hydroeinsta.cpp

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/* This file is part of Cloudy and is copyright (C)1978-2017 by Gary J. Ferland and
 * others.  For conditions of distribution and use see copyright notice in license.txt */
/*HydroEinstA calculates Einstein A's from  osillator strengths*/
#include "cddefines.h"
#include "hydroeinsta.h"
#include "hydro_bauman.h"
#include "hydrooscilstr.h"
#include "iso.h"

STATIC double hydro_transprob_collapsed_to_collapsed( long nelem, long nHi, long nLo );
STATIC double hydro_transprob_collapsed_to_resolved( long nelem, long nHi, long nLo, long lLo );

double HydroEinstA(long int n1, 
          long int n2)
{
        long int lower, iupper;
        double EinstA_v, 
          ryd, 
          xl, 
          xmicron, 
          xu;

        DEBUG_ENTRY( "HydroEinstA()" );
        /* (lower,upper) of Johnson 1972.  */

        /* strictly n -> n' transition probabilities
         * no attempt to distribute according to l,l' */

        /* sort out the order of upper and lower, so can be called either way */
        lower = MIN2( n1 , n2 );
        iupper = MAX2( n1, n2 );
        if( lower < 1 || lower == iupper )
        {
                fprintf(ioQQQ," HydroEinstA called with impossible ns, =%li %li\n", lower, iupper);
                cdEXIT(EXIT_FAILURE);
        }

        xl = (double)lower;
        xu = (double)iupper;
        ryd = 1./POW2(xl) - 1./POW2(xu);
        xmicron = 1.E4/(ryd*RYD_INF);
        EinstA_v = HydroOscilStr(xl,xu)*TRANS_PROB_CONST*1e8f/(POW2(xmicron))*xl*xl/xu/xu;
        return( EinstA_v );
}

realnum hydro_transprob( long nelem, long ipHi, long ipLo )
{
        double Aul;
        long ipISO = ipH_LIKE;
        /* charge to 4th power, needed for scaling laws for As*/
        double z4 = POW4((double)nelem+1.);
        DEBUG_ENTRY( "hydro_transprob()" );

        if( ipHi >= iso_sp[ipISO][nelem].numLevels_max-iso_sp[ipISO][nelem].nCollapsed_max )
        {
                if( ipLo >= iso_sp[ipISO][nelem].numLevels_max-iso_sp[ipISO][nelem].nCollapsed_max )
                {
                        Aul = hydro_transprob_collapsed_to_collapsed( nelem, N_(ipHi), N_(ipLo) );
                        iso_put_error(ipISO,nelem,ipHi,ipLo,IPRAD,0.001f,0.001f);

                        ASSERT( Aul > 0.);
                }
                else 
                {
                        Aul = hydro_transprob_collapsed_to_resolved( nelem, N_(ipHi), N_(ipLo), L_(ipLo) );
                        iso_put_error(ipISO,nelem,ipHi,ipLo,IPRAD,0.01f,0.01f);
                }
        }
        else
        {
                if(  N_(ipHi) == N_(ipLo)  )
                {       
                        Aul = SMALLFLOAT;
                        iso_put_error(ipISO,nelem,ipHi,ipLo,IPRAD,0.001f,0.001f);
                }
                else if( ipLo == 0 && ipHi == 1 )
                {
                        // >> refer     H-like  As      Marrus, E. \& Mohr, P. J. Advances in Atomic and Molecular Physics, Vol. 14, Academic, New York, 1978, p. 181
                        Aul =  2.46e-6*powi((double)(nelem+1.),10);
                        iso_put_error(ipISO,nelem,ipHi,ipLo,IPRAD,0.001f,0.001f);
                }
                else if( ipLo == 0 && ipHi == 2 )
                {
                        Aul = 6.265e8*z4;
                        iso_put_error(ipISO,nelem,ipHi,ipLo,IPRAD,0.001f,0.001f);
                }
                else if( abs( L_(ipLo) - L_(ipHi) )== 1 )
                {
                        Aul = H_Einstein_A( N_(ipHi), L_(ipHi), N_(ipLo), L_(ipLo), nelem+1 );
                        iso_put_error(ipISO,nelem,ipHi,ipLo,IPRAD,0.001f,0.001f);
                }
                else
                {
                        ASSERT( N_(ipHi) > N_(ipLo) );
                        ASSERT( (L_(ipHi) == L_(ipLo)) || 
                                ( abs(L_(ipHi)-L_(ipLo)) > 1) );
                        Aul = SMALLFLOAT;
                        iso_put_error(ipISO,nelem,ipHi,ipLo,IPRAD,0.001f,0.001f);
                }
        }

        return (realnum)Aul;
}

STATIC double hydro_transprob_collapsed_to_collapsed( long nelem, long nHi, long nLo )
{
        DEBUG_ENTRY( "hydro_transprob_collapsed_to_collapsed()" );

        double Aul = 0.;
        ASSERT( nHi > nLo );

        for( long lLo=0; lLo < nLo; ++lLo )
        {
                double Aul1 = hydro_transprob_collapsed_to_resolved( nelem, nHi, nLo, lLo );
                Aul += Aul1;
        }

        return Aul;
}

STATIC double hydro_transprob_collapsed_to_resolved( long nelem, long nHi, long nLo, long lLo )
{
        DEBUG_ENTRY( "hydro_transprob_collapsed_to_resolved()" );
                
        long ipISO = ipH_LIKE;  
        t_iso_sp *sp = &iso_sp[ipISO][nelem];
        long nResMax = sp->n_HighestResolved_max;
        long ipLoRes = sp->IndexIfAllResolved[nLo][lLo][2];
        ASSERT( nLo > nResMax || ipLoRes <= sp->numLevels_max - sp->nCollapsed_max );

        /* Lower level resolved, upper not. First calculate Aul
         * from upper level with ang mom one higher.    */
        double Aul = H_Einstein_A( nHi, lLo+1, nLo, lLo, nelem+1 );

        sp->CachedAs[ nHi-nResMax-1 ][ ipLoRes ][0] = (realnum)Aul;

        Aul *= (2.*(lLo+1.)+1.) * 2. / (2.*(double)nHi*(double)nHi);

        if( lLo != 0 )
        {
                /* For all l>0, add in transitions from upper level with ang mom one lower.     */
                double Aul1 = H_Einstein_A( nHi, lLo-1, nLo, lLo, nelem+1 );
        
                sp->CachedAs[ nHi-nResMax-1 ][ ipLoRes ][1] = (realnum)Aul1;

                /* now add in this part after multiplying by stat weight for lHi = lLo-1.       */
                Aul += Aul1*(2.*(lLo-1.)+1.) * 2. / (2.*(double)nHi*(double)nHi);
        }
        else
                sp->CachedAs[ nHi-nResMax-1 ][ ipLoRes ][1] = 0.f;

        ASSERT( Aul > 0.);

        return Aul;
}