ORIGINAL PAPER

Fine-structure energy levels and radiative rates in Si-like chlorine

G P Gupta1, Vikas Tayal2* and A Z Msezane3

1Department of Physics, S. D. (Postgraduate) College, Muzaffarnagar 251 001, India

2Department of Physics, Dronacharya College of Engineering, Greater Noida 250 004, India

3Department of Physics and Center for Theoretical Studies of Physical Systems, Clark Atlanta University, Atlanta, GA 30314, USA

Received: 22 September 2010 / Accepted: 07 January 2011 / Published online: 29 February 2012

Abstract: Excitation energies and radiative rates for electric dipole (E1) transitions among the 86 fine-structure levels

belonging to the configurations (1s22s22p6)3s23p2, 3s3p3, 3s23p3d, 3p4, 3s23p4s, 3s23p4p, 3s3p2(2S)4s, 3s3p2(2P)4s,

3s3p2(4P)4s, 3s3p2(2D)4s, 3s23p4d and 3s23p4f of Cl IV are calculated using extensive configuration-interaction (CI) wave

functions obtained with the CIV3 computer code of Hibbert. The relativistic effects in intermediate coupling are incor-

porated by means of the Breit-Pauli Hamiltonian. In order to keep the calculated energy splittings close to the energy values

of the National Institute for Standards and Technology, we have made small adjustments to the diagonal elements of the

Hamiltonian matrices. Our calculated energy levels, including their orderings, are in excellent agreement with the available

NIST values. The mixing among several fine-structure levels is found to be very strong. From our radiative rates we have

also calculated radiative lifetimes of the fine-structure levels. Significant differences between our calculated lifetimes and

those from a sophisticated calculation for a few low lying levels are noted and discussed. In this calculation, we also predict

new data for several fine-structure levels where no other theoretical and/or experimental results are available.

Keywords: Atomic energy levels; Oscillator strengths; Transition probabilities; Lifetimes

PACS Nos.: 32.10.Fn; 32.70.Cs; 95.30.Ky

1. Introduction

Emission lines due to allowed and intercombination tran-

sitions in multiply charged Si-like ions are observed in

solar corona and laser produced plasma. The lines arising

from intercombination transitions, in particular, have been

shown to be very useful, for instance, in understanding

density fluctuations and elementary processes which occur

in both interstellar and laboratory plasmas. The excitation

energies and the radiative rates of these lines, needed for a

qualitative analysis of the spectra, are not well known. This

is mainly because these weak lines are usually sensitive to

the theoretical modeling and have been a challenge for the

atomic structure calculations. The study of these parame-

ters is also useful in many astrophysical applications and in

technical plasma modeling [1–3].

The study of atomic spectra and excited-state lifetimes

of Cl IV, a moderately ionized atomic system, may rep-

resent traditional testing grounds for electron-correlation

calculations of excited-state structures and, in particular, of

transition probabilities for heavy ions. Most of the exper-

imental and theoretical data of energy levels, oscillator

strengths, transition probabilities and lifetimes of the ions

of Si isoelectronic sequence, available in the literature, are

either limited to a few transitions among the terms

belonging to the 3s23p2, 3s3p3, and 3s23p3d configurations,

or lack accuracy. The calculations of these parameters for a

number of allowed and intercombination transitions in

Si-like ions have been previously studied [4–21].

Recently, Tayal et al. [21] calculated the excitation ener-

gies, oscillator strengths, transition probabilities for electric-

dipole-allowed and inter-combination transitions among the

(1s22s22p6)3s23p2(1S, 3P, 1D), 3s3p3(3,5So, 1,3Po, 1,3Do),

3s23p3d(1,3Po, 1,3Do, 1,3Fo), 3p4(1S, 3P, 1D), 3s23p4s(1,3Po),

3s23p4p(1,3S, 1,3P, 1,3D), 3s3p2(2S)4s(1S, 3S), 3s3p2(2P)4s(1P,3P), 3s3p2(4P)4s(3P, 5P), 3s3p2(2D)4s(1D, 3D), 3s23p4d(1,3Po,1,3Do, 1,3Fo) and 3s23p4f(1,3D, 1,3F, 1,3G) states and the

� 2012 IACS

Electronic supplementary material The online version of thisarticle (doi:10.1007/s12648-012-0006-5) contains supplementarymaterial, which is available to authorized users.

*Corresponding author, E-mail: tayalvikas11@rediffmail.com

Indian J Phys (January 2012) 86(1):1–8

DOI 10.1007/s12648-012-0006-5

radiative lifetimes of some of the levels of Ar V in both LS and

intermediate-coupling schemes using the configuration-

interaction code [22] and the Breit-Pauli Hamiltonian [23]. In

this article, we have extended our calculation of these

parameters for Si-like chlorine in intermediate-coupling

schemes only to compare with the other existing data.

2. Choice of radial wave functions and configurations

The 46 LS states belonging to the (1s22s22p6)3s23p2, 3s3p3,

3s23p3d, 3p4, 3s23p4s, 3s23p4p, 3s3p2(2S)4s, 3s3p2(2P)4s,

3s3p2(4P)4s, 3s3p2(2D)4s, 3s23p4d and 3s23p4f configura-

tions of Cl IV give rise to 86 fine-structure levels corre-

sponding to various J values, see Table 1. The atomic state

wave functions are represented by the J-dependent CI

expansions of the form [23]

WiðJMJÞ ¼XK

j¼1

bij/j ajLjSjJMJ

� �; ð1Þ

where each of the j single-configuration functions, /j is

constructed from one-electron functions and aj defines the

coupling of the orbital Lj and the spin Sj angular momenta to

give the total angular momentum J. The mixing coefficients

bij are the eigenvector components of the Hamiltonian

matrix h/i Hj j/ji with the basis /j [23]. The Hamiltonian

represents the non-relativistic electrostatic interactions plus

the Breit-Pauli terms such as one-body mass correction,

Darwin term, and spin–orbit, spin-other-orbit, and spin–

spin operators. The inclusion of mass correction and Darwin

terms shifts the energy of a configuration as a whole while

the spin–orbit and spin-other-orbit terms cause the fine-

structure splitting. The spin–spin term contributes both to

the energy of the configuration as well as to the fine-

structure splitting. In order to determine the configuration

mixing, it is desirable to include spin–orbit, spin-other-

orbit, and spin–spin terms in the total Hamiltonian even for

low Z. The explicit form of the Breit-Pauli Hamiltonian is

given in Eqs. 7–14 in the paper of Glass and Hibbert [23].

The complete description of individual terms of the Breit-

Pauli Hamiltonian can be found in chapter 7 of the book of

written by Froese Fischer et al. [24], and references therein.

The radial parts of the one-electron functions are

expressed in analytic form as a sum of Slater-type orbitals

PnlðrÞ ¼Xk

j¼1

Cjnl vjnlðrÞ; n [ l ð2Þ

where

vjnlðrÞ ¼2njnl

� �2Ijnlþ1

2Ijnl

� �!

" #12

rIjnl exp �njnlr� �

ð3Þ

and

Z1

0

PnlðrÞPn0lðrÞdr ¼ dnn0 ; lþ 1� n0 � n; ð4Þ

n and l are the principal and orbital quantum numbers,

respectively. The parameters Cjnl, njnl and Ijnl in Eqs. 2 and

3 are the expansion coefficients, exponents, and powers of

r, respectively, of the radial functions. In the optimization

process the parameters, namely the coefficients (Cjnl) and

the exponents (njnl) are determined variationally as

described by Hibbert [22] while Ijnl, being integral powers,

are generally kept fixed. The wave functions given by

Eq. 1 are then used to calculate the excitation energies of

the fine-structure levels, length and velocity forms of the

oscillator strengths, and transition probabilities among the

fine-structure levels.

The radiative lifetime of an excited state is related to the

radiative transition probabilities Aji as [25]

sj ¼ 1=RiAji; ð5Þ

where the sum over i is over all accessible final states and

DE (=Ej-Ei), is the transition energy.

3. Results and discussion

In our calculations, we have used 15 orthogonal one-

electron orbitals up to n = 5. The 1s, 2s, 2p, 3s, and

3p radial functions are chosen as the Hartree–Fock (HF)

functions of the ground state (1s22s22p6)3s23p2 of Cl IV

given by Clementi and Roetti [26] and the remaining radial

functions have been obtained using the CIV3 computer

code of Hibbert [22]. The 3d, 4s, 4p, 4d, and 4f functions

are chosen as spectroscopic-type and are optimized on the

excited states 3s23p3d(3Po), 3s23p4s(3Po), 3s23p4p(3P),

3s23p4d(3Do), and 3s23p4f(3F), respectively. The 5s, 5p,

5d, 5f, and 5g orbitals are chosen as correlation-type and

optimized on the excited states to minimize the energies of

the 3s23p4s(1Po), 3s3p3(3Po), 3s23p3d(1Po), 3s23p3d(3Po),

and 3s23p3d(1Po) states, respectively. In order to represent

all the energy levels by a single set of orthogonal functions,

it is necessary to use the correlation functions in addition to

the spectroscopic functions. In all the cases we have chosen

k = n - l so that the coefficients Cjnl are uniquely speci-

fied by the orthogonality condition on Pnl [22].

In Table 1, our calculated fine-structure excitation ener-

gies relative to the ground level are compared with the

compiled energy values of the National Institute for stan-

dards and Technology (NIST) [27], which are available at

http://physics.nist.gov/PhysRefData/ASD/levels_form.html.

For comparison, we have also included the multi-configu-

ration Hartree–Fock (MCHF) results of Froese Fischer et al.

2 G. P. Gupta et al.

Table 1 Fine-structure energy levels (in cm-1) of Cl IV relative to the ground level

Key Level J Present calculation NIST MCHF

(a) (b)

1 3s23p2 3P 0 0.0 0.0 0.0 0.0

2 1 431.2 488.9 492.0 448.92

3 2 1188.0 1332.9 1341.9 1217.08

4 1D 2 14835.7 13831.0 13767.6 13949.90

5 1S 0 33528.5 32623.5 32547.8 32924.00

6 3s3p3 5S� 2 68368.1 65051.0 65000.0 70738.61

7 3D� 1 102164.5 102016.3 102752.0 102060.49

8 2 102193.8 102053.2 102787.0 102094.24

9 3 102255.8 102138.6 102869.0 102165.40

10 3P� 2 121023.9 119840.9 120256.0 119922.94

11 1 121055.8 119877.8 120274.0 119962.06

12 0 121069.2 119911.3 120300.0 119967.03

13 3s23p3d 1D� 2 129855.9 129581.3 129340.0 129356.77

14 3F� 2 156684.0 156684.9 155104.63

15 3 157099.3 157099.3 155532.84

16 4 157669.4 157670.3 156122.05

17 3s3p3 3S� 1 168331.6 164975.9 164721.0 167134.17

18 1P� 1 171313.8 167835.1 166742.0 168057.84

19 3s23p3d 3P� 2 185303.9 182309.1 181643.0 182916.49

20 1 185641.3 182706.8 182073.0 183273.72

21 0 185817.9 182925.3 182300.0 183463.49

22 3D� 1 191322.7 187970.4 187008.0 188547.47

23 2 191480.1 188134.5 187174.0 188716.58

24 3 191635.8 188299.5 187346.0 188880.42

25 3s3p3 1D� 2 192967.9 192749.3 189684.72

26 3s23p3d 1F� 3 207888.1 207887.3 204713.25

27 1P� 1 215546.2 214782.7 212315.53

28 3s23p4s 3P� 0 216860.7 215127.6 215026.0 215867.54

29 1 217193.1 215491.8 215389.3 216216.21

30 2 218066.3 216554.3 216468.1 217177.08

31 1P� 1 221557.6 219579.2 219454.0 220618.75

32 3p4 1D 2 231410.9 231404.2 230432.02

33 3s23p4p 1P 1 246579.8 246481.9 244837.15

34 3D 1 249995.7 247830.6 247575.4 247623.86

35 2 250387.5 248188.1 248026.2 248042.48

36 3 251142.7 249101.5 248961.2 248884.70

37 3P 0 252694.1 251572.2 251471.4 251300.88

38 1 252883.3 251875.3 251725.8 251528.80

39 2 253484.4 252478.1 252396.7 252125.89

40 3S 1 254079.7 254021.1 253140.84

41 1D 2 259657.3 259652.3 257254.53

42 1S 0 271031.9 271007.7 262372.99

43 3p4 3P 2 272829.5 272830.3 271305.18

44 1 273423.9 273424.7 271918.51

45 0 273758.8 273758.8 272257.66

46 3s3p2(4P)4s 5P 1 297290.8 292278.3 292150.0

47 2 297716.9 292785.7 292660.0

Fine-structure energy levels 3

[19]. In general, our ab initio calculation, denoted ‘‘Present

(a),’’ agree within 3.0% with the corresponding NIST results,

except for the levels 3s23p2(3P1,2 and 1D2) where the dif-

ferences are within 7–12%. In order to keep our ab initio

energies as close as possible to the NIST values, we have

made small J-dependent adjustments to the diagonal

elements of the Hamiltonian matrices. These adjustments

improve the accuracy of the mixing coefficients bij of Eq. 1,

which depends, partly on the accuracy of the eigenvalues.

This is a fine-tuning technique [28] that has been further

Table 1 continued

Key Level J Present calculation NIST MCHF

(a) (b)

48 3 298334.8 293522.4 293400.0

49 3s23p4d 1D� 2 296040.8 296039.9

50 3F� 2 297454.9 297455.7

51 3 297698.5 297699.3

52 3D� 1 298179.9 298182.4

53 3F� 4 298465.4 298466.2

54 3D� 2 298471.2 298473.8

55 3 298775.2 298777.7

56 3P0 2 300967.9 300964.5

57 1 301281.8 301278.5

58 0 301453.5 301449.3

59 1F� 3 304636.6 304637.4

60 1P� 1 306188.8 306166.2

61 3s23p4f 3F 2 307793.0 307793.8

62 3 307923.6 307924.4

63 4 308129.5 308130.4

64 3s3p2(4P)4s 3P 0 309999.1 309980.7

65 1 310347.3 310329.8

66 2 311012.1 310995.4

67 3s23p4f 1F 3 314379.4 314380.3

68 3D 2 315404.2 315404.2

69 1G 4 317740.1 317740.9

70 1D 2 318834.3 318831.8

71 3G 3 319283.1 319283.9

72 4 319746.9 319747.7

73 5 320150.5 320151.3

74 3s3p2(2D)4s 3D 1 330388.9 330383.1

75 2 330404.0 330397.3

76 3 330422.4 330415.7

77 3s23p4f 3D 3 334238.5 334236.8

78 1 334790.2 334788.6

79 3p4 1S 0 338485.8 338484.9

80 3s3p2(2D)4s 1D 2 340152.7 340152.7

81 3s3p2(2S)4s 3S 1 364821.2 364821.7

82 1S 0 373315.3 373315.3

83 3s3p2(2P)4s 3P 0 378960.8 378956.6

84 1 379119.8 379115.7

85 2 379650.7 379646.5

86 1P 1 382482.2 382483.0

Present (a) ab initio calculation; Present (b) Adjusted energy calculation; NIST National Institute for standards and Technology [27]; MCHFmulti-configuration Hartree–Fock results of Froese Fischer et al. [19]

4 G. P. Gupta et al.

Table 2 Comparison of our present (corresponding to adjusted energy values) oscillator strengths (dimensionless) and transition probabilities

(in s-1) for some transition in Cl IV with other available data (a ± b : a 9 10±b)

Transitions Present MCHF RQDO MCDF HFR

fL AL f A f A f f

1 20 0.805 5.97 ? 09 0.808 6.033 ? 09 0.483 3.539 ? 09 0.632 0.821

1 22 1.410 1.10 ? 10 1.406 1.112 ? 10 1.486 1.148 ? 10 1.616 1.370

1 29 0.118 1.22 ? 09 0.136 1.419 ? 09 0.194 1.987 ? 09

2 19 0.377 4.99 ? 09 0.375 4.998 ? 09 0.201 2.620 ? 09 0.561 0.391

2 20 0.130 2.88 ? 09 0.131 2.920 ? 09 0.121 2.638 ? 09 0.146 0.121

2 21 0.224 1.49 ? 10 0.221 1.478 ? 10 0.161 1.059 ? 10 0.203 0.220

2 22 0.422 9.89 ? 09 0.424 1.001 ? 10 0.371 8.559 ? 09 0.354 0.425

2 23 1.060 1.49 ? 10 1.052 1.492 ? 10 1.150 1.545 ? 10 1.078 1.020

2 28 0.040 3.68 ? 09 0.046 4.237 ? 09 0.065 5.982 ? 09

2 29 0.029 8.94 ? 08 0.034 1.050 ? 09 0.049 1.489 ? 09

2 30 0.051 9.43 ? 08 0.058 1.097 ? 09 0.079 1.470 ? 09

3 19 0.444 9.70 ? 09 0.435 9.581 ? 09 0.361 7.779 ? 09 0.289 0.423

3 20 0.164 6.00 ? 09 0.156 5.764 ? 09 0.121 4.352 ? 09 0.154 0.158

3 22 0.023 9.03 ? 08 0.024 9.194 ? 08 0.015 5.651 ? 08 0.011 0.025

3 23 0.290 6.76 ? 09 0.292 6.857 ? 09 0.223 5.098 ? 09 0.264 0.299

3 24 1.300 2.16 ? 10 1.302 2.184 ? 10 1.249 2.045 ? 10 1.269 1.290

3 29 0.030 1.51 ? 09 0.035 1.778 ? 09 0.049 2.480 ? 09

3 30 0.091 2.80 ? 09 0.105 3.261 ? 09 0.144 4.405 ? 09

4 31 0.128 6.02 ? 09 0.145 6.884 ? 09 0.166 7.764 ? 09

5 31 0.525 4.08 ? 09 0.408 3.192 ? 09 1.673 1.291 ? 10

19 34 0.0004 1.73 ? 06 0.0001 4.755 ? 06

19 35 0.0001 3.78 ? 05 0.0016 1.983 ? 07

19 36 0.0017 3.65 ? 06 0.0092 1.983 ? 07

19 38 0.034 1.83 ? 08 0.037 1.944 ? 08 0.045 2.426 ? 08

19 39 0.049 1.60 ? 08 0.043 1.383 ? 08 0.135 4.491 ? 08

20 34 0.00005 1.40 ? 05 0.0027 1.403 ? 07

20 35 0.0028 4.82 ? 06 0.0081 5.177 ? 06

20 37 0.0289 2.74 ? 08 0.0264 2.441 ? 08 0.059 5.671 ? 08

20 38 0.0076 2.44 ? 07 0.0037 1.156 ? 07 0.0446 1.433 ? 08

20 39 0.0280 5.47 ? 07 0.0255 4.843 ? 07 0.075 1.475 ? 08

21 34 0.0029 2.70 ? 06 0.0107 1.009 ? 07

21 38 0.0531 5.61 ? 07 0.0387 3.985 ? 07 0.178 1.896 ? 08

22 34 0.0135 3.22 ? 07 0.0142 3.312 ? 07 0.030 7.177 ? 07

22 35 0.0051 7.44 ? 06 0.0050 7.128 ? 06 0.010 1.453 ? 07

22 37 0.0364 2.95 ? 08 0.0351 2.769 ? 08 0.064 5.276 ? 08

22 38 0.0347 9.45 ? 07 0.0320 8.466 ? 07 0.048 1.326 ? 08

22 39 0.0039 6.51 ? 06 0.0038 6.182 ? 06 0.003 5.384 ? 06

23 34 0.005 1.98 ? 07 0.005 1.997 ? 07 0.0059 2.380 ? 07

23 35 0.015 3.62 ? 07 0.014 3.259 ? 07 0.0273 6.694 ? 07

23 36 0.0034 6.10 ? 06 0.0035 5.989 ? 06 0.0061 1.098 ? 07

23 38 0.0453 2.05 ? 08 0.0408 1.789 ? 08 0.0861 3.962 ? 08

23 39 0.0269 7.43 ? 07 0.0261 6.998 ? 07 0.0285 8.039 ? 07

24 35 0.0046 1.53 ? 07 0.0047 1.526 ? 07 0.0044 1.492 ? 07

24 36 0.0226 5.56 ? 07 0.0216 5.175 ? 07 0.0347 8.741 ? 07

24 39 0.0717 2.76 ? 08 0.0686 2.561 ? 08 0.1142 4.820 ? 08

28 34 0.515 1.22 ? 08 0.454 1.018 ? 08 0.529

Fine-structure energy levels 5

justified in a paper on Na III [29] and most recently on Cl I

[30]. These adjustments also affect the composition of the

eigenvectors slightly. In a way, they rectify the ab initio

approach for the neglected core-valence correlation, which

has been shown to contribute significantly in neutral mag-

nesium (see, for instance: Jonsson et al. [31]). Our adjusted

theoretical energies, (Present (b)) are also listed in Table 1

and are in much better agreement (lesser than 1%) with the

NIST levels, including levels 3s23p2(3P1,2 and 1D2). We have

arranged our adjusted energy levels in ascending order.

In our CIV3 calculation, we identify the levels by their

dominant eigenvector [32]. As can be seen, the two levels

3s23p3d(1D2) and 3s3p3(1D2) mix very strongly

3s3p3 1D2

� �¼ 0:7197 52%ð Þ3s3p3 þ 0:6419 41%ð Þ3s23p3d

3s23p3d 1D2

� �¼ 0:7294 53%ð Þ3s23p3d

þ 0:6403 41%ð Þ3s3p3

Perhaps due to this enormous mixing the level

3s23p3d(1D2) in the NIST data appears to be designated

as level 3s3p3(1D2) when compared with the two

calculations. It may be mentioned that the level

3s23p3d(1D2) is missing in the NIST data. We have now

redesignated in the NIST data the 3s3p3(1D2) level as

3s23p3d(1D2) and obtained good agreement between the

NIST data set and the two calculations. The calculated

results of Froese Fischer et al. [19], for the levels

3s23p2(3P1,2), differ by 10% from the NIST data and are

closer to our ab initio values (Present (a)). However, for

other levels their results are closer to the NIST values as

well as to our adjusted energy levels. As seen from the

Table 1, large gaps in the NIST and calculated, particularly

in the latter, energy levels exist, thereby justifying the

present calculation further. Beyond level number 48 there

are no theoretical energy values other than the present

ones.

In Table 2, we report our calculated oscillator strengths

(fL) and transition probabilities (AL) for only those transi-

tions for which the results of other calculations are avail-

able to compare with our calculations. In calculating these

parameters, we used our adjusted theoretical energy split-

tings, corresponding to the ‘‘Present (b)’’ in Table 1. Our

results for fL and AL are compared with the multi-config-

uration Hartree–Fock (MCHF) calculation of Froese

Fischer et al. [19] and the relativistic quantum defect

orbital (RQDO) calculation of Charro and Martın [15].

Also for a few transitions, multi-configuration Dirac–Fock

(MCDF) calculation of Huang [9] and the relativistic

Hartree–Fock (HFR) calculation of Fawcett [10], for dif-

ferent oscillator strengths (f), are available to compare with

our calculation. It is seen that our results are in excellent

agreement with the f-values of Fawcett [10]. Also for the

strong transitions, our calculations are in good agreement

with the theoretical results of Froese Fischer et al. [19],

Charro and Martın [15], and Huang [9]. However, for

relatively weaker transitions, the two calculation,

(1) RQDO calculation of Charro and Martın [15] and

(2) MCDF calculation of Huang [9], differ significantly

with all other available calculations.

In this calculation, for all strong dipole-allowed transi-

tions there is good agreement between the length and

velocity values of the oscillator strengths. Also, for some

levels where strong mixing between singlets and triplets

exists, intercombination lines are comparable to allowed

transitions, so there is reasonably good agreement between

the fL and fV values for these transitions. However,

Table 2 continued

Transitions Present MCHF RQDO MCDF HFR

fL AL f A f A f f

28 38 0.325 9.76 ? 07 0.287 8.106 ? 07 0.352

29 34 0.084 5.85 ? 07 0.078 5.146 ? 07 0.131

29 35 0.398 1.70 ? 08 0.337 1.368 ? 08 0.399

29 37 0.102 2.66 ? 08 0.087 2.144 ? 08 0.116

29 38 0.120 1.06 ? 08 0.115 9.586 ? 07 0.087

29 39 0.100 5.45 ? 07 0.083 4.298 ? 07 0.148

30 34 0.003 3.36 ? 06 0.005

30 35 0.058 3.84 ? 07 0.046 2.902 ? 07 0.078

30 36 0.426 2.15 ? 08 0.350 1.677 ? 08 0.449

30 38 0.048 6.67 ? 07 0.030 3.922 ? 07 0.086

30 39 0.253 2.17 ? 08 0.213 1.740 ? 08 0.262

Present: adjusted energy calculation; MCHF multi-configuration Hartree–Fock calculation of Froese Fischer et al. [19]; RQDO relativistic

quantum defect orbital calculation of Charro and Martın [15]; MCDF multi-configuration Dirac–Fock calculation of Huang [9]; HFR relativistic

Hartree–Fock calculation of Fawcett [10]

6 G. P. Gupta et al.

the magnitudes of the oscillator strengths for many inter-

combination transitions are smaller by several orders of

magnitude than those for allowed transitions and there is a

significant difference between the fL and fV values for

many of these transitions. For intercombination lines to

have length and velocity in agreement, additional relativ-

istic operators need be added to the velocity form. This is

not included in CIV3 and that is why often intercombina-

tion lines do not have these forms in agreement. In such

cases the length form of our oscillator strength is recom-

mended since it remains stable with respect to the addition

of more and more configurations.

In Table 3, our calculated lifetimes (in seconds) for

several fine-structure levels are compared with the multi-

configuration Hartree–Fock (MCHF) results of Froese

Fischer et al. [19]. For the low lying levels 3s3p3(5S,3P,3D),

our results show significant disagreement (18–45%) with

the MCHF calculations [19]. However, for other levels

there is reasonably good agreement (within 7%) between

the two calculations except for the level 3s23p3d(1D2) for

which the difference is about 15%. These differences in

the lifetimes between the two calculations may be due to

the significant differences in the energy values [19] of the

levels belonging to the configuration 3s23p2. It is worth

mentioning here that for these levels, our energy values

are in excellent agreement (within 1%) with the NIST

values.

4. Summary and conclusion

In summary, we have carried out extensive CI calculations

of excitation energies, oscillator strengths, and transition

probabilities among the levels belonging to the (1s22s2

2p6)3s23p2, 3s3p3, 3s23p3d, 3p4, 3s23p4s, 3s23p4p, 3s3p2

(2S)4s, 3s3p2(2P)4s, 3s3p2(4P)4s, 3s3p2(2D)4s, 3s23p4d and

3s23p4f configurations of Cl IV. In our calculation, we have

used an extensive set of CI wave functions and included

correlation effects in the excitation up to the 5g orbital. Our

calculated excitation energies, covering the eighty six fine-

structure levels, are in excellent agreement with the

available compiled energy values of the NIST. Also, our

calculated wavelengths and absorption oscillator strengths,

for most of the strong transitions, are in good agreement

with the other available theoretical results. However, for

some relatively weaker transitions there are noticeable

differences among all the calculations. Significant differ-

ences between our calculated lifetimes and those of Froese

Fisher et al. [19], for few low lying levels, are noticed and

discussed. In conclusion, we believe that the present results

are the most extensive and definitive to date and will be

useful in many astrophysical applications and in technical

plasma modeling.

Acknowledgments This research is supported by the Division of

Chemical Sciences, Office of Basic Energy Sciences, Office of

Energy Research, United States Department of Energy (AZM).

Table 3 Comparison of present (corresponding to adjusted energy

values) lifetimes (in seconds) of some fine-structure levels with other

results (a ± b : a 9 10±b)

Conf. Term J Present MCHF

3s3p3 5S� 2 3.73–05 2.06–053D� 1 9.64–09 6.60–09

2 9.73–09 6.67–09

3 9.91–09 6.81–093P� 2 2.31–09 1.86–09

1 2.23–09 1.82–09

0 2.20–09 1.80–09

3s23p3d 1D� 2 2.72–09 2.30–093F� 2 4.31–07 4.19–07

3 3.97–07 4.27–07

3s3p3 3S� 1 5.92–11 6.33–111P� 1 1.15–10 1.20–10

3s23p3d 3P� 2 6.80–11 6.85–11

1 6.73–11 6.79–11

0 6.70–11 6.76–113D� 1 4.58–11 4.54–11

2 4.61–11 4.56–11

3 4.63–11 4.58–11

3s3p3 1D� 2 4.99–11 5.25–11

3s23p3d 1F� 3 4.20–11 4.34–111P� 1 6.12–11 5.79–11

3s23p4s 3P� 0 2.72–10 2.36–10

1 2.34–10 2.27–10

2 2.67–10 2.29–101P� 1 9.88–11 9.88–11

3s23p4 1D 2 1.82–09 1.67–09

3s23p4p 1P 1 8.72–10 8.55–103D 1 7.48–10 6.82–10

2 7.32–10 6.77–10

3 7.28–10 6.75–103P 0 5.85–10 6.02–10

1 5.83–10 6.02–10

2 5.80–10 5.97–103S 1 6.03–10 6.44–101D 2 7.89–10 9.38–101S 0 2.57–09 2.89–09

3s23p4 3P 2 8.02–11 8.52–11

1 7.99–11 8.48–11

0 8.04–11 8.53–11

Present: adjusted energy calculation; MCHF multi-configuration

Hartree–Fock results of Froese Fischer et al. [19]

Fine-structure energy levels 7

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