atom_hyperfine.cpp

Go to the documentation of this file.

/* This file is part of Cloudy and is copyright (C)1978-2013 by Gary J. Ferland and
 * others.  For conditions of distribution and use see copyright notice in license.txt */
/* HyperfineCreat establish space for hf arrays, reads atomic data from hyperfine.dat */
/* HyperfineCS - returns collision strengths for hyperfine struc transitions */
/*H21cm computes rate for H 21 cm from upper to lower excitation by atomic hydrogen */ 
/*h21_t_ge_20 compute rate for H 21 cm from upper to lower excitation by atomic hydrogen */ 
/*h21_t_lt_20 compute rate for H 21 cm from upper to lower excitation by atomic hydrogen */ 
/*H21cm_electron compute H 21 cm rate from upper to lower excitation by electrons - call by CoolEvaluate */
/*H21cm_H_atom - evaluate H atom spin changing collision rate, called by CoolEvaluate */
/*H21cm_proton - evaluate proton spin changing H atom collision rate, */
#include "cddefines.h"
#include "conv.h"
#include "lines_service.h"
#include "phycon.h"
#include "dense.h"
#include "rfield.h"
#include "taulines.h"
#include "iso.h"
#include "trace.h"
#include "hyperfine.h"
#include "physconst.h"  
 
/* H21_cm_pops - fine level populations for 21 cm with Lya pumping included 
 * called in CoolEvaluate */
void H21_cm_pops( void )
{
        /*atom_level2( HFLines[0] );*/
        /*return;*/
        /*
        things we know on entry to this routine:
        total population of 2p: iso_sp[ipH_LIKE][ipHYDROGEN].st[ipH2p].Pop
        total population of 1s: iso_sp[ipH_LIKE][ipHYDROGEN].st[ipH1s].Pop
        continuum pumping rate (lo-up) inside 21 cm line: HFLines[0].pump()
        upper to lower collision rate inside 21 cm line: HFLines[0].cs*dense.cdsqte
        occupation number inside Lya: OccupationNumberLine( &iso_sp[ipH_LIKE][ipHYDROGEN].trans(ipH2p,ipH1s) )
 
        level populations (cm-3) must be computed:
        population of upper level of 21cm: HFLines[0].Hi->Pop
        population of lower level of 21cm: (*HFLines[0].Lo()).Pop
        stimulated emission corrected population of lower level: HFLines[0].Emis->PopOpc()
        */
 
        double x,
                PopTot;
        double a32,a31,a41,a42,a21, occnu_lya ,
                rate12 , rate21 , pump12 , pump21 , coll12 , coll21,
                texc , occnu_lya_23 , occnu_lya_13,occnu_lya_24,occnu_lya_14, texc1, texc2;
 
        PopTot = iso_sp[ipH_LIKE][ipHYDROGEN].st[ipH1s].Pop();
        /* population can be zero in certain tests where H is turned off,
         * also if initial solver does not see any obvious source of ionization
         * also possible to set H0 density to zero with element ionization command,
         * as is done in func_set_ion test case */
        if( PopTot <0 )
                TotalInsanity();
        else if( PopTot == 0 )
        {
                /*return after zeroing local variables */
                (*HFLines[0].Hi()).Pop() = 0.;
                (*HFLines[0].Lo()).Pop() = 0.;
                HFLines[0].Emis().PopOpc() = 0.;
                HFLines[0].Emis().phots() = 0.;
                HFLines[0].Emis().xIntensity() = 0.;
                HFLines[0].Emis().ColOvTot() = 0.;
                hyperfine.Tspin21cm = 0.;
                return;
        }
 
        a31 = 2.08e8;   /* Einstein co-efficient for transition 1p1/2 to 0s1/2 */
        a32 = 4.16e8;   /* Einstein co-efficient for transition 1p1/2 to 1s1/2 */
        a41 = 4.16e8;   /* Einstein co-efficient for transition 1p3/2 to 0s1/2 */
        a42 = 2.08e8;   /* Einstein co-efficient for transition 1p3/2 to 1s1/2 */
        /* These A values are determined from eqn. 17.64 of "The theory of Atomic structure
         * and Spectra" by R. D. Cowan 
         * A hyperfine level has degeneracy Gf=(2F + 1)
         * a2p1s = 6.24e8;  Einstein co-efficient for transition 2p to 1s */
        a21 = 2.85e-15; /* Einstein co-efficient for transition 1s1/2 to 0s1/2 */
 
        /* above is spontaneous rate - the net rate is this times escape and destruction
         * probabilities */
        a21 *= (HFLines[0].Emis().Pdest() + HFLines[0].Emis().Pesc() + HFLines[0].Emis().Pelec_esc());
        ASSERT( a21>0. );
 
        /* hyperfine.lgLya_pump_21cm is option to turn off Lya pump
         * of 21 cm, with no 21cm lya pump command - note that this
         * can be negative if Lya mases - can occur during search phase */
        occnu_lya = OccupationNumberLine( iso_sp[ipH_LIKE][ipHYDROGEN].trans(ipH2p,ipH1s) ) *
                hyperfine.lgLya_pump_21cm;
        if( occnu_lya<0 )
        {
                static bool lgCommentDone = false;
                /* Lya is masing - could be due to very bad solution in search phase */
                if( !conv.lgSearch && !lgCommentDone )
                {
                        fprintf(ioQQQ,
                        "NOTE Lya masing will invert 21 cm, occupation number set zero\n");
                        lgCommentDone = true;
                }
                occnu_lya = 0.;
        }
 
        /* Lya occupation number for the hyperfine levels 0S1/2 and 1S1/2 are different*/
        texc = TexcLine( iso_sp[ipH_LIKE][ipHYDROGEN].trans(ipH2p,ipH1s) );
        /* Energy difference between 2p1/2 and 2p3/2 taken from NSRDS */
        if( texc > 0. )
        {
                /* convert to Boltzmann factor, which will applied to occupation 
                 * number of higher energy transition */
                texc1 = sexp(0.068/texc);
                texc2 = sexp(((82259.272-82258.907)*T1CM)/texc);
        }
        else
        {
                texc1 = 0.;
                texc2 = 0.;
        }
 
        /* the continuum within Lya seen by the two levels is not exactly the same brightness.  They
         * differ by the exp when Lya is on Wein tail of black body, which must be true if 21 cm is important */
 
        occnu_lya_23 = occnu_lya;
        occnu_lya_13 = occnu_lya*texc1;
    occnu_lya_14 = occnu_lya_13*texc2;
    occnu_lya_24 = occnu_lya*texc2;
 
        /* this is the 21 cm upward continuum pumping rate [s-1] for the attenuated incident and
         * local continuum and including line optical depths */
        pump12 = HFLines[0].Emis().pump();
        pump21 = pump12 * (*HFLines[0].Lo()).g() / (*HFLines[0].Hi()).g();
 
        /* collision rates s-1 within 1s,
         * were multiplied by collider density when evaluated in CoolEvaluate */
        /* ContBoltz is Boltzmann factor for wavelength of line */
        ASSERT( HFLines[0].Coll().col_str()>0. );
        coll12 = HFLines[0].Coll().col_str()*dense.cdsqte/(*HFLines[0].Lo()).g()*rfield.ContBoltz[HFLines[0].ipCont()-1];
        coll21 = HFLines[0].Coll().col_str()*dense.cdsqte/(*HFLines[0].Hi()).g();
 
        /* set up rate (s-1) equations
         * all process out of 1 that eventually go to 2 */
        rate12 = 
                /* collision rate (s-1) from 1 to 2 */
                coll12 + 
                /* direct external continuum pumping (s-1) in 21 cm line - usually dominated by CMB */
                pump12 +
                /* pump rate (s-1) up to 3, times fraction that decay to 2, hence net 1-2 */
                3.*a31*occnu_lya_13 *a32/(a31+a32)+
                /* pump rate (s-1) up to 4, times fraction that decay to 2, hence net 1-2 */
                /* >>chng 05 apr 04, GS, degeneracy corrected from 6 to 3 */
                3.*a41*occnu_lya_14 *a42/(a41+a42);
 
        /* set up rate (s-1) equations
         * all process out of 2 that eventually go to 1 */
        /* spontaneous + induced 2 -> 1 by external continuum inside 21 cm line */
        /* >>chng 04 dec 03, do not include spontaneous decay, for numerical stability */
        rate21 = 
                /* collisional deexcitation */
                coll21 +
                /* net spontaneous decay plus external continuum pumping in 21 cm line */
                pump21 +
                /* rate from 2 to 3 time fraction that go back to 1, hence net 2 - 1 */
                /* >>chng 05 apr 04,GS, degeneracy corrected from 2 to unity */
                occnu_lya_23*a32 * a31/(a31+a32)+
                occnu_lya_24*a42*a41/(a41+a42);
 
        /* x = (*HFLines[0].Hi()).Pop/(*HFLines[0].Lo()).Pop */
        x = rate12 / SDIV(a21 + rate21);
 
        /* the Transitions term is the total population of 1s */
        (*HFLines[0].Hi()).Pop() = (x/(1.+x))* PopTot;
        (*HFLines[0].Lo()).Pop() = (1./(1.+x))* PopTot;
        ASSERT( (*HFLines[0].Hi()).Pop() >0. );
        ASSERT( (*HFLines[0].Lo()).Pop() >0. );
 
        /* the population with correction for stimulated emission */
        HFLines[0].Emis().PopOpc() = (*HFLines[0].Lo()).Pop()*((3*rate21- rate12) + 3*a21)/SDIV(3*(a21+ rate21));
 
        /* number of escaping line photons, used elsewhere for outward beam */
        HFLines[0].Emis().phots() = (*HFLines[0].Hi()).Pop() * HFLines[0].Emis().Aul() *
                (HFLines[0].Emis().Pesc() + HFLines[0].Emis().Pelec_esc());
        ASSERT( HFLines[0].Emis().phots() >= 0. );
        /* intensity of line */
        HFLines[0].Emis().xIntensity() = HFLines[0].Emis().phots()*HFLines[0].EnergyErg();
 
        /* ratio of collisional to total (collisional + pumped) excitation */
        HFLines[0].Emis().ColOvTot() = coll12 / rate12;
 
        /* finally save the spin temperature */
        if( (*HFLines[0].Hi()).Pop() > SMALLFLOAT )
        {
                hyperfine.Tspin21cm = TexcLine( HFLines[0] );
                /* this line must be non-zero - it does strongly mase in limit_compton_hi_t sim -
                 * in that sim pop ratio goes to unity for a float and TexcLine ret zero */
                if( hyperfine.Tspin21cm == 0. )
                        hyperfine.Tspin21cm = phycon.te;
        }
        else
        {
                hyperfine.Tspin21cm = phycon.te;
        }
 
        return;
}
 
/*H21cm_electron computes rate for H 21 cm from upper to lower excitation by electrons - call by CoolEvaluate
 * >>refer      H1      CS      Smith, F. J. 1966, Planet. Space Sci., 14, 929 */
double H21cm_electron( double temp )
{
        double hold;
        temp = MIN2(1e4 , temp );
        /* following fit is from */
        /* >>refer      H1      21cm    Liszt, H. 2001, A&A, 371, 698 */
 
        hold = -9.607 + log10( sqrt(temp)) * sexp( pow(log10(temp) , 4.5 ) / 1800. );
        hold = pow(10.,hold );
        return( hold );
}
 
/* computes rate for H 21 cm from upper to lower excitation by atomic hydrogen 
 * from 
 * >>refer      H1      CS      Allison, A. C., & Dalgarno A. 1969, ApJ 158, 423 */
/* the following is the best current survey of 21 cm excitation */
/* >>refer      H1      21cm    Liszt, H. 2001, A&A, 371, 698 */
#if 0
STATIC double h21_t_ge_20( double temp )
{
        double y;
        double x1,
                teorginal = temp;
        /* data go up to 1,000K must not go above this */
        temp = MIN2( 1000.,temp );
        x1 =1.0/sqrt(temp);
        y =-21.70880995483007-13.76259674006133*x1;
        y = exp(y);
 
        /* >>chng 02 feb 14, extrapolate above 1e3 K as per Liszt 2001 recommendation 
         * page 699 of */
        /* >>refer      H1      21cm    Liszt, H. 2001, A&A, 371, 698 */
        if( teorginal > 1e3 )
        {
                y *= pow(teorginal/1e3 , 0.33 );
        }
 
        return( y );
}
 
/* this branch for T < 20K, data go down to 1 K */
STATIC double h21_t_lt_20( double temp )
{
        double y;
        double x1;
 
        /* must not go below 1K */
        temp = MAX2( 1., temp );
        x1 =temp*log(temp);
        y =9.720710314268267E-08+6.325515312006680E-08*x1;
        return(y*y);
}
#endif
 
/* >> chng 04 dec 15, GS. The fitted rate co-efficients (cm3s-1) in the temperature range 1K to 300K is from
 * >>refer      H1      CS      Zygelman, B. 2005, ApJ, 622, 1356 
 * The rate is 4/3 times the Dalgarno (1969) rate for the 
 temperature range 300K to 1000K. Above 1000K, the rate is extrapolated according to Liszt 2001.*/
STATIC double h21_t_ge_10( double temp )
{
        double y;
        double x1,x2,x3,
        teorginal = temp;
        /* data go up to 300K  */
        temp = MIN2( 300., temp );
        x1 =temp;
        y =1.4341127e-9+9.4161077e-15*x1-9.2998995e-9/(log(x1))+6.9539411e-9/sqrt(x1)+1.7742293e-8*(log(x1))/pow2(x1);
        if( teorginal > 300. )
        {
                /* data go up to 1000*/
                x3 = MIN2( 1000., teorginal );
                x2 =1.0/sqrt(x3);
                y =-21.70880995483007-13.76259674006133*x2;
                y = 1.236686*exp(y);
 
        }
        if( teorginal > 1e3 )
        {
                /*data go above 1000*/
                y *= pow(teorginal/1e3 , 0.33 );
        }
        return( y );
}
/* this branch for T < 10K, data go down to 1 K */
STATIC double h21_t_lt_10( double temp )
{
        double y;
        double x1;
 
        /* must not go below 1K */
        temp = MAX2(1., temp );
        x1 =temp;
        y =8.5622857e-10+2.331358e-11*x1+9.5640586e-11*pow2(log(x1))-4.6220869e-10*sqrt(x1)-4.1719545e-10/sqrt(x1);
        return(y);
}
 
/*H21cm_H_atom - evaluate H atom spin changing H atom collision rate, 
 * called by CoolEvaluate 
 * >>refer      H1      CS      Allison, A. C. & Dalgarno, A. 1969, ApJ 158, 423 
 */
double H21cm_H_atom( double temp )
{
        double hold;
        if( temp >= 10. )
        {
                hold = h21_t_ge_10( temp );
        }
        else
        {
                hold = h21_t_lt_10( temp );
        }
 
        return hold;
}
 
/*H21cm_proton - evaluate proton spin changing H atom collision rate, 
* called by CoolEvaluate */
double H21cm_proton( double temp )
{
        /*>>refer       21cm    p coll  Furlanetto, S. R. & Furlanetto, M. R. 2007, MNRAS, 379, 130
         * previously had used proton rate, which is 3.2 times H0 rate according to
         *>>refer       21cm    CS      Liszt, H. 2001, A&A, 371, 698 */
        /* fit to table 1 of first paper */
        /*--------------------------------------------------------------*
        TableCurve Function: c:\storage\litera~1\21cm\atomic~1\p21cm.c Jun 20, 2007 3:37:50 PM
        proton coll deex
        X= temperature (K)
        Y= rate coefficient (1e-9 cm3 s-1)
        Eqn# 4419  y=a+bx+cx^2+dx^(0.5)+elnx/x
        r2=0.9999445384690351
        r2adj=0.9999168077035526
        StdErr=5.559328579039901E-12
        Fstat=49581.16793656295
        a= 9.588389834316704E-11
        b= -5.158891920816405E-14
        c= 5.895348443553458E-19
        d= 2.05304960232429E-11
        e= 9.122617940315725E-10
        *--------------------------------------------------------------*/
 
        double hold;
        /* only fit this range, did not include T = 1K point which 
         * causes an inflection */
        temp = MAX2( 2. , temp );
        temp = MIN2( 2e4 , temp );
 
        /* within range of fitted rate coefficients */
        double x1,x2,x3,x4;
        x1 = temp;
        x2 = temp*temp;
        x3 = sqrt(temp);
        x4 = log(temp)/temp;
        hold =9.588389834316704E-11 - 5.158891920816405E-14*x1
                +5.895348443553458E-19*x2 + 2.053049602324290E-11*x3
                +9.122617940315725E-10*x4;
 
        return hold;
}
 
/* 
 * HyperfineCreate, HyperfineCS written July 2001
 * William Goddard for Gary Ferland
 * This code calculates line intensities for known
 * hyperfine transitions.
 */
 
/* two products, the transition structure HFLines, which contains all information for the lines,
 * and nHFLines, the number of these lines.  
 *
 * these are in taulines.h
 *
 * info to create them contained in hyperfine.dat
 *
 * abundances of nuclei are also in hyperfine.dat, stored in 
 */
 
/* Ion contains twelve varying temperatures, specified above, used for */
/* calculating collision strengths.                                                                        */   
typedef struct 
{
        double strengths[12];
} Ion;
 
static  Ion *Strengths;
 
/* HyperfineCreate establish space for hf arrays, reads atomic data from hyperfine.dat */
void HyperfineCreate(void)
{
        FILE *ioDATA;
        char chLine[INPUT_LINE_LENGTH];
        bool lgEOL;
        /*double c, h, k, N, Ne, q12, q21, upsilon, x;*/
        realnum spin, wavelength;
        long int i, j, mass, nelec, ion, nelem;
 
        DEBUG_ENTRY( "HyperfineCreate()" );
 
        /* list of ion collision strengths for the temperatures listed in table */
        /* HFLines containing all the data in Hyperfine.dat, and transition is          */
        /* defined in cddefines.h                                                                                               */
 
        /*transition *HFLines;*/
 
        /* get the line data for the hyperfine lines */
        if( trace.lgTrace )
                fprintf( ioQQQ," Hyperfine opening hyperfine.dat:");
 
        ioDATA = open_data( "hyperfine.dat", "r" );
 
        /* first line is a version number and does not count */
        if( read_whole_line( chLine , (int)sizeof(chLine) , ioDATA ) == NULL )
        {
                fprintf( ioQQQ, " Hyperfine could not read first line of hyperfine.dat.\n");
                cdEXIT(EXIT_FAILURE);
        }
        /* count how many lines are in the file, ignoring all lines
         * starting with '#' */
        nHFLines = 0;
        while( read_whole_line( chLine , (int)sizeof(chLine) , ioDATA ) != NULL )
        {
                /* we want to count the lines that do not start with #
                 * since these contain data */
                if( chLine[0] != '#')
                        ++nHFLines;
        }
 
        /* allocate the transition HFLines array */
        HFLines.resize(nHFLines);
        AllTransitions.push_back(HFLines);
        /* initialize array to impossible values to make sure eventually done right */
        for( i=0; i< nHFLines; ++i )
        {
                HFLines[i].Junk();
                HFLines[i].AddHiState();
                HFLines[i].AddLoState();
                HFLines[i].AddLine2Stack();
        }
 
        Strengths = (Ion *)MALLOC( (size_t)(nHFLines)*sizeof(Ion) );
        hyperfine.HFLabundance = (realnum *)MALLOC( (size_t)(nHFLines)*sizeof(realnum) );
 
        /* now rewind the file so we can read it a second time*/
        if( fseek( ioDATA , 0 , SEEK_SET ) != 0 )
        {
                fprintf( ioQQQ, " Hyperfine could not rewind hyperfine.dat.\n");
                cdEXIT(EXIT_FAILURE);
        }
 
        /* check that magic number is ok, read the line */
        if( read_whole_line( chLine , (int)sizeof(chLine) , ioDATA ) == NULL )
        {
                fprintf( ioQQQ, " Hyperfine could not read first line of hyperfine.dat.\n");
                cdEXIT(EXIT_FAILURE);
        }
 
        /* check that magic number is ok, scan it in */
        i = 1;
        nelem = (long)FFmtRead(chLine,&i,sizeof(chLine),&lgEOL);
        nelec = (long)FFmtRead(chLine,&i,sizeof(chLine),&lgEOL);
        ion = (long)FFmtRead(chLine,&i,sizeof(chLine),&lgEOL);
 
        {
                /* the following is the set of numbers that appear at the start of hyperfine.dat 01 07 12 */ 
                static int iYR=2,  iMN=10, iDY=28;
                if( ( nelem != iYR ) || ( nelec != iMN ) || ( ion != iDY ) )
                {
                        fprintf( ioQQQ, 
                                " Hyperfine: the version of hyperfine.dat in the data directory is not the current version.\n" );
                        fprintf( ioQQQ, 
                                " I expected to find the number %i %i %i and got %li %li %li instead.\n" ,
                                iYR, iMN , iDY ,
                                nelem , nelec , ion );
                        fprintf( ioQQQ, "Here is the line image:\n==%s==\n", chLine );
                        cdEXIT(EXIT_FAILURE);
                }
        }
 
        /* 
         * scan the string taken from Hyperfine.dat, parsing into
         * needed variables.
         * nelem is the atomic number.
         * IonStg is the ionization stage.  Atom = 1, Z+ = 2, Z++ = 3, etc.
         * Aul is used to find the einstein A in the function GetGF.
         * most of the variables are floats.
         */
 
        /* this will count the number of lines */
        j = 0;
 
        while( read_whole_line( chLine , (int)sizeof(chLine) , ioDATA ) != NULL )
        {
                /* only look at lines without '#' in first col */
                /* make sure line in data file is < 140 char   */
                if( chLine[0] != '#')
                {
                        double Aul;
                        ASSERT( j < nHFLines );
 
                        double help[3];
                        sscanf(chLine, "%li%i%le%i%le%le%le%le%le%le%le%le%le%le%le%le%le%le%le", 
                               &mass, 
                               &(*HFLines[j].Hi()).nelem(),
                               &help[0],
                               &(*HFLines[j].Hi()).IonStg(),
                               &help[1],
                               &help[2],
                               &Aul,
                               &Strengths[j].strengths[0],
                               &Strengths[j].strengths[1],
                               &Strengths[j].strengths[2],
                               &Strengths[j].strengths[3],
                               &Strengths[j].strengths[4],
                               &Strengths[j].strengths[5],
                               &Strengths[j].strengths[6],
                               &Strengths[j].strengths[7],
                               &Strengths[j].strengths[8],
                               &Strengths[j].strengths[9],
                               &Strengths[j].strengths[10],
                               &Strengths[j].strengths[11]);
                        spin = (realnum)help[0];
                        hyperfine.HFLabundance[j] = (realnum)help[1];
                        wavelength = (realnum)help[2];
                        HFLines[j].Emis().Aul() = (realnum)Aul;
                        HFLines[j].Emis().damp() = 1e-20f;
                        (*HFLines[j].Hi()).g() = (realnum) (2*(spin + .5) + 1);
                        (*HFLines[j].Lo()).g() = (realnum) (2*(spin - .5) + 1);
                        HFLines[j].WLAng() = wavelength * 1e8f;
                        HFLines[j].EnergyWN() = (realnum) (1. / wavelength);
                        HFLines[j].Emis().gf() = (realnum)(GetGF(HFLines[j].Emis().Aul(), HFLines[j].EnergyWN(), (*HFLines[j].Hi()).g()));
                        /*fprintf(ioQQQ,"HFLinesss1\t%li\t%.2e\t%.2e\t%.2e\t%.2e\t%.2e\n",
                                j,HFLines[j].opacity() , HFLines[j].Emis().gf() , HFLines[j].Emis().Aul() , HFLines[j].EnergyWN,HFLines[j].Lo()->g());*/
                        (*HFLines[j].Lo()).nelem() = (*HFLines[j].Hi()).nelem();
                        (*HFLines[j].Lo()).IonStg() = (*HFLines[j].Hi()).IonStg();
 
 
                        ASSERT(HFLines[j].Emis().gf() > 0.);
                        /* increment the counter */
                        j++;
                }
 
        }
        ASSERT( j==nHFLines );
 
        /* closing the file */
        fclose(ioDATA);
 
#       if 0
        /* for debugging and developing only */
        /* calculating the luminosity for each isotope */
        for(i = 0; i < nHFLines; i++)
        {
                N = dense.xIonDense[(*HFLines[i].Hi()).nelem()-1][(*HFLines[i].Hi()).IonStg()-1];
                Ne = dense.eden;
 
                h = 6.626076e-27;                       /* erg * sec */
                c = 3e10;                                       /* cm / sec      */
                k = 1.380658e-16;                       /* erg / K   */
 
                upsilon = HyperfineCS(i);
                                /*statistical weights must still be identified */
                q21 = COLL_CONST * upsilon / (phycon.sqrte * (*HFLines[i].Hi()).g());
 
                q12 = (*HFLines[i].Hi()).g()/ (*HFLines[i].Lo()).g() * q21 * exp(-1 * h * c * HFLines[i].EnergyWN / (k * phycon.te)); 
 
                x = Ne * q12 / (HFLines[i].Emis().Aul() * (1 + Ne * q21 / HFLines[i].Aul()));
                HFLines[i].xIntensity() = N * HFLines[i].Emis().Aul() * x / (1.0 + x) * h * c / (HFLines[i].WLAng() / 1e8);
 
        }
#       endif
 
        return;
}
 
 
/*HyperfineCS returns interpolated collision strength for element nelem and ion ion */
double HyperfineCS( long i )
{
 
        /*Search HFLines to find i of ion               */
        int /*i = 0,*/ j = 0;
#       define N_TE_TABLE 12
        double  slope, upsilon, TemperatureTable[N_TE_TABLE] = {.1e6, .15e6, .25e6, .4e6, .6e6, 
                1.0e6, 1.5e6, 2.5e6, 4e6, 6e6, 10e6, 15e6};
 
        DEBUG_ENTRY( "HyperfineCS()" );
 
        /*while(i < nHFLines+1 && (*HFLines[i].Hi()).nelem() != nelem && (*HFLines[i].Hi()).IonStg() != ion)
                ++i;*/
        ASSERT( i >= 0. && i <= nHFLines );
 
        /*j = temperature       */
        /* calculate actual cooling rate for isotope.                                                           */
        /* The temperature-dependent collision strength must first be calculated.       */
        /* phycon.te is compared to the first, last and intermediate values of strengths[]*/
        /* and interpolated by taking the log of the collision strength                         */
        /* and temperature.                                                                                                                     */
 
        if( phycon.te <= TemperatureTable[0])
        {
                /* temperature below bounds of table */
                j = 0;
                slope = (log10(Strengths[i].strengths[j+1]) - log10(Strengths[i].strengths[j])) /
                        (log10(TemperatureTable[j+1]) - log10(TemperatureTable[j]));
                upsilon = (log10((phycon.te)) - (log10(TemperatureTable[j])))*slope + log10(Strengths[i].strengths[j]);
                upsilon = pow(10., upsilon);
        }
        else if(  phycon.te >= TemperatureTable[N_TE_TABLE-1])
        {
                /* temperature above bounds of table */
                j = N_TE_TABLE - 1;
                slope = (log10(Strengths[i].strengths[j-1]) - log10(Strengths[i].strengths[j])) /
                        (log10(TemperatureTable[j-1]) - log10(TemperatureTable[j]));
                upsilon = (log10((phycon.te)) - (log10(TemperatureTable[j])))*slope + log10(Strengths[i].strengths[j]);
                upsilon = pow(10., upsilon);
        }
        else
        {
                j = 1;
                /* want Table[j-1] < te < Table[j] */
                /*while ( phycon.te >= TemperatureTable[j] && j < N_TE_TABLE )*/
                /*while ( TemperatureTable[j] < phycon.te  && j < N_TE_TABLE )*/
                while ( j < N_TE_TABLE && TemperatureTable[j] < phycon.te )
                        j++;
 
                ASSERT( j >= 0 && j < N_TE_TABLE);
                ASSERT( (TemperatureTable[j-1] <= phycon.te ) && (TemperatureTable[j] >= phycon.te) );
 
                if( fp_equal( phycon.te, TemperatureTable[j] ) )
                {
                        upsilon = Strengths[i].strengths[j];
                }
                /*phycon.te must be less than TemperatureTable[j], greater than TemperatureTable[j-1][0]*/
                else if( phycon.te < TemperatureTable[j])
                {
                        slope = (log10(Strengths[i].strengths[j-1]) - log10(Strengths[i].strengths[j])) /
                                  (log10(TemperatureTable[j-1]) - log10(TemperatureTable[j]));
 
                        upsilon = (log10((phycon.te)) - (log10(TemperatureTable[j-1])))*slope + log10(Strengths[i].strengths[j-1]);
                        upsilon = pow(10., upsilon);
                }
                else 
                {
                        upsilon = Strengths[i].strengths[j-1];
                }
        }
 
        return upsilon;
}