/* 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 */ #include "cddefines.h" #include "physconst.h" #include "iso.h" #include "helike.h" #include "taulines.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 = iso_sp[ipHE_LIKE][nelem].st[ipLo].n(); long int lqn = iso_sp[ipHE_LIKE][nelem].st[ipLo].l(); long int S = iso_sp[ipHE_LIKE][nelem].st[ipLo].S(); long int s; if( S==1 ) s = 0; else if( S==3 ) s = 1; else if( S < 0 ) { ASSERT( n > iso_sp[ipHE_LIKE][nelem].n_HighestResolved_max ); s = S; } else TotalInsanity(); DEBUG_ENTRY( "helike_quantum_defect()" ); ASSERT(n >= 1L); ASSERT(lqn >= 0 || n > iso_sp[ipHE_LIKE][nelem].n_HighestResolved_max); ASSERT(n > lqn); /* Only Helium and up, and only those turned on. */ ASSERT((nelem >= ipHELIUM) && (nelem < LIMELM)); if( n > iso_sp[ipHE_LIKE][nelem].n_HighestResolved_max ) { /* collapsed levels are assumed to have zero quantum defect. */ qd = 0.; } else if( nelem == ipHELIUM ) { if( ipLo= 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 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_sp[ipISO][nelem].n_HighestResolved_max ) { /* \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 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; }