cool_nitr.cpp

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/* 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 */
/*CoolNitr evaluate total cooling due to nitrogen */
#include "cddefines.h"
#include "taulines.h"
#include "dense.h"
#include "phycon.h"
#include "ligbar.h"
#include "thermal.h"
#include "lines_service.h"
#include "embesq.h"
#include "atoms.h"
#include "cooling.h"
#include "nitro.h"
/* xNI_coll_stren: Author: Terry Yun 2006 */
/* This routine interpolates the collision strength of NI 
 * We are only interested in the first 5 levels, therefore there are 10 transitions.
 * Used polynomial fit, eqn: CS = a*t+b*t^1.5+c*t^0.5
 * The range of temp is 0 - 50,000 K */
/* #define PRINT */
static const int N1_SIZE = 10;
 
static const double aNI[N1_SIZE] = {2.755e-5,4.123e-5,7.536e-6,1.486e-5,4.516e-5,
                                    -2.935e-6,4.000e-6,3.751e-6,-2.176e-6,1.024e-5};
static const double bNI[N1_SIZE] = {-8.150e-8,-1.220e-7,-2.226e-8,-4.390e-8,-1.130e-7,
                                    8.000e-9,-1.1447e-8,-1.061e-8,5.610e-9,-3.227e-8};
static const double cNI[N1_SIZE] = {2.140e-4,3.272e-4,-4.944e-6,3.473e-6,-8.772e-4,
                                    1.654e-3,1.675e-3,1.123e-3,3.867e-3,3.376e-4};
 
static double NI[6][6][3]; /* coefficients a b c into array */
 
/*xNI_coll_stren interpolate the collision strength of NI  */
STATIC double xNI_coll_stren(int ipLo, int ipHi)
{
        /* incorporating the N0 collision strengths give in
         *>>refer       N1      cs      Tayal, S.S., 2006, ApJS, 163, 207 */
 
        double CS; /* collision strength */
 
        // Tayal's energy index IS NOT IN INCREASING ENERGY ORDER
        // call routine with proper energy order, swap it around
        // to Tayal order
        int ipLoTayal=-1, ipHiTayal=-1;
 
        /* Invalid entries returns '-1':the initial indices are smaller than the final indices */
        if(ipLo >= ipHi)
                return( -1. );
 
        /* Invalid returns '-1': the indices are greater than 5 or smaller than 0 */
        if(ipLo < 1 || ipHi > 5)
                return( -1. );
 
        int ipTayalOrder[6]={0,1,3,2,4,5};
        ipLoTayal = ipTayalOrder[ipLo];
        ipHiTayal = ipTayalOrder[ipHi];
        // special case of 2-3, must swap order again
        if( ipLo==2 && ipHi==3 )
        {
                ipLoTayal = 2;
                ipHiTayal = 3;
        }
 
        static bool lgMustInit = true;
        if( lgMustInit )
        {
                lgMustInit = false;
                /* assigning array initially to zero */ 
                for(long i=0; i<6; i++)
                {
                        for(long j=0; j<6; j++)
                        {
                                set_NaN(NI[i][j][0]); /* coeff a */
                                set_NaN(NI[i][j][1]); /* coeff b */
                                set_NaN(NI[i][j][2]); /* coeff c */
                        }
                }
 
                /* reading coeffs into 3D array */   
                /* The index is in physics scale */
                int index = 0;
                for(int i=1; i<6; i++)
                {
                        for(int j=i+1; j<6; j++)
                        {
                                NI[i][j][0] = aNI[index];
                                NI[i][j][1] = bNI[index];
                                NI[i][j][2] = cNI[index];
                                index++;
                        }
                }
        }
 
#       ifdef PRINT
        /* physical index goes from 1 to 5 */
        for(long i=1; i<6; i++)
        {
                for(long j=i+1; j<6; j++)
                {
                        printf("NI %i%i a:%e ", i, j, NI[i][j][0]);
                        printf("%i%i b:%e\n", i, j, NI[i][j][1]);
                        /* printf("%i%i c:%lf\n", i, j, NI[i][j][2]); */
                }
        }
#       endif
 
        double temp_max = 50e3;
        double temp_min = 0;
        double temp = phycon.te;
        temp = MAX2(temp, temp_min); /* return lager temp */
        temp = MIN2(temp, temp_max); /* return smaller temp */
        /* eqn: CS = a*t+b*t^1.5+c*t^0.5 */
        CS = NI[ipLoTayal][ipHiTayal][0]*phycon.te + NI[ipLoTayal][ipHiTayal][1]*phycon.te32 + 
                NI[ipLoTayal][ipHiTayal][2]*phycon.sqrte;
 
        return CS;
}
 
 
void CoolNitr(void)
{
        realnum p2;
        double a21, 
          a31, 
          a32, 
          cs, 
          cs2s2p, 
          cs2s3p, 
          cs21, 
          cs31, 
          cs32, 
          p3;
        long int i;
 
        double a12, 
          a13, 
          a14, 
          a15, 
          a23, 
          a24, 
          a25, 
          a34, 
          a35, 
          a45, 
          cs12, 
          cs13, 
          cs14, 
          cs15, 
          cs23, 
          cs24, 
          cs25, 
          cs34, 
          cs35, 
          cs45;
 
        double pop[5];
 
        DEBUG_ENTRY( "CoolNitr()" );
 
        static const double gN1[5]={4.,6.,4.,2.,4.};
        static const double exN1[4]={19224.464,8.713,9605.74,0.386};
 
        /* trans prob from 
         * >>refer      n1      as      Froese Fischer, C. & Tachiev, G. 2004, ADNDT, 87, 1
         */
        // 5200, g_up = 6, cs=0.337 @ 1e4K in Tayal06, 
        // NB - his J levels in ^2D are not in energy order
        cs12 = xNI_coll_stren(1, 2);
        a12 = 7.57e-6;
        double a12Tot = a12 + atoms.d5200r;
 
        // 5198, g_up = 4, cs=0.224 @ 1e4K in Tayal06
        // NB - his J levels in ^2D are not in energy order
        cs13 = xNI_coll_stren(1, 3);
        a13 = 2.03e-5;
        double a13Tot = a13 + atoms.d5200r;
 
        // 3466.543 0.055 @ 1e4K, g_up = 2
        cs14 = xNI_coll_stren(1, 4);
        a14 = 2.61e-3;
 
        // 3466.497 0.109 @ 1e4K, g_up = 4
        cs15 = xNI_coll_stren(1,5);
        a15 = 6.50e-3;
 
        /* this is fraction of 2D excitations that emit a photon in the 5200 multiplet
         * this is used for collisional quenching in prt lines routine
         * true line emission is in numerator while all loss terms are in
         * denominator */
        nitro.quench_5200 = (a12+a13) / ((a12Tot+a13Tot) + (cs12 + cs13) * dense.cdsqte);
 
        // 0.257 @ 1e4K, g_up = 4
        cs23 = xNI_coll_stren(2, 3);
        a23 = 1.07e-8;
 
        // 10398.2 0.139 @ 1e4K, g_up = 2
        cs24 = xNI_coll_stren(2, 4);
        a24 = 3.45e-2;
 
        // 10397.7 0.366 @ 1e4K, g_up = 4
        cs25 = xNI_coll_stren(2, 5);
        a25 = 6.14e-2;
 
        // 10407.6 0.141 @ 1e4K, g_up = 2
        cs34 = xNI_coll_stren(3, 4);
        a34 = 5.27e-2;
 
        // 10407.2 0.195 @ 1e4K, g_up = 4
        cs35 = xNI_coll_stren(3, 5);
        a35 = 2.75e-2;
 
        // 0.123 @ 1e4K, g_up = 4
        cs45 = xNI_coll_stren(4, 5);
        a45 = 9.50e-17;
 
        // FUV allowed and intercombination lines that pump [NI]
        // the branching ratios used below are based on
        // >>refer      n1      as      Froese Fischer, C. & Tachiev, G. 2004, ADNDT, 87, 1
        //
        // the colission strengths are taken from
        // >>refer      n1      cs      Tayal, S. S., 2006, ApJS, 163, 207
        // the fits are based on data between 500K and 50 kK
        //
        // update rates for the driving transitions
        cs = exp(-11.3423 + 0.8379*min(phycon.alnte,10.82));
        PutCS( cs, TauLines[ipNI_pumpIndirect] );
        atom_level2( TauLines[ipNI_pumpIndirect] );
 
        static const double csN1_a[NI_NDP] = {
                -12.3982, -9.4523, -12.5580, -10.8813, -13.6532, -9.9035, -11.4470, -5.4776, -6.3304
        };
        static const double csN1_b[NI_NDP] = {
                0.7458, 0.3865, 0.7330, 0.6853, 0.7712, 0.3919, 0.6734, 0.1789, 0.1966
        };
 
        for( i=0; i < NI_NDP; ++i )
        {
                cs = exp(csN1_a[i] + csN1_b[i]*min(phycon.alnte,10.82));
                PutCS( cs, TauLines[ipNI_pumpDirect[i]] );
                atom_level2( TauLines[ipNI_pumpDirect[i]] );
        }
        // units of pump rate s-1
        double RPI = TauLines[ipNI_pumpIndirect].Emis().pump();
        double RPD0 = TauLines[ipNI_pumpDirect[0]].Emis().pump();
        double RPD1 = TauLines[ipNI_pumpDirect[1]].Emis().pump();
        double RPD2 = TauLines[ipNI_pumpDirect[2]].Emis().pump();
        double RPD3 = TauLines[ipNI_pumpDirect[3]].Emis().pump();
        double RPD4 = TauLines[ipNI_pumpDirect[4]].Emis().pump();
        double RPD5 = TauLines[ipNI_pumpDirect[5]].Emis().pump();
        double RPD6 = TauLines[ipNI_pumpDirect[6]].Emis().pump();
        double RPD7 = TauLines[ipNI_pumpDirect[7]].Emis().pump();
        double RPD8 = TauLines[ipNI_pumpDirect[8]].Emis().pump();
        // correct for removal of photons that go straight back to ground
        // beta is the branching ratio directly back to ground
        // for pumping lines not listed below, beta is less than 0.01
        double beta = 0.7955;
        double Premove = TauLines[ipNI_pumpIndirect].Emis().Pesc() +
                TauLines[ipNI_pumpIndirect].Emis().Pelec_esc() + TauLines[ipNI_pumpIndirect].Emis().Pdest();
        RPI *= (1.-beta)/(1.-beta*(1.-Premove));
        beta = 0.1384;
        Premove = TauLines[ipNI_pumpDirect[0]].Emis().Pesc() +
                TauLines[ipNI_pumpDirect[0]].Emis().Pelec_esc() + TauLines[ipNI_pumpDirect[0]].Emis().Pdest();
        RPD0 *= (1.-beta)/(1.-beta*(1.-Premove));
        // the branching ratios to the lowest 4 excited levels are calculated in the low-density
        // limit (i.e. no collisions are treated) and exclude transitions straight back to ground
        // from the upper level of the driving line
        double pump14 = 0.0113*RPI + 0.0239*RPD0 + 0.0090*RPD1 + 0.1617*RPD2 + 0.0167*RPD3 + 0.4404*RPD4;
        double pump15 = 0.0112*RPI + 0.0265*RPD0 + 0.6253*RPD1 + 0.5108*RPD2 + 0.0824*RPD3 + 0.2588*RPD4;
        double pump13 = 0.3441*RPI + 0.8621*RPD0 + 0.0233*RPD1 + 0.0895*RPD2 + 0.1068*RPD3 + 0.1644*RPD4;
        double pump12 = 0.0417*RPI + 0.0468*RPD0 + 0.3408*RPD1 + 0.2328*RPD2 + 0.7937*RPD3 + 0.1338*RPD4;
 
        pump14 += 0.4881*RPD5 + 0.0876*RPD6 + 0.0450*RPD7 + 0.1777*RPD8;
        pump15 += 0.1569*RPD5 + 0.0484*RPD6 + 0.2240*RPD7 + 0.0854*RPD8;
        pump13 += 0.2908*RPD5 + 0.8397*RPD6 + 0.0694*RPD7 + 0.7369*RPD8;
        pump12 += 0.0623*RPD5 + 0.0238*RPD6 + 0.6615*RPD7 + 0.0000*RPD8;
 
        // estimate of pumping contribution to intensity of [NI] 5199
        nitro.pump5199 = (pump12+pump13+0.9710*pump14+0.9318*pump15) * nitro.quench_5200 * 
                dense.xIonDense[ipNITROGEN][0] * 3.82e-12;
 
        /**** Terry's addition, recombination from N+ **************/
        /* rate coefficient (cm3 s-1) from Table 3 of
         *>>refer       NI      rec     Pequignot, D., Petijean, P. & Boisson, C. 1991, A&A, 251, 680 */
        double eff_recrate_2D = 1.108e-13 * pow(phycon.te*1e-4, -0.6085) /
                (1. - 0.0041 * pow(phycon.te*1e-4, -0.3975) );
        double eff_recrate_2P = 0.659e-13 * pow(phycon.te*1e-4, -0.6158);
        double fac_n1;
        if( dense.xIonDense[ipNITROGEN][0] > 0. )
                fac_n1 = dense.eden * dense.xIonDense[ipNITROGEN][1] / dense.xIonDense[ipNITROGEN][0];
        else
                fac_n1 = 0.;
 
        // assume levels are populated according to statistical weight
        double rec14 = eff_recrate_2P * fac_n1 * 2./6.;
        double rec15 = eff_recrate_2P * fac_n1 * 4./6.;
        double rec13 = eff_recrate_2D * fac_n1 * 4./10.;
        double rec12 = eff_recrate_2D * fac_n1 * 6./10.;
 
        // estimate of recombination contribution to intensity of [NI] 5199
        nitro.rec5199 = (rec12+rec13+0.9710*rec14+0.9318*rec15) * nitro.quench_5200 * 
                dense.xIonDense[ipNITROGEN][0] * 3.82e-12;
 
        pump14 += rec14;
        pump15 += rec15;
        pump13 += rec13;
        pump12 += rec12;
 
        double Cooling , CoolingDeriv;
        atom_pop5(gN1,exN1,cs12,cs13,cs14,cs15,cs23,cs24,cs25,cs34,cs35,
                cs45,a12Tot,a13Tot,a14,a15,a23,a24,a25,a34,a35,a45,pop,
                dense.xIonDense[ipNITROGEN][0], &Cooling , &CoolingDeriv ,
                pump12 , pump13 , pump14 , pump15 );
 
        nitro.xN5200 = pop[1]*a12*3.818e-12;
        nitro.xN5198 = pop[2]*a13*3.821e-12;
        nitro.xN3467 = pop[3]*a14*5.729e-12;
        nitro.xN3466 = pop[4]*a15*5.729e-12;
        nitro.xN10398 = pop[3]*a24*1.910e-12;
        nitro.xN10397 = pop[4]*a25*1.910e-12;
        nitro.xN10408 = pop[3]*a34*1.908e-12;
        nitro.xN10407 = pop[4]*a35*1.908e-12;
 
        // population of excited NI - used in ionization balance routines
        atoms.p2nit = (realnum)(pop[1]+pop[2])/SDIV(dense.xIonDense[ipNITROGEN][0]);
 
        // total cooling from 5-level system
        thermal.dCooldT += CoolingDeriv;
        CoolAdd("N  1",5199, Cooling );
 
        /* N I 1200, cs from trans probability */
        PutCS(4.1,TauLines[ipT1200]);
        atom_level2(TauLines[ipT1200]);
 
        /* N II 1084, cs from trans prob */
        PutCS(5.5,TauLines[ipT1085]);
        atom_level2(TauLines[ipT1085]);
 
        /* [N II] coll data from 
         * >>referold   n2      cs      Stafford, R.P., Bell, K.L, Hibbert, A. & Wijesundera, W.P.,
         * >>rereroldcon 1994, MNRAS 268, 816,
         * at 10,000K (v weak T dep)
         * >>chng 00 dec 11, to Lennon & Burke
         * >>referold   n2      cs      Lennon, D.J., & Burke, V.M., 1994, A&AS, 103, 273-277
         * transit prob from 
         * >>referold   n2      as      Nussbaumer, H., & Rusca, C. 1979, A&A, 72, 129
         * >>chng 00 dec 11, to Lennon & Burke cs
         *>>refer       n2      as      Froese Fischer, C., & Tachiev, G. 2004, At. Data Nucl. Data Tables, 87, 1
         */
        a21 = 3.889e-3;
        a31 = 0.03140;
        a32 = 1.136;
        /* >>chng 02 may 02, put in option to switch between Lennon Burke and Stafford et al. ,
         * default state of this var is true */
        cs21 = 2.722;
        cs31 = 0.3162;
        cs32 = 0.806;
 
        /* POP3(   G1,G2,G3,   O12,  O13,  O23,  A21, A31, A32,*/
        p3 = atom_pop3(  9.,5.,1.,  cs21, cs31, cs32, a21, a31, a32 ,
          /*   E12,E23,P2,ABUND,GAM2) */
          21955.,24982.,&p2,dense.xIonDense[ipNITROGEN][1],0.,0.,0.);
 
        nitro.c5755 = p3*a32*3.46e-12;
 
        nitro.c6584 = p2*a21*3.03e-12;
        thermal.dCooldT += nitro.c6584*(2.2e4*thermal.tsq1 - thermal.halfte);
        CoolAdd("N  2",5755,nitro.c5755);
        CoolAdd("N  2",6584,nitro.c6584);
 
        /* nitro.xN2_A3_tot is fraction of excitations that produce a photon 
         * and represents the correction for collisiona deexcitation */
        nitro.xN2_A3_tot = (a31+a32) /(a31+a32 + (cs31+cs32)/1.*dense.cdsqte );
        ASSERT( nitro.xN2_A3_tot <= 1. );
 
        /* N II fine structure lines, */
        /* >>chng 00 dec 11, to Lennon & Burke CS
        * >>refer       n2      cs      Hudson, C.E. & Bell, K.L. 2004, MNRAS, 348, 1275 and A&A, 430, 725
         */
        cs21 = 0.431;
        cs32 = 1.15;
        cs31 = 0.273;
 
        PutCS(cs21,TauLines[ipT205]);
        PutCS(cs32,TauLines[ipT122]);
        PutCS(cs31,*TauDummy);
        atom_level3(TauLines[ipT205],TauLines[ipT122],*TauDummy);
 
        /* N II 2140, data 
         * >>referold   n2      cs      Stafford, R.P., Bell, K.L, Hibbert, A. & Wijesundera, W.P. 1994, MNRAS, 268, 816
         * >>referold   n2      cs      Lennon, D.J., & Burke, V.M., 1994, A&AS, 103, 273-277
         * A from 
         * >>referold   n2      as      Brage, T., Hibbert, A., Leckrone, D.S. 1997, ApJ, 478, 423
         * >>refer      n2      as      Froese Fischer, C., & Tachiev, G. 2004, At. Data Nucl. Data Tables, 87, 1
         * >>refer      n2      cs      Hudson, C.E. & Bell, K.L. 2004, MNRAS, 348, 1275 and A&A, 430, 725
         */
        cs21 = 1.125;
 
        PutCS(cs21,TauLines[ipT2140]);
        atom_level2(TauLines[ipT2140]);
 
        /* N III 989.8, cs from 
         * >>refer      N3      cs      Blum, R.D., & Pradhan, A.K. 1992, ApJS 80, 425 */
        PutCS(7.12,TauLines[ipT990]);
        atom_level2(TauLines[ipT990]);
 
        /* 57 micron N III, A=
         * >>refer      n3      as      Froese Fischer, C. 1983, J.Phys. B, 16, 157
         * collision strength from 
         * >>refer      n3      cs      Blum, R.D., & Pradhan, A.K. 1992, ApJS 80, 425 */
        cs = MIN2(1.90,0.2291*phycon.te10*phycon.te10);
        PutCS(cs,TauLines[ipT57]);
 
        static vector< pair<TransitionList::iterator,double> > N3Pump;
        N3Pump.reserve(32);
 
        /* one time initialization if first call */
        if( N3Pump.empty() )
        {
                // set up level 1 pumping lines
                pair<TransitionList::iterator,double> ppa( TauLines.begin()+ipT990, 1./6. ); 
                N3Pump.push_back( ppa );
                pair<TransitionList::iterator,double> ppb( TauLines.begin()+ipT374g, 1./6. ); 
                N3Pump.push_back( ppb );
                pair<TransitionList::iterator,double> ppc( TauLines.begin()+ipT315, 1./6. ); 
                N3Pump.push_back( ppc );
                pair<TransitionList::iterator,double> ppd( TauLines.begin()+ipT324, 1./2. ); 
                N3Pump.push_back( ppd );
                pair<TransitionList::iterator,double> ppe( TauLines.begin()+ipT333, 2./3. ); 
                N3Pump.push_back( ppe );
                // set up level 2 pumping lines
                for( i=0; i < nWindLine; ++i )
                {
                        /* don't test on nelem==ipIRON since lines on physics, not C, scale */
                        if( (*TauLine2[i].Hi()).nelem() == 7 && (*TauLine2[i].Hi()).IonStg() == 3 )
                        {
#                               if      0
                                DumpLine( TauLine2.begin()+i );
#                               endif
                                double branch_ratio;
                                // the branching ratios used here ignore cascades via intermediate levels
                                // usually the latter are much slower, so this should be reasonable
                                if( fp_equal( (*TauLine2[i].Hi()).g(), realnum(2.) ) )
                                        branch_ratio = 2./3.; // 2S upper level
                                else if( fp_equal( (*TauLine2[i].Hi()).g(), realnum(6.) ) )
                                        branch_ratio = 1./2.; // 2P upper level
                                else if( fp_equal( (*TauLine2[i].Hi()).g(), realnum(10.) ) )
                                        branch_ratio = 1./6.; // 2D upper level
                                else
                                        TotalInsanity();
                                pair<TransitionList::iterator,double> pp2( TauLine2.begin()+i, branch_ratio ); 
                                N3Pump.push_back( pp2 );
                        }
                }
        }
 
        /* now sum pump rates */
        double pump_rate = 0.;
        vector< pair<TransitionList::iterator,double> >::const_iterator n3p;
        for( n3p=N3Pump.begin(); n3p != N3Pump.end(); ++n3p )
        {
                const TransitionList::iterator t = n3p->first;
                double branch_ratio = n3p->second;
                pump_rate += (*t).Emis().pump()*branch_ratio;
#               if      0
                dprintf( ioQQQ, "N III %.3e %.3e\n",
                         (*t).WLAng , (*t).Emis().pump()*branch_ratio );
#               endif
        }
 
        /* N III] N 3, N  3, 1765 multiplet */
        /*atom_level2(TauLines[ipT57]);*/
        /*AtomSeqBoron compute cooling from 5-level boron sequence model atom */
        AtomSeqBoron(TauLines[ipT57], 
          TauLines[ipN3_1749], 
          TauLines[ipN3_1747], 
          TauLines[ipN3_1754], 
          TauLines[ipN3_1752], 
          TauLines[ipN3_1751], 
          0.201 , 1.088 , 0.668 , 2.044 , pump_rate,"N  3");
        /*fprintf(ioQQQ," n4 %.3e\n",  (
                TauLines[ipN3_1749].xIntensity() + 
                TauLines[ipN3_1747].xIntensity() + 
                TauLines[ipN3_1754].xIntensity()+ 
                TauLines[ipN3_1752].xIntensity()+ 
                TauLines[ipN3_1751].xIntensity()) / dense.xIonDense[ipNITROGEN][2] );*/
 
        /* N IV 1486, N 4, N  4,collisions within 3P just guess
         * cs to ground from 
         * >>refer      n4      cs      Ramsbottom, C.A., Berrington, K.A., Hibbert, A., Bell, K.L. 1994,
         * >>refercon Physica Scripta, 50, 246 */
        if( phycon.te > 1.584e4 )
        {
                cs = 21.346/(phycon.te10*phycon.te10*phycon.te10*phycon.te02);
        }
        else
        {
                cs = 75.221/(phycon.sqrte/phycon.te03/phycon.te02);
        }
        /* >>chng 01 sep 09, AtomSeqBeryllium will reset this to 1/3 so critical density correct */
        cs = MAX2(0.01,cs);
        PutCS(cs,TauLines[ipT1486]);
        AtomSeqBeryllium(.9,.9,3.0,TauLines[ipT1486],.0115);
        embesq.em1486 = (realnum)(atoms.PopLevels[3]*0.0115*1.34e-11);
        /*fprintf(ioQQQ," n4 %.3e\n", (TauLines[ipT1486].xIntensity() + embesq.em1486 ) / dense.xIonDense[ipNITROGEN][3] );*/
 
        /* N IV 765, cs from 
         * >>refer      n4      cs      Ramsbottom, C.A., Berrington, K.A., Hibbert, A., Bell, K.L. 1994,
         * >>refercon Physica Scripta, 50, 246 */
        /* >>refer      n4      as      Flemming, J., Brage, T., Bell, K.L., Vaeck, N., Hibbert, A., 
         * >>refercon   Godefroid, M., & Froese Fischer, C., 1995, ApJ, 455, 758*/
        cs = MIN2(4.0,1.864*phycon.te03*phycon.te03);
        PutCS(cs,TauLines[ipT765]);
        atom_level2(TauLines[ipT765]);
 
        /* N V 1240
         * >>refer      n5      cs      Cochrane, D.M., & McWhirter, R.W.P. 1983, PhyS, 28, 25 */
        ligbar(7,TauLines[ipT1239],TauLines[ipT209],&cs2s2p,&cs2s3p);
        PutCS(cs2s2p,TauLines[ipT1239]);
        PutCS(cs2s2p*0.5,TauLines[ipT1243]);
        PutCS(1.0,*TauDummy);
        atom_level3(TauLines[ipT1243],*TauDummy,TauLines[ipT1239]);
        /*fprintf(ioQQQ," n5 %.3e\n", (TauLines[ipT1243].xIntensity() + TauLines[ipT1239].xIntensity() ) / dense.xIonDense[ipNITROGEN][4] );*/
 
        /* N V 209 */
        PutCS(cs2s3p,TauLines[ipT209]);
        atom_level2(TauLines[ipT209]);
        return;
}