDwing escape probability for CRD with wings */
/*esc_CRDcore escape probability for CRD with no wings */
/*esca0k2 derive Hummer's K2 escape probability for Doppler core only */
/*RT_DestProb returns line destruction probability due to continuum opacity */
/*RT_LineWidth determine half width of any line with known optical depths */
#include "cddefines.h"
#include "physconst.h"
#define SCALE   2.
#include "dense.h"
#include "conv.h"
#include "rfield.h"
#include "opacity.h"
#include "lines_service.h"
#include "taulines.h"
#include "doppvel.h"
#include "pressure.h"
#include "wind.h"
#include "rt.h"
/*
 *variables used to pass continuum optical depth and temp to
 *routine that integrates over continuum
 */
static double chnukt_ContTkt, chnukt_ctau;

/*escmase escape probability for negative (masing) optical depths,*/
STATIC double escmase(double tau);
/*RTesc_lya_1side fit Hummer and Kunasz escape probability for hydrogen atom Lya */
STATIC void RTesc_lya_1side(double taume, 
  double beta, 
  realnum *esc, 
  realnum *dest,
  /* position of line in frequency array on c scale */
  long ipLine );

double esc_PRD_1side(double tau, 
  double a)
{
        double atau, 
          b, 
          escinc_v;

        DEBUG_ENTRY( "esc_PRD_1side()" );
        ASSERT( a>0.0 );

        /* this is one of the three fundamental escape probability routines
         * the three are esc_CRDwing_1side, esc_PRD_1side, and RTesc_lya
         * it computes esc prob for incomplete redistribution
         * */
#       if 0
        if( strcmp(rt.chEscFunSubord,"SIMP") == 0 )
        {
                /* this set with "escape simple" command, used for debugging */
                escinc_v = 1./(1. + tau);
                return( escinc_v );
        }
#       endif

        if( tau < 0. )
        {
                /* line mased */
                escinc_v = escmase(tau);
        }
        else if( tau < 10. )
        {
                /* linear part of doppler core */
                escinc_v = 1./(1. + 1.6*tau);
        }
        else
        {
                /* first find coefficient b(tau) */
                atau = a*tau;
                if( atau > 1. )
                {
                        b = 1.6 + (3.*pow(2.*a,-0.12))/(1. + atau);
                }
                else
                {
                        b = 1.6 + (3.*pow(2.*a,-0.12))/(1. + 1./sqrt(atau));
                }
                b = MIN2(6.,b);

                escinc_v = 1./(1. + b*tau);
        }
        return( escinc_v );
}

/*esc_CRDwing_1side fundamental escape probability radiative transfer routine, for complete redistribution */
double esc_CRDwing_1side(double tau, 
  double a )
{
        double esccom_v;

        DEBUG_ENTRY( "esc_CRDwing_1side()" );

        /* this is one of the three fundamental escape probability routines
         * the three are esc_CRDwing_1side, esc_PRD_1side, and RTesc_lya
         * it computes esc prob for complete redistribution with wings
         * computes escape prob for complete redistribution in one direction
         * */

        /* this is the only case that this routine computes,
         * and is the usual case for subordinate lines, 
         * complete redistribution with damping wings */
        esccom_v = esca0k2(tau);
        if( tau > 1e3 )
        {
                esccom_v += 0.333*sqrt(a/(SQRTPI*tau));
        }
        return( esccom_v );
}

/*RTesc_lya escape prob for hydrogen atom Lya, using 
 >>refer        La      escp    Hummer, D.G., & Kunasz, P.B., 1980, ApJ, 236, 609
 * called by hydropesc, return value is escape probability */
double RTesc_lya(
        /* the inward escape probability */
        double *esin, 
        /* the destruction probility */
        double *dest, 
        /* abundance of the species */
        double abund, 
        /* element number,  0 for H */
        long int nelem)
{
        double beta, 
          conopc, 
          escla_v;
         realnum dstin, 
          dstout;

        DEBUG_ENTRY( "RTesc_lya()" );

        /* 
         * this is one of the three fundamental escape probability functions
         * the three are esc_CRDwing_1side, esc_PRD_1side, and RTesc_lya
         * evaluate esc prob for LA
         * optical depth in outer direction always defined
         */

        /* check charge */
        ASSERT( nelem >= 0 && nelem < LIMELM );

        if( Transitions[ipH_LIKE][nelem][ipH2p][ipH1s].Emis->TauTot - 
          Transitions[ipH_LIKE][nelem][ipH2p][ipH1s].Emis->TauIn < 0. )
        {
                /* this is the case if we overrun the optical depth scale
                 * just leave things as they are */
                escla_v = Transitions[ipH_LIKE][nelem][ipH2p][ipH1s].Emis->Pesc;
                rt.fracin = Transitions[ipH_LIKE][nelem][ipH2p][ipH1s].Emis->FracInwd;
                *esin = rt.fracin;
                *dest = Transitions[ipH_LIKE][nelem][ipH2p][ipH1s].Emis->Pdest;
                return( escla_v );
        }

        /* incomplete redistribution */
        conopc = opac.opacity_abs[Transitions[ipH_LIKE][nelem][ipH2p][ipH1s].ipCont-1];
        if( abund > 0. )
        {
                /* the continuous opacity is positive, we have a valid soln */
                beta = conopc/(abund/SQRTPI*Transitions[ipH_LIKE][nelem][ipH2p][ipH1s].Emis->opacity/
                  DoppVel.doppler[nelem] + conopc);
        }
        else
        {
                /* abundance is zero, set miniumum dest prob */
                beta = 1e-10;
        }

        /* find rt.wayin, the escape prob in inward direction */
        RTesc_lya_1side(
          Transitions[ipH_LIKE][nelem][ipH2p][ipH1s].Emis->TauIn,
          beta,
          &rt.wayin,
          &dstin , 
          /* position of line in energy array on C scale */
          Transitions[ipH_LIKE][nelem][ipH2p][ipH1s].ipCont-1);

        ASSERT( (rt.wayin <= 1.) && (rt.wayin >= 0.) && (dstin <= 1.) && (dstin >= 0.) );

        /* find rt.wayout, the escape prob in outward direction */
        RTesc_lya_1side(MAX2(Transitions[ipH_LIKE][nelem][ipH2p][ipH1s].Emis->TauTot/100.,
          Transitions[ipH_LIKE][nelem][ipH2p][ipH1s].Emis->TauTot-Transitions[ipH_LIKE][nelem][ipH2p][ipH1s].Emis->TauIn),
          beta,
          &rt.wayout,
          &dstout, 
          Transitions[ipH_LIKE][nelem][ipH2p][ipH1s].ipCont-1);

        ASSERT( (rt.wayout <= 1.) && (rt.wayout >= 0.) && (dstout <= 1.) && (dstout >= 0.) );

        /* esc prob is mean of in and out */
        escla_v = (rt.wayin + rt.wayout)/2.;
        /* the inward escaping part of the line */
        *esin = rt.wayin;

        /* dest prob is mean of in and out */
        *dest = (dstin + dstout)/2.f;
        /* >>chng 02 oct 02, sum of escape and dest prob must be less then unity,
         * for very thin models this forces dest prob to go to zero, 
         * rather than the value of DEST0, caught by Jon Slavin */
        *dest = (realnum)MIN2( *dest , 1.-escla_v );
        /* but dest prob can't be negative */
        *dest = (realnum)MAX2(0., *dest );

        /* fraction of line emitted in inward direction */
        rt.fracin = rt.wayin/(rt.wayin + rt.wayout);
        ASSERT( escla_v >=0. && *dest>=0. && *esin>=0. );
        return( escla_v );
}

/*esc_PRD escape probability radiative transfer for incomplete redistribution */
double esc_PRD(double tau, 
  double tau_out, 
  double damp )
{
        double escgrd_v, 
          tt;

        DEBUG_ENTRY( "esc_PRD()" );

        /* find escape prob for incomp redis, average of two 1-sided probs*/

        if( iteration > 1 )
        {
                /*  outward optical depth if defined */
                tt = tau_out - tau;
                /*  help convergence by not letting tau go to zero at back edge of
                 *  when there was a bad guess for the total optical depth
                 *  note that this test is seldom hit since RTMakeStat does check
                 *  for overrun */
                if( tt < 0. )
                {
                        tt = tau/SCALE;
                }

                rt.wayin = (realnum)esc_PRD_1side(tau,damp);
                rt.wayout = (realnum)esc_PRD_1side(tt,damp);
                rt.fracin = rt.wayin/(rt.wayin + rt.wayout);
                escgrd_v = 0.5*(rt.wayin + rt.wayout);
        }
        else
        {
                /*  outward optical depth not defined, dont estimate fraction out */
                rt.fracin = 0.;
                rt.wayout = 1.;
                escgrd_v = esc_PRD_1side(tau,damp);
                rt.wayin = (realnum)escgrd_v;
        }

        ASSERT( escgrd_v > 0. );
        return( escgrd_v );
}

/*esc_CRDwing escape probability radiative transfer for CRDS in core only */
double esc_CRDwing(double tau_in, 
  double tau_out, 
  double damp)
{
        double escgrd_v, 
          tt;

        DEBUG_ENTRY( "esc_CRDwing()" );

        /* find escape prob for CRD with damping wings, average of two 1-sided probs*/

        /* crd with wings */
        if( iteration > 1 )
        {
                /*  outward optical depth if defined */
                /* >>chng 03 jun 07, add test for masers here */
                if( tau_out <0 || tau_in < 0. )
                {
                        /* we have a maser, use smallest optical depth to damp it out */
                        tt = MIN2( tau_out , tau_in );
                        tau_in = tt;
                }
                else
                {
                        tt = tau_out - tau_in;
                        /*  help convergence by not letting tau_in go to zero at back edge of
                         *  when there was a bad guess for the total optical depth
                         *  note that this test is seldom hit since RTMakeStat does check
                         *  for overrun */
                        if( tt < 0. )
                        {
                                tt = tau_in/SCALE;
                        }
                }

                rt.wayin = (realnum)esc_CRDwing_1side(tau_in,damp);
                rt.wayout = (realnum)esc_CRDwing_1side(tt,damp);
                rt.fracin = rt.wayin/(rt.wayin + rt.wayout);
                escgrd_v = 0.5*(rt.wayin + rt.wayout);
        }
        else
        {
                /*  outward optical depth not defined, dont estimate fraction out */
                rt.fracin = 0.;
                rt.wayout = 1.;
                escgrd_v = esc_CRDwing_1side(tau_in,damp);
                rt.wayin = (realnum)escgrd_v;
        }

        ASSERT( escgrd_v > 0. );
        return( escgrd_v );
}

/*esc_CRDwing escape probability radiative transfer for incomplete redistribution */
double esc_CRDcore(double tau_in, 
  double tau_out)
{
        double escgrd_v, 
          tt;

        DEBUG_ENTRY( "esc_CRDcore()" );

        /* find escape prob for CRD with damping wings, average of two 1-sided probs*/

        /* crd with wings */
        if( iteration > 1 )
        {
                /*  outward optical depth if defined */
                /* >>chng 03 jun 07, add test for masers here */
                if( tau_out <0 || tau_in < 0. )
                {
                        /* we have a maser, use smallest optical depth to damp it out */
                        tt = MIN2( tau_out , tau_in );
                        tau_in = tt;
                }
                else
                {
                        tt = tau_out - tau_in;
                        /*  help convergence by not letting tau_in go to zero at back edge of
                         *  when there was a bad guess for the total optical depth
                         *  note that this test is seldom hit since RTMakeStat does check
                         *  for overrun */
                        if( tt < 0. )
                        {
                                tt = tau_in/SCALE;
                        }
                }

                rt.wayin = (realnum)esca0k2(tau_in);
                rt.wayout = (realnum)esca0k2(tt);
                rt.fracin = rt.wayin/(rt.wayin + rt.wayout);
                escgrd_v = 0.5*(rt.wayin + rt.wayout);
        }
        else
        {
                /*  outward optical depth not defined, dont estimate fraction out */
                rt.fracin = 0.;
                rt.wayout = 1.;
                escgrd_v = esca0k2(tau_in);
                rt.wayin = (realnum)escgrd_v;
        }

        ASSERT( escgrd_v > 0. );
        return( escgrd_v );
}

/*esca0k2 derive Hummer's K2 escape probability for Doppler core only */
double esca0k2(double taume)
{
        double arg, 
          esca0k2_v, 
          suma, 
          sumb, 
          sumc, 
          sumd, 
          tau;
        static double a[5]={1.00,-0.1117897,-0.1249099917,-9.136358767e-3,
          -3.370280896e-4};
        static double b[6]={1.00,0.1566124168,9.013261660e-3,1.908481163e-4,
          -1.547417750e-7,-6.657439727e-9};
        static double c[5]={1.000,19.15049608,100.7986843,129.5307533,-31.43372468};
        static double d[6]={1.00,19.68910391,110.2576321,169.4911399,-16.69969409,
          -36.664480000};

        DEBUG_ENTRY( "esca0k2()" );

        /* compute Hummer's K2 escape probability function for a=0
         * using approx from 
         * >>refer      line    escp    Hummer, D.G., xxxx, JQRST, 26, 187.
         *
         * convert to David's opacity */
        tau = taume*SQRTPI;

        if( tau < 0. )
        {
                /* the line mased */
                esca0k2_v = escmase(taume);

        }
        else if( tau < 0.01 )
        {
                esca0k2_v = 1. - 2.*tau;

        }
        else if( tau <= 11. )
        {
                suma = a[0] + tau*(a[1] + tau*(a[2] + tau*(a[3] + a[4]*tau)));
                sumb = b[0] + tau*(b[1] + tau*(b[2] + tau*(b[3] + tau*(b[4] + 
                  b[5]*tau))));
                esca0k2_v = tau/2.5066283*log(tau/SQRTPI) + suma/sumb;

        }
        else
        {
                /* large optical depth limit */
                arg = 1./log(tau/SQRTPI);
                sumc = c[0] + arg*(c[1] + arg*(c[2] + arg*(c[3] + c[4]*arg)));
                sumd = d[0] + arg*(d[1] + arg*(d[2] + arg*(d[3] + arg*(d[4] + 
                  d[5]*arg))));
                esca0k2_v = (sumc/sumd)/(2.*tau*sqrt(log(tau/SQRTPI)));
        }
        return( esca0k2_v );
}

/*escmase escape probability for negative (masing) optical depths */
STATIC void FindNeg( void )
{
        long int i;

        DEBUG_ENTRY( "FindNeg()" );

        /* do the level 1 lines */
        for( i=1; i <= nLevel1; i++ )
        {
                /* check if a line was a strong maser */
                if( TauLines[i].Emis->TauIn < -1. )
                        DumpLine(&TauLines[i]);
        }

        /* Generic atoms & molecules from databases 
         * added by Humeshkar Nemala*/
        for( i = 0; i <linesAdded2; i++)
        {
                /* check if a line was a strong maser */
                if(atmolEmis[i].TauIn < -1. )
                        DumpLine(atmolEmis[i].tran);
        }

        /* now do the level 2 lines */
        for( i=0; i < nWindLine; i++ )
        {
                if( TauLine2[i].Hi->IonStg < TauLine2[i].Hi->nelem+1-NISO )
                {
                        /* check if a line was a strong maser */
                        if( TauLine2[i].Emis->TauIn < -1. )
                                DumpLine(&TauLine2[i]);
                }
        }

        /* now do the hyperfine structure lines */
        for( i=0; i < nHFLines; i++ )
        {
                /* check if a line was a strong maser */
                if( HFLines[i].Emis->TauIn < -1. )
                        DumpLine(&HFLines[i]);
        }

        /* now do the co carbon monoxide lines */
        for( i=0; i < nCORotate; i++ )
        {
                /* check if a line was a strong maser */
                if( C12O16Rotate[i].Emis->TauIn < -1. )
                        DumpLine(&C12O16Rotate[i]);
                /* check if a line was a strong maser */
                if( C13O16Rotate[i].Emis->TauIn < -1. )
                        DumpLine(&C13O16Rotate[i]);
        }
        return;
}

STATIC double escmase(double tau)
{
        double escmase_v;

        DEBUG_ENTRY( "escmase()" );

        /* this is the only routine that computes maser escape probabilities */
        ASSERT( tau <= 0. );

        if( tau > -0.1 )
        {
                escmase_v = 1. - tau*(0.5 + tau/6.);
        }
        else if( tau > -30. )
        {
                escmase_v = (1. - exp(-tau))/tau;
        }
        else
        {
                fprintf( ioQQQ, " DISASTER escmase called with 2big tau%10.2e\n", 
                  tau  );
                fprintf( ioQQQ, " This is zone number%4ld\n", nzone );
                FindNeg();
                ShowMe();
                cdEXIT(EXIT_FAILURE);
        }

        ASSERT( escmase_v >= 1. );
        return( escmase_v );
}

/*escConE2 one of the forms of the continuum escape probability */
/*cone2 generate e2 function needed for continuum transport */
STATIC double cone2(double t);

double escConE2(double x)
{
        double conesc_v;

        DEBUG_ENTRY( "escConE2()" );

        conesc_v = exp(-chnukt_ContTkt*(x-1.))/
                x*cone2(chnukt_ctau/x/x/x);
        return( conesc_v );
}

/*cone2 generate second exponential integral e2 function needed for continuum transport */
STATIC double cone2(double t)
{
        double cone2_v, 
          remain, 
          tln;

        DEBUG_ENTRY( "cone2()" );

        if( t < 80. )
        {
                tln = exp(-t);
        }
        else
        {
                cone2_v = 0.;
                return( cone2_v );
        }

        /* fit of second exponential integral;
         * T is optical depth, and TLN is EXP(-t)
         * */
        if( t < 0.3 )
        {
                remain = (1.998069357 + t*(66.4037741 + t*107.2041376))/(1. + 
                  t*(37.4009646 + t*105.0388805));

        }
        else if( t < 20. )
        {
                remain = (1.823707708 + t*2.395042899)/(1. + t*(2.488885899 - 
                  t*0.00430538));

        }
        else
        {
                remain = 1.;
        }

        cone2_v = remain*tln/(2. + t);
        return( cone2_v );
}

/* a continuum escape probability */
STATIC double conrec(double x)
{
        double conrec_v;

        DEBUG_ENTRY( "conrec()" );

        conrec_v = exp(-chnukt_ContTkt*(x-1.))/x;
        return( conrec_v );
}

/*esccon continuum escape probability */
double esccon(double tau, 
  double hnukt)
{
        double dinc, 
          escpcn_v, 
          sumesc, 
          sumrec;

        DEBUG_ENTRY( "esccon()" );

        /* computes continuum escape probabilities */
        if( tau < 0.01 )
        {
                escpcn_v = 1.;
                return( escpcn_v );
        }

        else if( hnukt > 1. && tau > 100. )
        {
                escpcn_v = 1e-20;
                return( escpcn_v );
        }

        chnukt_ContTkt = hnukt;
        chnukt_ctau = tau;

        dinc = 10./hnukt;
        sumrec = qg32(1.,1.+dinc,conrec);
        sumesc = qg32(1.,1.+dinc,escConE2);

        if( sumrec > 0. )
        {
                escpcn_v = sumesc/sumrec;
        }
        else
        {
                escpcn_v = 0.;
        }
        return( escpcn_v );
}

/*RTesc_lya_1side fit Hummer and Kunasz escape probability for hydrogen atom Lya */
STATIC void RTesc_lya_1side(double taume, 
  double beta, 
  realnum *esc, 
  realnum *dest,
  /* position of line in frequency array on c scale */
  long ipLine )
{
        double esc0, 
          fac, 
          fac1, 
          fac2, 
          tau, 
          taucon, 
          taulog;

        /* DEST0 is the smallest destruction probability to return
         * in high metallicity models, in rt.h
        const double DEST0=1e-8;*/

        DEBUG_ENTRY( "RTesc_lya_1side()" );

        /* fits to numerical results of Hummer and Kunasz Ap.J. 80 */
        tau = taume*SQRTPI;

        /* this is the real escape probability */
        esc0 = 1./((0.6451 + tau)*(0.47 + 1.08/(1. + 7.3e-6*tau)));

        esc0 = MAX2(0.,esc0);
        esc0 = MIN2(1.,esc0);

        if( tau > 0. )
        {
                taulog = log10(MIN2(1e8,tau));
        }
        else
        {
                /* the line mased 
                 *>>chng 06 sep 08, kill xLaMase 
                hydro.xLaMase = MIN2(hydro.xLaMase,(realnum)tau);*/
                taulog = 0.;
                *dest = 0.;
                *esc = (realnum)esc0;
        }

        if( beta > 0. )
        {
                taucon = MIN2(2.,beta*tau);

                if( taucon > 1e-3 )
                {
                        fac1 = -1.25 + 0.475*taulog;
                        fac2 = -0.485 + 0.1615*taulog;
                        fac = -fac1*taucon + fac2*POW2(taucon);
                        fac = pow(10.,fac);
                        fac = MIN2(1.,fac);
                }
                else
                {
                        fac = 1.;
                }

                *esc = (realnum)(esc0*fac);
                /* MIN puts cat at 50 */
                *dest = (realnum)(beta/(0.30972 - MIN2(.28972,0.03541667*taulog)));
        }

        else
        {
                *dest = 0.;
                *esc = (realnum)esc0;
        }

        *dest = MIN2(*dest,1.f-*esc);
        *dest = MAX2(0.f,*dest);

        /* >>chng 99 apr 12, limit destruction prob in case where gas dominated by scattering.
         * in this case scattering is much more likely than absorption on this event */
        *dest = (realnum)( (1. - opac.albedo[ipLine]) * *dest + opac.albedo[ipLine]*DEST0);
        /* this is for debugging H Lya */
        {
                /*@-redef@*/
                enum {BUG=false};
                /*@+redef@*/
                if( BUG )
                {
                        fprintf(ioQQQ,"scatdest tau %.2e beta%.2e 1-al%.2e al%.2e dest%.2e \n",
                        taume,
                        beta, 
                        (1. - opac.albedo[ipLine]), 
                        opac.albedo[ipLine] ,
                        *dest 
                        );
                }
        }
        return;
}

/*RT_DestProb returns line destruction probability due to continuum opacity */
double RT_DestProb(
          /* abundance of species */
          double abund, 
          /* its line absorption cross section */
          double crsec, 
          /* pointer to energy within continuum array, to get background opacity,
           * this is on the f not c scale */
          long int ipanu, 
          /* line width */
          double widl, 
          /* escape probability */
          double escp, 
          /* type of redistribution function */
          int nCore)
{
        /* this will be the value we shall return */
        double eovrlp_v;

        double conopc, 
          beta;

        /* DEST0 is the smallest destruction probability to return
         * in high metallicity models 
         * this was set to 1e-8 until 99nov18,
         * in cooling flow model the actual Lya ots dest prob was 1e-16,
         * and this lower limit of 1e-8 caused energy balance problems,
         * since dest prob was 8 orders of magnitude too great.  
         * >>chng 99 nov 18, to 1e-20, but beware that comments indicate that
         * this will cause problems with high metallicity clouds(?) */
        /* >>chng 00 jun 04, to 0 since very feeble ionization clouds, with almost zero opacity,
         * this was a LARGE number */
        /*const double DEST0=1e-20;
        const double DEST0=0.;*/

        DEBUG_ENTRY( "RT_DestProb()" );

        /* computes "escape probability" due to continuum destruction of
         *
         * if esc prob gt 1 then line is masing - return small number for dest prob */
        /* >>>chng 99 apr 10, return min dest when scattering greater than abs */
        /* no idea of opacity whatsoever, on very first soln for this model */
        /* >>chng 05 mar 20, add test on line being above upper bound of frequency 
         * do not want to evaluate opacity in this case since off scale */
        if( escp >= 1.0 || !conv.nTotalIoniz || ipanu >= rfield.nflux )
        {
                eovrlp_v = 0.;
                return( eovrlp_v );
        }

        /* find continuum opacity */
        conopc = opac.opacity_abs[ipanu-1];

        ASSERT( crsec > 0. );

        /* may be no population, cannot use above test since return 0 not DEST0 */
        if( abund <= 0. || conopc <= 0. )
        {
                /* do not set this to DEST0 since energy not then conserved */
                eovrlp_v = 0.;
                return( eovrlp_v );
        }

        /* fac of 1.7 convert to Hummer convention for line opacity */
        beta = conopc/(abund*SQRTPI*crsec/widl + conopc);
        /* >>chng 04 may 10, rm * 1-pesc)
        beta = MIN2(beta,(1.-escp)); */

        if( nCore == ipDEST_INCOM )
        {
                /*  fits to 
                 *  >>>refer    la      esc     Hummer and Kunasz 1980 Ap.J. 236,609.
                 *  the max value of 1e-3 is so that we do not go too far
                 *  beyond what Hummer and Kunasz did, discussed in
                 * >>refer      rt      esc proc        Ferland, G.J., 1999, ApJ, 512, 247 */
                eovrlp_v = MIN2(1e-3,8.5*beta);
        }
        else if( nCore == ipDEST_K2 )
        {
                /*  Doppler core only; a=0., Hummer 68 
                eovrlp_v = RT_DestHummer(beta);*/
                eovrlp_v = MIN2(1e-3,8.5*beta);
        }
        else if( nCore == ipDEST_SIMPL )
        {
                /*  this for debugging only 
                eovrlp_v = 8.5*beta;*/
                /* >>chng 04 may 13, use same min function */
                eovrlp_v = MIN2(1e-3,8.5*beta);
        }
        else
        {
                fprintf( ioQQQ, " chCore of %i not understood by RT_DestProb.\n", 
                  nCore );
                cdEXIT(EXIT_FAILURE);
        }

        /* renorm to unity */
        eovrlp_v /= 1. + eovrlp_v;

        /* multiply by 1-escape prob, since no destruction when optically thin */
        eovrlp_v *= 1. - escp;

        /*check results in bounds */
        ASSERT( eovrlp_v >= 0.  );
        ASSERT( eovrlp_v <= 1.  );

        {
                /* debugging code for Lya problems */
                /*@-redef@*/
                enum {DEBUG_LOC=false};
                /*@+redef@*/
                if( DEBUG_LOC )
                {
                        if( rfield.anu[ipanu-1]>0.73 && rfield.anu[ipanu-1]<0.76 &&
                            fp_equal( abund, Transitions[ipH_LIKE][ipHYDROGEN][ipH2p][ipH1s].Emis->PopOpc ) )
                        {
                                fprintf(ioQQQ,"%li RT_DestProb\t%g\n",
                                        nzone, eovrlp_v  );
                        }
                }
        }

        /* >>chng 04 may 10, rm min */
        /* this hack removed since no fundamental reason for it to be here,
         * this should be added to scattering escape, if included at all */
#       if 0
        /* >>chng 99 apr 12, limit destruction prob in case where gas dominated by scattering.
         * in this case scattering is much more likely than absorption on this event
        eovrlp_v = (1. - opac.albedo[ipanu-1]) * eovrlp_v + 
                opac.albedo[ipanu-1]*DEST0; */
        /* >>chng 01 aug 11, add factor of 3 for increase in mean free path, and min on 0 */
        /*eovrlp_v = MAX2(DEST0,1. - 3.*opac.albedo[ipanu-1]) * eovrlp_v + 
                opac.albedo[ipanu-1]*DEST0;*/
        eovrlp_v = POW2(1. - opac.albedo[ipanu-1]) * eovrlp_v + 
                opac.albedo[ipanu-1]*0.;
#       endif

        return( eovrlp_v );
}

/*RT_LineWidth compute line width (cm/sec), using optical depth array information 
 * this is where effects of wind are done */
double RT_LineWidth(const transition * t)
{
        double RT_LineWidth_v, 
          aa, 
          atau, 
          b, 
          r, 
          vth;
        realnum tau; 

        DEBUG_ENTRY( "RT_LineWidth()" );

        /* uses line width from 
         * >>refer      esc     prob    Bonilha et al. Ap.J. (1979) 233 649
         * return value is half velocity width*(1-ESC PROB) [cm s-1]
         * this assumes incomplete redistribution, damp.tau^1/3 width */

        /* thermal width */
        vth = DoppVel.doppler[ t->Hi->nelem-1 ];

        /* optical depth in outer direction is defined
         * on second and later iterations. 
         * smaller of inner and outer optical depths is chosen for esc prob */
        if( iteration > 1 )
        {
                /* optical depth to shielded face */
                realnum tauout = t->Emis->TauTot - t->Emis->TauIn;

                /* >>chng 99 apr 22 use smaller optical depth */
                tau = MIN2( t->Emis->TauIn , tauout );
        }
        else
        {
                tau = t->Emis->TauIn;
        }
        /* do not evaluate line width if quite optically thin - will be dominated
         * by noise in this case */
        if( tau <1e-3 )
                return 0;

        double Pesc =  esc_PRD_1side( tau , t->Emis->damp);

        /* max optical depth is thermalization length */
        realnum therm = (realnum)(5.3e16/dense.eden);
        if( tau > therm )
        {
                pressure.lgPradDen = true;
                tau = therm;
        }

        /* >>chng 01 jun 23, use wind vel instead of rt since rt deleted */
        /* >>chng 04 may 13, use thermal for subsonic cases */
        if( wind.windv <= 0. )
        {
                /* static geometry */
                /* esc prob has noise if smaller than FLT_EPSILON, or is masing */
                if( (tau-opac.taumin)/100. < FLT_EPSILON )
                {
                        RT_LineWidth_v = 0.;
                }
                else if( tau <= 20. )
                {
                        atau = -6.907755;
                        if( tau > 1e-3 )
                                atau = log(tau);
                        aa = 4.8 + 5.2*tau + (4.*tau - 1.)*atau;
                        b = 6.5*tau - atau;
                        RT_LineWidth_v = vth*0.8862*aa/b*(1. - MIN2( 1., 
                                ( Pesc + t->Emis->Pelec_esc + t->Emis->Pdest) ) );
                        /* small number roundoff can dominate this process */
                        if( Pesc < 10. * FLT_EPSILON )
                                RT_LineWidth_v = 0.;
                }
                else
                {
                        ASSERT( t->Emis->damp*tau >= 0.);
                        atau = log(MAX2(0.0001,tau));
                        aa = 1. + 2.*atau/pow(1. + 0.3*t->Emis->damp*tau,0.6667) + pow(6.5*
                          t->Emis->damp*tau,0.333);
                        b = 1.6 + 1.5/(1. + 0.20*t->Emis->damp*tau);
                        RT_LineWidth_v = vth*0.8862*aa/b*(1. - MIN2( 1. , 
                                (Pesc+ t->Emis->Pelec_esc + t->Emis->Pdest)) );
                }

                /* we want full width, not half width */
                RT_LineWidth_v *= 2.;

        }
        else
        {
                /* wind */
                r = t->Emis->damp*tau/PI;
                if( r <= 1. )
                {
                        RT_LineWidth_v = vth*sqrt(log(MAX2(1.,tau))*.2821);
                }
                else
                {
                        RT_LineWidth_v = 2.*fabs(wind.windv0);
                        if( r*vth <= RT_LineWidth_v )
                        {
                                RT_LineWidth_v = vth*r*log(RT_LineWidth_v/(r*vth));
                        }
                }
        }

        ASSERT( RT_LineWidth_v >= 0. );
        return( RT_LineWidth_v );
}

/*RT_DestHummer evaluate Hummer's betaF(beta) function */
double RT_DestHummer(double beta) /* beta is ratio of continuum to mean line opacity,
                                                                         * returns dest prob = beta F(beta) */
{
        double fhummr_v, 
          x;

        DEBUG_ENTRY( "RT_DestHummer()" );

        /* evaluates Hummer's F(beta) function for case where damping
         * constant is zero, are returns beta*F(beta)
         * fit to Table 1, page 80, of Hummer MNRAS 138, 73-108.
         * beta is ratio of continuum to line opacity; FUMMER is
         * product of his F() times beta; the total destruction prob
         * this beta is Hummer's normalization of the Voigt function */

        ASSERT( beta >= 0.);/* non-positive is unphysical */
        if( beta <= 0. )
        {
                fhummr_v = 0.;
        }
        else
        {
                x = log10(beta);
                if( x < -5.5 )
                {
                        fhummr_v = 3.8363 - 0.56329*x;
                }
                else if( x < -3.5 )
                {
                        fhummr_v = 2.79153 - 0.75325*x;
                }
                else if( x < -2. )
                {
                        fhummr_v = 1.8446 - 1.0238*x;
                }
                else
                {
                        fhummr_v = 0.72500 - 1.5836*x;
                }
                fhummr_v *= beta;
        }
        return( fhummr_v );
}

---