/home66/gary/public_html/cloudy/c08_branch/source/helike_energy.cpp

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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 */
#include "cddefines.h"
#include "physconst.h" 
#include "iso.h"
#include "helike.h"

/*
  Energy order within 2 3P

  The order of the levels within the 2 3P level of atomic helium is opposite
  from the order within astrophysically abundant ions.  The indices below
  consistently point to the correct level, and the energies are correct,
  so the J levels within 2 3P are not in increasing energy order for helium itself. 
  This is ok since the atomic data is correct, and the difference in energies is so small.
*/

/* Ionization potentials (in wavenumber) for each ion in the iso-seq up to Z=30.
 * These are exactly what you get if you take EionRYD below and multiply by RYD_INF.    */
static double EionWN[LIMELM] =       
        /* the first, or H-like, element is not defined for he-like species */
        {-DBL_MAX,
        198310.6679     ,610003.839889137,1241136.72201499,2091948.45665631,3162116.52584231,
        4452446.95015668,5962133.81875305,7692790.05069734,9645221.44709864,11814589.7994457,
        14209766.0528639,16822685.5022862,19661412.9625169,22717883.6187518,26000162.0663204,
        29508248.5246975,33234078.1790787,37185715.7345311,41363161.0813172,45766414.4389118,
        50395475.4781030,55258409.0136949,60339085.8550283,65653635.1927626,71202056.8074231,
        76976286.4328920,82984388.3352872,89194104.5722390,95726403.3055320};

/* Ionization potentials (in Rydbergs) for each ion in the iso-seq up to Z=30.  
 * These are exactly what you get if you take Verner's numbers in atmdat_ph1(0,1,nelem,0) 
 * and multiply by (0.9998787/EVRYD), exactly as is done elsewhere in Cloudy.   */
static double EionRYD[LIMELM] =       
        /* the first, or H-like, element is not defined for he-like species */
        {-DBL_MAX,
        1.807387521,5.558764,11.310070,19.063237,28.815326,40.573682,54.330961,70.101861,
        87.893725,107.662464,129.488916,153.299590,179.167978,207.020588,236.930910,
        268.898946,302.851204,338.861175,376.928858,417.054255,459.237363,503.551674,
        549.850208,598.279945,648.840883,701.459535,756.209388,812.796486,872.323172};

/* experimental energies, in wavenumbers, for atomic helium */
#define NHE1LEVELS 111
/* These energies from Drake 1996, except these divided by c */
static double He1Energies[NHE1LEVELS] =
{0.0       , 159855.9734, 166277.4390, 169087.8298, 169086.8417, 169086.7652, 171134.8957,
183236.7908, 184864.8281, 185564.6657, 186101.5615, 186104.9656, 186209.3638, 190298.6619,
190940.6075, 191217.0826, 191444.4868, 191446.4547, 191451.8805, 191451.8964, 191492.7108,
193346.9900, 193663.5106, 193800.7280, 193917.1538, 193918.2888, 193921.1207, 193921.1298,
193921.6166, 193921.6209, 193942.4612, 194936.1184, 195114.8672, 195192.7542, 195260.0724,
195260.7694, 195262.4251, 195262.4307, 195262.7236, 195262.7261, 195262.7930, 195262.7947, 
195274.9074, 195868.2357, 195978.8938, 196027.3216, 196069.6730, 196070.1273, 196071.1763,
196071.1800, 196071.3686, 196071.3702, 196071.4141, 196071.4151, 196071.4283, 196071.4290,
196079.0865, 196461.3605, 196534.5628, 196566.7159, 196595.0620, 196595.3730, 196596.0785,
196596.0810, 196596.2092, 196596.2103, 196596.2404, 196596.2411, 196596.2503, 196596.2508,
196596.2541, 196596.2544, 196601.3992, 196861.9861, 196912.9014, 196935.3339, 196955.2261,
196955.4477, 196955.9445, 196955.9463, 196956.0373, 196956.0380, 196956.0595, 196956.0600,
196956.0666, 196956.0670, 196956.0693, 196956.0696, 196956.0705, 196956.0707, 196959.6917,
197145.2320, 197182.0643, 197198.3343, 197212.8252, 197212.9885, 197213.3513, 197213.3527,
197213.4194, 197213.4200, 197213.4358, 197213.4362, 197213.4411, 197213.4414, 197213.4431,
197213.4433, 197213.4440, 197213.4442, 197213.4445, 197213.4446, 197216.0885};
/* Last energy is 10^1P.        */

/* >>chng 05 sep 06, RP - update energies of excited states */
#define NIONLEVELS 31
/* These energies are from Chianti 5, up to 5^1P 
 * -1 is flag to use quantum defect routines instead 
 * >>refer He-like      Energies        Landi et al., 2005; ApJSS, in press 
 * >>refer He-like      Energies        Dere, K. P. et al. 1997, 
 * >>refercon    Astronomy and Astrophysics Suppl. Ser., Vol. 125, pp. 149-173 */
static double IonEnergies[LIMELM-2][NIONLEVELS] = 
{
/* ipLITHIUM=2; */
{0.00,  476034.98,      491374.60,      494266.57,      494261.17,      494263.44,      501808.59,
        554754.45,      558777.88,      559501.16,      561243.67,      561273.62,      561752.82,
        579981.33,      581596.77,      581886.34,      582613.64,      582630.95,      582642.97,
        582644.04,      582830.11,      591184.26,      591989.55,      592134.36,      592504.32,
        592514.43,      592520.11,      592521.11,      -1.00   ,       -1.00   ,       592634.91},
/* ipBERYLLIUM=3;*/
{0.00,  956502.00,      981178.00,      983366.00,      983355.00,      983370.00,      997454.00,
        1121184.00,     1127705.00,     1128300.00,     1131383.00,     1131462.00,     1132390.00,
        1175295.00,     1178005.00,     1178174.00,     1179451.00,     1179495.00,     1179515.00,
        1179514.00,     1179830.00,     1199650.00,     -1.00   ,       1201060.00,     1201702.00,
        1201800.00,     1201730.00,     1201742.00,     -1.00   ,       -1.00   ,       1201894.00},
/* ipBORON=4;*/
{0.00,  1601545.00,     1635720.00,     1636938.00,     1636922.00,     1636975.00,     1657980.00,
        1882740.00,     1891790.00,     1892221.00,     1896710.00,     1896836.00,     1898063.00,
        1976420.00,     -1.00   ,       1980291.11,     1982132.67,     1982220.00,     1982262.67,
        1982240.00,     1982762.00,     -1.00   ,       -1.00   ,       2020730.00,     2021700.00,
        -1.00   ,       2021665.71,     2021760.00,     2021770.00,     2021770.00,     2022044.00},
/* ipCARBON=5;*/
{0.00,  2411262.00,     2455024.00,     2455162.74,     2455150.23,     2455286.01,     2483371.00,
        2839562.00,     2851180.00,     2851418.00,     2857309.67,     2857529.00,     2859375.00,
        2983541.00,     -1.00   ,       2988359.00,     2990776.00,     2990923.00,     2990923.40,
        2990923.40,     2991710.00,     3048927.00,     -1.00   ,       3051332.00,     3052589.00,
        3052656.00,     3052653.30,     3052653.30,     3052659.40,     3052659.40,     3053044.00},
/* ipNITROGEN=6;*/
{0.00,  3385890.00,     3439274.00,     3438312.46,     3438321.13,     3438612.15,     3473790.00,
        3991860.00,     -1.00   ,       4006160.00,     4013460.00,     4013770.00,     4016390.00,
        4196800.00,     4202520.00,     4202620.00,     4205820.00,     4205830.00,     4205810.00,
        4205820.00,     4206810.00,     4290150.00,     4293020.00,     4293080.00,     4294570.00,
        4294670.00,     4294700.00,     4294700.00,     -1.00   ,       -1.00   ,       4296090.00},
/* ipOXYGEN=7;*/
{0.00,  4524640.00,     4588380.00,     4585620.76,     4585679.58,     4586231.19,     4629201.00,
        5338820.00,     5356420.00,     5355670.00,     5364422.67,     5365470.00,     5368550.00,
        5616340.00,     5623100.00,     5622600.00,     5626225.33,     5626670.00,     5626210.00,
        5626840.00,     5628100.00,     5742610.00,     -1.00   ,       5745440.00,     5747509.33,
        5748230.00,     5747200.00,     5747820.00,     -1.00   ,       -1.00   ,       5748450.00},
/* ipFLUORINE=8;*/
{0.00,  5830040.00,     5903100.00,     5900600.00,     5900750.00,     5901700.00,     5949900.00,
        6885090.00,     6903270.00,     6902560.00,     6914073.33,     6915900.00,     6916590.00,
        7244270.00,     -1.00   ,       7250390.00,     7255960.00,     7254240.00,     7256750.00,
        7257260.00,     7256370.00,     -1.00   ,       -1.00   ,       7410270.00,     7413940.00,
        7412290.00,     7414760.00,     7415300.00,     7414780.00,     -1.00   ,       7414000.00},
/* ipNEON=9;*/
{0.00,  7299940.00,     7382680.00,     7378205.53,     7378506.43,     7380050.00,     7436560.00,
        8623000.00,     8644880.00,     8644744.44,     8657128.67,     8662400.00,     8660530.00,
        9075200.00,     9084060.00,     9084141.11,     9090355.33,     -1.00   ,       9089800.00,
        9094400.00,     9090630.00,     9282200.00,     9286650.00,     9286713.33,     9288500.00,
        -1.00   ,       9289800.00,     9294400.00,     -1.00   ,       -1.00   ,       9290000.00},
/* ipSODIUM=10;*/
{0.00,  8935337.00,     9027981.00,     9022354.10,     9022876.10,     9025284.70,     9088700.00,
        10558946.00,    10583431.00,    10583323.56,    10596783.40,    10597475.00,    10601080.00,
        11115065.00,    11124986.00,    11125102.78,    11130639.00,    11131017.00,    11131051.00,
        11131056.00,    11132393.00,    11369887.00,    11374868.00,    11374959.89,    11377767.00,
        11377984.00,    11377987.00,    11377991.00,    -1.00   ,       -1.00   ,       11378646.00},
/* ipMAGNESIUM=11;*/
{0.00,  10736136.00,    10838778.00,    10831985.83,    10832819.18,    10836391.13,    10906612.00,
        12691170.00,    12718304.00,    12718286.89,    12733392.33,    12734298.00,    12738006.00,
        13361991.00,    13372977.00,    13373168.22,    13379472.60,    13379830.00,    13379893.00,
        13379898.00,    13381265.00,    13669618.00,    13675137.00,    13675269.22,    13678467.13,
        13678680.00,    -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       13679363.00},
/* ipALUMINIUM=12;*/
{0.00,  12703061.00,    12815760.00,    12807847.00,    12809088.00,    12814213.00,    12891081.00,
        15020463.00,    15050257.00,    15050434.00,    15067287.07,    15068371.00,    15072141.00,
        15816791.00,    15828851.00,    15829158.67,    15836125.13,    15836581.00,    -1.00   ,
        -1.00   ,       15838068.00,    16182216.00,    16188281.00,    16188471.33,    16192010.13,
        16192244.00,    -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       16192975.00},
/* ipSILICON=13;*/
{0.00,  14835945.00,    14958753.00,    14949756.42,    14951532.63,    14958690.57,    15042040.00,
        17546734.00,    17579166.00,    17579686.44,    17598406.93,    17599605.00,    17603422.00,
        18479389.00,    18492532.00,    18493007.56,    18500821.00,    18501245.00,    -1.00   ,
        -1.00   ,       18502736.00,    18907613.00,    18914246.00,    18914502.78,    18918476.30,
        18918694.00,    -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       18919421.00},
/* ipPHOSPHORUS=14;*/
{0.00,  17135768.00,    17268828.00,    17258746.00,    17261164.00,    17270908.00,    17360546.00,
        20271100.00,    20306284.00,    20307209.11,    20327865.87,    20329412.00,    20332952.00,
        21350958.00,    21365192.00,    21365892.89,    21374428.00,    21375044.00,    21375302.00,
        21375302.00,    21376454.00,    21846994.00,    21854144.00,    21854552.89,    21858894.80,
        21859210.00,    21859340.00,    21859340.00,    -1.00   ,       -1.00   ,       21859464.00},
/* ipSULPHUR=15;*/
{0.00,  19602076.00,    19745473.00,    19734297.61,    19737518.84,    19750576.04,    19846285.00,
        23193163.00,    23231087.00,    23232596.56,    23255347.53,    23257195.00,    23260416.00,
        24431101.00,    24446439.00,    24447429.78,    24456981.30,    24457576.00,    -1.00   ,
        -1.00   ,       24458842.00,    24999972.00,    25007605.00,    25008238.11,    25013102.40,
        25013407.00,    -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       25014007.00},
/* ipCHLORINE=16;*/
{0.00,  22236180.00,    22390000.00,    22377820.00,    22381940.00,    22399100.00,    22500680.00,
        26314360.00,    26355050.00,    26357324.44,    26382328.67,    26384530.00,    26387270.00,
        27720900.00,    27738000.00,    27738966.67,    27749520.00,    27750400.00,    27757331.14,
        27757178.00,    27751600.00,    28367700.00,    28376500.00,    28376977.78,    28382286.67,
        28382800.00,    -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       28383400.00},
/* ipARGON=17;*/
{0.00,  25038230.00,    25202480.00,    25189388.10,    25194588.99,    25216810.57,    25323950.00,
        29634850.00,    29678210.00,    29681541.11,    29713920.00,    29715070.00,    29713740.00,
        31221700.00,    31239280.00,    31241087.78,    -1.00   ,       -1.00   ,       -1.00   ,
        -1.00   ,       31254280.00,    31951370.00,    31960150.00,    31961182.22,    -1.00   ,
        -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       31967860.00},
/* ipPOTASSIUM=18;*/
{0.00,  28004980.00,    28180480.00,    28165880.00,    28172670.00,    28200800.00,    28312910.00,
        33151930.00,    33198090.00,    33202622.22,    -1.00   ,       -1.00   ,       33237140.00,
        -1.00   ,       34948420.00,    -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,
        -1.00   ,       34964920.00,    35747360.00,    35756712.00,    35758032.00,    -1.00   ,
        -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       35765192.00},
/* ipCALCIUM=19;*/
{0.00,  31142150.00,    31328450.00,    31312818.51,    31320486.08,    31356326.72,    31473810.00,
        36870940.00,    36919930.00,    36925900.00,    -1.00   ,       -1.00   ,       36962850.00,
        38850670.00,    38870530.00,    38873536.67,    -1.00   ,       -1.00   ,       -1.00   ,
        -1.00   ,       38888680.00,    39761380.00,    39771310.00,    39772968.89,    -1.00   ,
        -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       39780630.00},
/* ipSCANDIUM=20;*/
{0.00,  34448120.00,    34645360.00,    34628770.00,    34638550.00,    34682810.00,    34805000.00,
        40790620.00,    40842480.00,    40850158.89,    -1.00   ,       -1.00   ,       40889690.00,
        42983370.00,    43004390.00,    43008165.56,    -1.00   ,       -1.00   ,       -1.00   ,
        -1.00   ,       43024380.00,    43992240.00,    44002740.00,    44004803.33,    -1.00   ,
        -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       44013010.00},
/* ipTITANIUM=21;*/
{0.00,  37923880.00,    38131640.00,    38114760.00,    38125260.00,    38180620.00,    38308340.00,
        44911910.00,    44966970.00,    44976472.22,    45016028.67,    45021140.00,    45018670.00,
        47328500.00,    47351600.00,    47355644.44,    47372326.67,    47374500.00,    -1.00   ,
        -1.00   ,       47373500.00,    48440800.00,    48452600.00,    48454581.11,    -1.00   ,
        -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       48463700.00},
/* ipVANADIUM=22;*/
{0.00,  41568880.00,    41787830.00,    41770130.00,    41782100.00,    41849950.00,    41982380.00,
        49234710.00,    49292760.00,    49304574.44,    49347922.67,    49353910.00,    49349740.00,
        51886600.00,    51910900.00,    51915955.56,    51934113.33,    51936800.00,    -1.00   ,
        -1.00   ,       51935100.00,    53107300.00,    53119700.00,    53122217.78,    -1.00   ,
        -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       53132000.00},
/* ipCHROMIUM=23;*/
{0.00,  45384110.00,    45614410.00,    45595910.00,    45609360.00,    45691820.00,    45828830.00,
        53760100.00,    53821190.00,    53835660.00,    53883181.33,    53890160.00,    53884060.00,
        56658500.00,    56684100.00,    56690288.89,    56710306.67,    56713200.00,    -1.00   ,
        -1.00   ,       56710700.00,    57992700.00,    58005800.00,    58008904.44,    -1.00   ,
        -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       58019400.00},
/* ipMANGANESE=24;*/
{0.00,  49370240.00,    49612040.00,    49592800.00,    49607700.00,    49707130.00,    49848620.00,
        58488800.00,    58553000.00,    58570522.22,    58622620.00,    58630700.00,    58622500.00,
        61644700.00,    61671800.00,    61679233.33,    61701013.33,    61704700.00,    -1.00   ,
        -1.00   ,       61701200.00,    63097900.00,    63111600.00,    63115327.78,    -1.00   ,
        -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       63126600.00},
/* ipIRON=25;*/
{0.00,  53527760.00,    53781230.00,    53761280.00,    53777570.00,    53896550.00,    54042490.00,
        63421700.00,    63489000.00,    63509966.67,    63567120.00,    63576500.00,    63565800.00,
        66846900.00,    66875000.00,    66884011.11,    66908120.00,    66912100.00,    -1.00   ,
        -1.00   ,       66907600.00,    68423800.00,    68438100.00,    68442730.00,    -1.00   ,
        -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       68454800.00},
/* ipCOBALT=26;*/
{0.00,  57857380.00,    58122700.00,    58102090.00,    58119680.00,    58261180.00,    58411430.00,
        68560000.00,    68630600.00,    68655444.44,    68718160.00,    68728900.00,    68715500.00,
        72266000.00,    72295500.00,    72306144.44,    72332586.67,    72337100.00,    -1.00   ,
        -1.00   ,       72331500.00,    73972000.00,    73987000.00,    73992318.89,    -1.00   ,
        -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       74005400.00},
/* ipNICKEL=27;*/
{0.00,  62358960.00,    62637200.00,    62615022.80,    62633778.00,    62800884.44,    62952670.00,
        73903340.00,    73976370.00,    74005924.44,    -1.00   ,       -1.00   ,       74070580.00,
        77900890.00,    77930480.00,    77943808.89,    -1.00   ,       -1.00   ,       -1.00   ,
        -1.00   ,       77970500.00,    79740940.00,    79755710.00,    79762730.00,    -1.00   ,
        -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       79776290.00},
/* ipCOPPER=28;*/
{0.00,  67035380.00,    67324970.00,    67303150.00,    67322950.00,    67519170.00,    67678080.00,
        79453200.00,    79530300.00,    79564500.00,    79640046.67,    79654200.00,    79634300.00,
        83754400.00,    83786500.00,    83801155.56,    83832993.33,    83838900.00,    -1.00   ,
        -1.00   ,       83830600.00,    85734300.00,    85750700.00,    85759175.00,    -1.00   ,
        -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       85773200.00},
/* ipZINC=29;*/
{0.00,  71886300.00,    72188400.00,    72166200.00,    72186600.00,    72415600.00,    72579000.00,
        85212700.00,    85293200.00,    85332955.56,    85415826.67,    85431900.00,    85408300.00,
        89828600.00,    89862000.00,    89879022.22,    89913666.67,    89920800.00,    -1.00   ,
        -1.00   ,       89910900.00,    91953400.00,    91970500.00,    91979222.22,    91995073.33,
        92000500.00,    -1.00   ,       -1.00   ,       -1.00   ,       -1.00   ,       91994500.00}};

/* helike_quantum_defect - calculate quantum defect for a given level and nuclear charge. */
double helike_quantum_defect( long int nelem, long int ipLo )  
{  
        /* The quantum defect, and parameters a,b, and c        */
        double qd,a,b,c;        

        /* These are values of quantum defects of Helium levels at n=10. 
         * First dimension is spin, second is angular momentum.  
         * The defects are assumed to be constant for all n>10 and
         * equal to these values. */
        double HeDefectAsymptotes[2][10] = {
                {1.40005E-01,-1.20673E-02,2.08056E-03,4.21484E-04,1.14868E-04,
                        4.08648E-05,1.73548E-05,8.33891E-06,4.39680E-06,2.42075E-06},
                {2.97063E-01,6.81567E-02,2.82381E-03,4.27703E-04,1.17319E-04,
                        4.25254E-05,1.85549E-05,9.24641E-06,5.30882E-06,3.02877E-06}
        };

        /* Parameters for fits to quantum defects for   */
        /* P triplet and S orbitals. The dimensions are */
        /*      first: l                                                                        */
        /*      second: n                                                                       */
        /*      third: parameters a,b,and c.                            */
        double param[3][4][3]=  
        { 
                {{0.6451941,0.3119437,-1.2722842},              /* ^3S  */
                        {0.7664874,0.3455675,-1.3976462}, 
                        {0.8247101,0.3603131,-1.4520500}, 
                        {0.8878402,0.3714450,-1.4995732}}, 

                {{1.4203514,0.5311096,-2.6728087},              /* ^1S  */
                        {1.5733513,0.5997339,-2.9253834}, 
                        {1.4531025,0.5924751,-2.8662756}, 
                        {1.6038999,0.6342552,-3.0298071}}, 

                {{-2.2323488,0.0890840,-0.5166053},             /* ^3P  */
                        {-2.0463691,0.1222081,-0.6672983}, 
                        {-1.9904104,0.1328918,-0.7150879}, 
                        {-1.9500974,0.1452111,-0.7649031}} 
        };   

        /* Because they cannot be fit to a funtion of the same form as the other orbitals,
         * the P singlets are fit to a different function, with these parameters and dimensions */
        /*      first: n                                                                        */
        /*      second: parameters a and b.                                     */
        double P1[4][2]=
        {
                {-56.65245,-3.661923},
                {-52.03411,-4.941075},
                {-50.43744,-5.525750},
                {-49.45137,-5.908615}
        };

        long int n = StatesElem[ipHE_LIKE][nelem][ipLo].n;
        long int lqn = StatesElem[ipHE_LIKE][nelem][ipLo].l;
        long int S = StatesElem[ipHE_LIKE][nelem][ipLo].S;
        long int s;

        if( S==1 )
                s = 0;
        else if( S==3 )
                s = 1;
        else if( S < 0 )
        {
                ASSERT( n > iso.n_HighestResolved_max[ipHE_LIKE][nelem] );
                s = S;
        }
        else
                TotalInsanity();

        DEBUG_ENTRY( "helike_quantum_defect()" );

        ASSERT(n >= 1L);
        ASSERT(lqn >= 0 || n > iso.n_HighestResolved_max[ipHE_LIKE][nelem]);
        ASSERT(n > lqn);
        /* Only Helium and up, and only those turned on.        */
        ASSERT((nelem >= ipHELIUM) && (nelem < LIMELM));       

        if( n > iso.n_HighestResolved_max[ipHE_LIKE][nelem] )
        {
                /* collapsed levels are assumed to have zero quantum defect. */
                qd = 0.;
        }
        else if( nelem == ipHELIUM )
        {
                if( ipLo<NHE1LEVELS && n<=iso.n_HighestResolved_max[ipHE_LIKE][nelem] )
                {
                        /* defects are calculated from theoretical energies. */
                        qd = n-sqrt(0.999862926*RYD_INF/(EionWN[ipHELIUM] - He1Energies[ipLo]));
                } 
                else if( lqn<=9 )
                {
                        ASSERT( s >= 0 && lqn >= 0 );
                        /* defects are set equal to the values at n=10. */
                        qd = HeDefectAsymptotes[s][lqn];
                }
                else if( s == 0 )
                {
                        /* a simple fit for singlet high-l defects. */
                        qd = 0.0497*pow((double)lqn, -4.4303);
                }
                else
                {
                        /* a simple fit for triplet high-l defects. */
                        qd = 0.0656*pow((double)lqn, -4.5606);
                }
        }
        else if( ipLo == ipHe1s1S )
        {
                /* Quantum defects for ground state are found from the rydberg
                 * equation, and the ionization potential of the ion.   
                 * the lint needs to see assert and not ASSERT */
                ASSERT(nelem>ipHYDROGEN && nelem<LIMELM );
                qd = 1.0 - nelem * sqrt(1/EionRYD[nelem]);
        }
        else
        {
                /* For levels with n > 5, the quantum defect    */
                /* is approximately the same as if n equaled 5. */
                if( n > 5L )
                {
                        n = 5L;
                }
                /* For P singlets       */
                if( lqn==1L && s==0L )
                {
                        qd = 1./(P1[n-2][0] + P1[n-2][1] * (nelem+1) * log((double)nelem+1.) );
                }
                /* Defects for orbitals with l>2 are approximately equal to zero.       */
                else if( lqn < 2L )
                {
                        a = param[2*(lqn+1)-s-1][n-2][0];  
                        b = param[2*(lqn+1)-s-1][n-2][1];  
                        c = param[2*(lqn+1)-s-1][n-2][2];  
                        qd = exp((a+c*(nelem+1))/(1.0+b*(nelem+1)));  
                }
                /* This fit is a simplification of table 11.9 from 
                 * >>refer Helike       defects Drake, G.W.F., editor.  Atomic, Molecular & Optical Physics Handbook.
                 * >>refercon   Chapter 11, "High Precision Calculations for Helium", G.W.F. Drake. 
                 * >>refercon   AIP Press: Woodbury, New York, 1996
                 * This will give quasi-real energies for all transitions, allowing a reasonable
                 * determination of which decays are zeroed due to being below the plasma frequency.
                 * The 1/nelem dependence is arbitray.          */
                else
                {
                        ASSERT( lqn >= 2L );
                        qd = ( ( 0.0612/(double)nelem ) / pow((double)lqn, 4.44) );
                }
        } 
        return qd;
}

/*helike_energy calculates energy of a given level.     */
double helike_energy(long int nelem, long int ipLev )
{
        double Ef, Eff_n;
        long ipISO=ipHE_LIKE;

        DEBUG_ENTRY( "helike_energy()" );

        if( N_(ipLev) > iso.n_HighestResolved_max[ipISO][nelem] )
        {
                /* \todo        2       make this number a constant in physconst.h */
                /* The first term is the ratio of the helium finite mass rydberg
                 * to the infinite mass rydberg. */
                Ef = 0.999862926* RYD_INF * POW2((double)nelem/(double)N_(ipLev));  
        }
        else if( nelem==ipHELIUM && ipLev<NHE1LEVELS )
        {
                /* for atomic helium use experimental energies */
                Ef = EionWN[ipHELIUM] - He1Energies[ipLev];
        } 
        else if( nelem > ipHELIUM && nelem <= ipZINC &&
                ipLev < NIONLEVELS && IonEnergies[nelem-2][ipLev] >= 0. )
        {
                Ef = EionWN[nelem] - IonEnergies[nelem-2][ipLev];
        }
        else 
        {
                Eff_n = N_(ipLev) - helike_quantum_defect( nelem, ipLev );
                /* quantum defect can only be negative for singlet P */
                ASSERT( ( L_(ipLev)==1 && S_(ipLev)==1 ) || ( N_(ipLev) - Eff_n >= 0. ) );

                /* energies (in wavenumbers) that correspond to quantum defect */
                Ef = 0.999862926 * RYD_INF * POW2((double)nelem/Eff_n);
                Ef = 0.999862926 * RYD_INF * (nelem/Eff_n) * (nelem/Eff_n);  
        }

        ASSERT(Ef > 0.);

        return Ef;
}

---