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Indian Joual of Chemistry Vol.39A, Jan-March 20 , pp.40-47 Excited states of highly stripped ions B Saha, T K Mukherjee, A K Das & P K Mukherjee* Department of Spectroscopy, Indian Association for the Cultivation of Science Calcutta 7 032, India Received 15 November 1 999; accepted 2 December 1 999 Time-dependent perturbation theory (TDPT) has been very successful in predicting the positions of the excited energy levels of atomic and molecular systems. TD can be associated with dirent formalis ms to yield results of different degrees of accuracy. The method was original ly used to predict structure properties connected with single excitations. However, later developments show its potentiality towards evaluation of atomic data connected with double and multiple excitations. In the present context we have used TDPT within a variational framework to calculate singly and doubly excited energy levels of several highly stripped ions of different electronic configurations and estimated their transition properties like osci l lator strengths, transition probabilities, etc. A free atom or ion is subjected to a time-dependent exteal harmonic field and the linear response properties of the atom are evaluated. The effect of the exteal field is to generate single or multiple excitation of the electronic charge cIo]ld. Depending upon the nature of the perturbing field one can get al lowed as well as forbidden transitions involving spatial and spin symmetries. The positions of the excited energy levels and analytic representations of their wave functions are directly obtained from our formalism by analyzing the positions of the poles of an appropriately constructed linearised variational functional with respect to exteal frequency. Transition energies and other structural parameters agree wel l with existing data wherever avai lable. 1. Introduction Spectroscopic studies of highly stripped ions have be- come very important in recent years because on one hand, (i) experiments i nvolvi ng satellites like IUE, Copeicus, YOHKOH, Hubble space teles c ope, etc., have provided wealth of information about the presence of various ki nds of such ions with wide range of electronic configurati"lls in the spectra of solar flare and corona l.\ (ii) recent developments i n laboratory experiments for the spectra of such ions in Tokamaks, laser pro- duced plasmas and beam foi l spectroscopic mea- surements yield huge amount of such atomic data 2 . 4 -7. (iii) investigations o n doubly excited states of highly stripped ions by photo-absorption, ionization and other col lision experiments x . ,o , double photo-ab- sorption ", double excitation of two-electron io ns at intermediate velocities 1 2 and double capture of electrons by bare nuclei at low velocities J 3 yield data on excited states of atoms. On the other hand, spectral lines of the highly stripped ions of various iso-electronic sequence are useful for the diagnostic determination of high temperature plasmas occurring in astrophysics, laboratory tokamaks or laser produced plasmas. Atomic data needed for such pur- pose are the transition energies, oscil lator strengths, trrul- sition probabilities, io nization and recombination rates, etc. Besides, such data which are useful for the study of stel lar opacity goveed by the bound-bound and bound- free transitions of the constituent atomic ions, are also needed for the theory of stel lar structure and pulsations, radiative power loss studies in f usion reactors, in testi ng the empirical mode of solar photosphere, to derive ac- curate values of microturbulence and to test local ther- modynamic equilibriaI4.19• In addition to optical ly al lowed transition, forbidden transitio ns in neutral atoms and their highly stripped iso� electronic ions are useful for the diagnostic determi na- tion of electron density and temperature i n solar co- rona, falres and in gaseous nebulae 1 4 .2 0. 22 . The wave- length of the forbidden lines relative to those of the al- lowed lines make them very good candidates for the

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  • Indian Journal of Chemistry Vol.39A, Jan-March 2000, pp.40-47

    Excited states of highly stripped ions

    B Saha, T K Mukherjee, A K Das & P K Mukherjee* Department of Spectroscopy, Indian Association for the Cultivation of Science

    Calcutta 700 032, India

    Received 15 November 1 999; accepted 2 December 1 999

    Time-dependent perturbation theory (TDPT) has been very successful in predicting the positions of the excited energy levels of atomic and molecular systems. TDPT can be associated with different formalisms to yield results of different degrees of accuracy. The method was originally used to predict structure properties connected with single excitations. However, later developments show its potentiality towards evaluation of atomic data connected with double and multiple excitations. In the present context we have used TDPT within a variational framework to calculate singly and doubly excited energy levels of several highly stripped ions of different electronic configurations and estimated their transition properties like oscillator strengths, transition probabilities, etc. A free atom or ion is subjected to a time-dependent external harmonic field and the linear response properties of the atom are evaluated. The effect of the external field is to generate single or multiple excitation of the electronic charge cIo].ld. Depending upon the nature of the perturbing field one can get allowed as well as forbidden transitions involving spatial and spin symmetries. The positions of the excited energy levels and analytic representations of their wave functions are directly obtained from our formalism by analyzing the positions of the poles of an appropriately constructed linearised variational functional with respect to external frequency. Transition energies and other structural parameters agree well with existing data wherever available.

    1. Introduction Spectroscopic studies of highly stripped ions have be

    come very important in recent years because on one hand,

    (i) exper iments invo lv ing s ate l l i tes l i ke IUE, Copernicus, YOHKOH, Hubble space telescope, etc., have provided wealth of information about the presence of various kinds of such ions with wide range of electronic configurati"lls in the spectra of solar flare and coronal .\

    (ii) recent developments in laboratory experiments for the spectra of such ions in Tokamaks, laser produced plasmas and beam foil spectroscopic measurements yield huge amount of such atomic data2.4-7.

    (iii) investigations on doubly excited states of highly stripped ions by photo-absorption, ionization and other collision experimentsx. ,o, double photo-absorption ", double excitation of two-electron ions at intermediate velocities 1 2 and double capture of electrons by bare nuclei at low velocities J 3 yield data on excited states of atoms.

    On the other hand, spectral lines of the highly stripped ions of various iso-electronic sequence are useful for the diagnostic determination of high temperature plasmas occurring in astrophysics, laboratory tokamaks or laser produced plasmas. Atomic data needed for such purpose are the transition energies, oscillator strengths, trrulsition probabilities, ionization and recombination rates, etc. Besides, such data which are useful for the study of stellar opacity governed by the bound-bound and boundfree transitions of the constituent atomic ions, are also needed for the theory of stellar structure and pulsations, radiative power loss studies in fusion reactors, in testing the empirical mode.! of solar photosphere, to derive accurate values of microturbulence and to test local thermodynamic equilibriaI4. 1 9 •

    In addition to optically allowed transition, forbidden transitions in neutral atoms and their highly stripped iso� electronic ions are useful for the diagnostic determination of electron density and temperature in solar corona, falres and in gaseous nebulae 14.20.22 . The wavelength of the forbidden l ines relative to those of the allowed lines make them very good candidates for the

  • SAHA et of. : EXCITED STATES OF HIGHLY STRIPPED IONS 4 1

    measurement of line profiles which are not complicated by the opacity effect2·3. Forbidden transition data for the metastable levels of two electron ions are useful in determin ing electron temperature and density of solar flares23, laser produced plasmas24 and of tokamak plasmas25 . In this context the transition properties of highly stripped free ions in a plasma environment have become important26 . .-

    Comprehensive reviews on the application of allowed and forbidden lines in hot astrophysical plasma and other branches of physics are now available27.29 . Doubly excited states of atoms and ions play a major role in multielectron phenomena in ion atom collisions, particularly in dielectonic recombination processes 14 which occur in low density coronal plasma where the distribution of atoms in\ various ionization stages and, in tum, the coronal equilibrium is mainly guided by the balance between the rates of various detailed ionization and recombination processes. Doubly excited states of highly stripped ions of helium sequence are particularly important for the coronal plasma diagnostics4 . Experimental spectroscopic data for several highly stripped ions are now available30-34.

    Importance of atomic data of highly stripped ions is responsible for their theoretical estimates for single excitation by a large number of approaches like random phase approximation with exchange (RPAE)35, R-matrix with configuration interaction (CI) calculation3\ relativistic many body theory 16, coupled cluster calculations with singles, doubles and triples37, relativistic random phase approximation (RRPA)3H, etc. For the doubly excited states close coupling calculations39, Feshbach projection operator method and its variants40A 1 , CI calculations36.42A3 yield important data.

    The present article projects some atomic data of highly stripped ions of different electronic configurations done by our group. The single excitation data is based on time-dependent coupled Hartree-Fock (TDCHF) theory while those of doubly exCited states are based on a I inearised version of TDPT within a variational framework developed by us which takes care of simultaneous excitations of two electronic correlated charge cloud. A brief discussion on the salient feature of the theory is given in Section 2 followed by a discussion of the results in Section 3 .

    2 . Theory The N electron atomic system described by the usual

    non-relativistic Hamiltonian is subjected to a harmonic

    perturbation of the form (in a. u)

    H'(r,t) ::: G(f)e-illlC + C.c . . . ( 1 ) where G(r ) is a symmetric sum of one particle operators simulating one electron multipolar excitations of same spin multiplicity. In case of change of spin multiplicity during excitations a suitable spin dependence has to be incorporated in H'. For !ls = 0, one can write

    N G(F) = A.�>;'P'(COSO,)

    '�l ... (2)

    where A. is a perturbation strength parameter and l denotes the multipolarity of excitations. For !ls :;t: 0, one has to incorporate spin dependence in G(r) according to the prescription adopted by Kundu and Mukherjee44, and Ray, Kundu and Mukherjee45 . The frequency dependence of the system is obtained by considering a time averaged variational functional46A7.

    . . . (3)

    where is the total wave function in presence of external field and H is the total Hamiltonian. The time averaging is performed over the period of the external field. The functional J[] is subjected to the optimization condition.

    ()j[] = ° . . . (4)

    with respect to parameters introduced in . The total wave function is expanded as

    N �(;:,t) :;: ATI[\II; + o\ll;e-1d + 0\11: eimt + . . . . . . . . . .] e-iE.' "i=1 . . . (5)

    where A is a normalized antisymmetriser, 8 0/;-and 8 '1';+ are the first order corrections to ground state orbital lfIi due to two components of the harmonic perturbation, Eo is the ground state energy.

    Substitution of given by Eq. (5) in Eq. (3) subject to Eq. (4) with respect to parameters introduced in 8 lf results in sets of matrix equations involving the variational parameters which are subsequently solved for given external frequency.

    The excitation energies and excited state wave functions are obtained by considering the position of poles

  • 42 INDIAN J CHEM. SEC. A. JAN - MARCH 2000

    of J[] with respect to external frequency. The procedural details are given elsewhere48•

    -> In case of double excitation, G(r ) is a symmetric sum

    of two particle operators simulating bielectronic excitations49 • The representation of the perturbed wave function is completely different in the two cases.

    4. Results and discussions In the present communication we will present sets of

    atomic data on transition energies, oscillator strengths, transition probabilities, quantum defect values for a wide range of highly stripped ions of various electronic configurations which we have calculated using our theoretical model. Both allowed and forbidden transitions involving single excitations of spatial and spin symmetries have been incorporated.

    Several transitions in highly stripped ions involving double excitations have also been studied and the data presented. For singly excited states the radial part of the perturbed orbitals 0'1'/ have been expanded in terms of S later type orbitals.

    o'l';(r) = I:C�r·"e-P'" q . . . (6)

    where the exponents of bases are preassigned and Ck4 are the variational parameters to be determined from optimization condition. The angular part of 8 \fIk is fixed by the nature of the perturbation and the ground state orbital on which it acts. For double excitations we propose to expand the perturbed admixture which is a twoparticle function in terms of product basis as

    . . . (7)

    where Ci. are the linear variation parameters and Xj is I a product basis formed out of suitable one particle Slater orbitals

    . . . (8)

    where 17k ' s are Slater bases. In Eq. (8), the plus sign refers to singlet excitations while the minus sign is for the triplet excitations. The number of Slater parameters for single excitations i s fixed by testing the convergence of the static limit of the frequency dependent polarizability values. In the present case this number is restricted

    to 1 5 for all types of excitations. In Table 1 we display the transition energy values, oscillator strengths in length form and transition probabilities for a large number ions of isoelectronic sequence of He, Li, Be, C, F, Ne, N a,Mg, CI, Ar, etc. Allowed as well as forbidden transition properties have been calculated. Spectroscopic data for the transition energies3O-34 have been displayed for comparison . For properties l ike oscillator strengths, etc. , results obtained by other theoretical estimates have also been incorporated. The accuracy in transition energies depends on the complexity of the ionic structure. Accuracy is relatively more for closed shell systems and also it increases when Z is increased along particular isoelectronic series. The reason for this is that for open shell systems electron correlation effect is more dominant because of configuration mixing. For large Z along an isoelectronic sequence, the nuclear potential becomes more dominant and relative accuracy increases.

    Also for excitations to orbitals with more spatial confinement such as ' s' orbitals relative accuracy is higher than excitations to 'p' or 'd' orbitals of the same principal quantum number. This is because of our finite basis set expansion . Table 2 displays the atomic data for several highly stripped ions of S i isoelectronic sequence. The ground state electronic configuration is 3p2 : 'P'. We studied the optically allowed transition from 3p�ns and 3p�nd for n � 7. We have calculated the quantum number n* from the relation n* = Ze/ �2£', where £, is the ionization potential of the orbital concerned. The oscillator strengths have been calculated using standard formulae50.5 1 . Table 3 contains a few selected data for doubly excited states of the highly stripped ions of He isoelectronic sequence. We listed the transition energies for double excitations from the ground state and the Coulomb repulsion term in the doubly excited state in order to get an idea about the consistency of analytic wave functions obtained from our study. We have chosen particularly those ions for which some spectroscopic data for transition energy are available. Results for singlet as well as triplet excitations are included. We have used radially correlated product basis set for most of the calculations. Effect of inclusion of angular correlation in the basis has been demonstrated in a few cases as shown in Table 3 . In all cases the agreement is extremely good. The formalism we have adopted is new and been developed and applied by US52.55 . For some of the excitations we have calculated the effective quantum numbers n* of the doubly excited energy levels using the formula56,

  • SAHA et ai. : EXCITED STATES OF HIGHLY STRIPPED IONS 43

    Table 1 - Transition energies (a.u.), oscillator strengths, transition probabilities (sec·l) and effective quantum number (n° ) of radiative and forbidden transitions for some selected highly stripped ions

    Ion State Transition energy Oscillator strength Transition probability Effective Quant no. Present Others Present Others Present Others Present Others

    S 14+ 2 3S 89. 1 06 89. 1 1 6' 1 .26(+6)" 1 .3 ( +6)h 3 3S 1 05 .453 5.68(+5)

    TiW+ 2 3S 1 7 1 .985 1 7 1 .994' 3 .38 (+7) 3.88 (+ 7)h 3 3S 203.583 1 .50(+7)

    Be+ 6 2P 0.6099 0.6 1 28" 0.0066 5.960 4.95 1" 6 2D 0.6 1 06 0.61 37" 5.998 5.998" 6 2F 0.6 1 05 0.61 37" 5.992 6.()()()d

    B2+ 6 2P 1 .2075 1 .2 1 08" 0.0224 4.967 4.956" 6 2D 1 .2099 1 .2 1 38" 5.000 6 2F 1 .2098 1 .2 1 40< 4.999

    C2+ 3p: Ip 1 . 1 505 1 . 1 798" 0.24 0.26 3d: ID 1 . 1 974 1 .2598"

    Ne6+ 5 3S 6.4300 6.54451 4.802 4.78 1 1 5 3P 6.472 1 3 .899 5 3D 6.4952 6.635Qf 4.963 4.998' 5 3F 6.5084 4.99 1 4 IS 5.8322 5.9558f 3.843 3 .836' 4 Ip 5.8954 0. 1 42 0. 1 43g 3.92 4 ID 5.9570 3.997 4 IF 5.9603 4.004

    02+ 4p: 3p 1 .6997 · 1 .6873f 9.999(-6) 9.2295(+5) 3 .6 1 6 3.682' 4f: 3F 1 .7606 1 .0926( -5) 1 .08 1 8(+6) 3.986

    Ti 16+ 3s: 3p 23.5344 23.3929f 0.6246 0.5761 3d: 3D 25.0624 25.082 1 ' 1 2. 19 1 4 1 2. 1 4 1 1

    C I s+ 3p: 2p. 9.4246 9.2607i 4.86(-4) 1 .38(+9) 2.72 4f: 2F" 1 2.3353 9.34 1 9k 2.57(-4) 1 .25(+9) 3.973

    ArY+ 3p: 2p" 1 1 . 1 500 5 .89(-4) 2.34 (+9) 2.74 1 4f.2P' 1 4.4506 4.52(-4) 3.02(+9) 3.859

    ArK+ 3s: Ip 9.3857 9.350l f 0.24 1 O. J 4 I 2.535(+ 1 1 ) 1 .3 (+ 1 1 ) 1 3p: ID 9.9979 1 0.00 1 3' 0. 1 00(-3) 3 . 1 89(+8)

    Fe16+ 3s: Ip 26.9960 27. 1 263m 0.224 1 .628(+ 1 2) 3p: ID 28. 1 4 1 4 28.0266m 0.3 19(-3) 8.076(+9)

    Kr26+ 3s: Ip 6 1 .5 1 68 62.6566m 0.21 1 7.476(+ 1 2) 3p: ID 63.3249 63. 1 7 1 om 0.758(-3) 9.7 1 0(+ 1 0)

    p4+ 7 2S 2.0561 2.0757f 6.3256 6.3 1 07' 8 2S 2. 1 754 8.0457 6 2D 2.01 1 3 2.03 1 3' 4.2(-6) 5 .9 1 56 5.90651 7 2D 2. 1 07 1 2. 1 273f 2.67(-6) 6.9 1 52 6.9033f

    S5. 6 2P 2.6373 2.6594" 0.0 1 1 4 0.01 27P 5.60 1 7 5 .5880" 7 2P 2.7984 0.0 1 09 O.OO72P 6.6055

    C16+ 7 2S 3.6663 6.9950 8 2S 3 .8S25 9.2795 6 2D 3.4655 3.49391 1 .22( -5) 5 .9098 5 .90971 7 2D 3.6539 7 . 1 6(-6) 6.9 1 00

    Ar7• 62P . 4.2379 4.2748f 0.024 0.01 88p 5.66 1 2 5.66451 7 2P 4.6997 0.0089 0.0 1 06P 7.72 1 9

    CP+ 4 1S 1 .84 1 5 3 .308 3 1P 0.6599 0.6787f 1 .387 1 .47� 2.524 2.497' 3 1D 1 .389 1 1 .0444f 4.67(-5) 3.29( -5)' 2.930 2.672f

    Ar6+ 4 1S 2.356 1 3.393

    (contd . . . . . )

  • 44 INDIAN J CHEM, SEC. A, JAN - MARCH 2000

    Table 1 - Transition energies (a.u.), oscillator strengths, transition probabilities (sec· l ) and effective quantum number (n" ) of radiative and forbidden transitions for some selected highly stripped ions (contd . . . . . . )

    .�--

    Ion State Transition energy Oscillator strength Transition probability Effective Quant no. Present Others Present Others Present Others Present

    4 1P 2.5486CY 2.580Y 0. 1 86 0. 1 64� 3.557 4 1 D 2.9007 2.35( -5) 2.932

    CaJ+ 4p: 2p" 1 .5803 1 .5003" 1 .266(-4) 1 .0 1 2(+7) 5p 1 .9798 1 .746(-5) 2. 1 88(+6) 4f: 2p' 1 .9949 1 . 1 52(-4) 1 .466(+7) 5f 2. 1 746 0.804(-4) 1 .2 1 3( + 7)

    Cr'+ 4p: 2p" 3.82 1 4 4.080(-4) 1 .904(+8) 5p 5.0788 I . 1 04(-4) 0.91 2(+8) 4f: zp. 4.767 1 0.990(-3) 7 . 1 82(+8) 5f 5.5046 0.388(-3) 3 .752(+8)

    Sc3+ 5p: ID 2. 1 846 2. 1 9331 0.736(-5) 1 .222(+6) 3.922 6p 2.3769 0.344(-5) 6.208(+5) 4.939 5f: ID 2.38 14 0. 1 38(-4) 2.502(+6) 4.974 6f 2.4783 0. 1 04(-4) 2.040(+6) 5.943

    ys+ 5s: Ip 3.5345 3.5490' 0.082 3.907 6s 3.9685 0.037 4.9 1 5 5d: Ip 3.8439 0. 1 1 0 4.549 6d 4. 1 347 0.028 5 .576

    Mn'+ 5s: Ip 5.2478 5.2808" 0.09 1 4.065 6s 5.9408 0.033 5.073 5d: Ip 5.6796 0. 1 25 4.6 1 2 6d 6. 1 653 0. 1 1 5 5 .63 1

    'Drake G W F. Phys Rev A. 3, ( 1 97 1 )908. "Freeman F F et al., Phil Trans Roy Soc (Lond.) A 270 ( 1 97 1 ) 1 27. "Bashkin S & Stoner J 0 (Ir), Atomic energy levels and grotrian diagrams, Yol. I , (North Holland, Amsterdam), 1 978. JMoore C E, Atomic energy levels, Cir. No. 467 NBS, Yol I , 1 974 "Weise W L et at., Atomic transition probabilities (NSRDS-NBS 4, Washington DC, US), 1 966. 'Bashkin S & Stoner J 0 (Jr), Atomic energy levels and grotrian diagrams, Yol I, (North Holland, Amsterdam), 1 975. �Stewart F, J Phys B, 8 ( 1 975) 1 . hGould H et ai, Phys Rev Lett, 3 1 ( 1 973)504. ;Fawcett B C, At Data Nucl Data Tables, 37 ( 1 987) 367. iExpt value quoted by Mohan M & Hibbert A, Phys Scr, 44 ( 1 99 1 ) 1 58. 'CI value of Mohan M & Hibbert A, Phys Scr, 44 ( 1 99 1 ) 1 58. IWeise W L et al., Atomic transition probabilities (NSRDS-NBS 4, Washington DC, US), 1 969. mCogodan J A & Lunnel S, Phys Scr, 33 ( 1 986)406. "Fawcett B C, Phys Scr, 70 ( 1 984) 326. "Moore C E, Atomic Energy Levels, (NBS Washington DC US) 1 949. PLindgard A & Nielsen S E, At Data Nucl Data Tables, 1 9 ( 1 972) 57 1 . �Shorer P, Lin C D & Johnson W R, Phys Rev A, 1 6 ( 1 977) 1 1 09. 'Godefroid M, Magnusson C E, Zetterberg P 0 & Zoelson I , Phys Scr; 32 ( 1 985) 1 25.

    Others

    3.5 1 01

    2.9 1 6'

    3 .97 1 '

    3 .833"

  • SAHA el al. : EXCITED STATES OF HIGHLY STRIPPED IONS 45

    Table 2 - Transition energies (a.u.), oscillator strengths, transition probabilities (sec·l) and quantum defect values of the highly ionized Si-Iike atoms

    Ions State Transition energy Oscillator strength Transition probability Quantum defect Present Others' Present Others' Present Others' Present Others'

    4s: 3p"

    5s

    6s

    7s

    4d:3 D"

    5d

    6d 7d

    Zn16+ 4s: 3p" 5s

    6s

    7s

    4d: �D"

    5d

    6d

    7d

    6.0922

    8.9328

    I l . I 57 1

    1 1 .6825

    7.2748

    9.4854

    1 0.6484

    1 1 .3433

    9.6370

    14 . 1 328

    1 6.4227

    1 7.7903

    1 1 . 1 762

    1 4.8674

    1 6. 8 1 54

    1 7.9666

    4s: �po 1 6.41 47

    5s 24.0795

    6s 28.0357

    7s 30.4049

    4d: 3D" 1 8.4873

    5d 25.08 1 7

    6d 28.5792

    7d 30.6650

    'a(±n) '" axl()±n

    6.0878

    7.2366

    '�hirai el at ( 1992, 1 99 1 , 1990, 1 987)

    0. 1 52

    0.308(- j > 0.850(-2)

    0. 1 69(-2)

    0.556

    0. 1 7 1

    0.732(- 1 )

    0.565(- 1 )

    0. 1 43

    0.292(- 1 )

    0.936(-2)

    0.604(-2)

    0.723

    0.203

    0.880(- 1 )

    0.806(- 1 )

    0. 1 34

    0.275(- 1 )

    0.996(-2)

    0.292(-2)

    0.894

    0.230

    0.975(- 1 )

    0.474(- 1 )

    0.088

    . . . (9)

    where E (in a.u) is the energy of the doubly excited state measured from the ionization threshold, N is the principal quantum number of the inner electron. As no other theoretical data exist for these states and experimental data are rather scanty, our results may serve as useful addition to literature. The doubly excited state wave

    1 .80(+ 1 1 )'

    7.86(+10)

    4.29(+10)

    0.74(+ 10)

    9.39(+ 1 1 )

    4.92(+ 1 1 )

    2.65(+1 1 )

    2.32(+ 1 1 )

    4.24(+1 1 )

    1 .86( + 1 1 )

    0.8 1 (+ 1 1 )

    0.6 1 (+ 1 1 )

    2.88(+1 2)

    1 .44(+1 2)

    0.80(+1 2)

    0.83(+ 1 2)

    l . I 5(+ 1 2)

    0.5 1 (+ 1 2)

    0.24(+1 2)

    0.86(+1 I )

    9.76(+1 2)

    4.62(+1 2)

    2.55(+1 2)

    1 .42(+ 1 2)

    1 .0(+ 1 1 ) 0.54 1

    0.526

    0.505

    0.577

    0.209

    0.201

    0. 1 93

    0. 1 69

    0.433

    0.4 1 9

    0.354

    0. 1 77

    0. 1 70

    0. 1 66

    0. 1 67

    0.350

    0.342

    0.332

    0.284

    0. 1 43

    0. 1 38

    0. 1 35

    0. 1 30

    0.570

    0.257

    0.444

    functions may be effectively used for collision calculation, important for the interpretation of the spectra of solar chromosphere .

    Our calculation is non-relativistic. This is more or less reasonable for the range of nuclear charge we studied. However, relativistic effects would be important for higher nuclear charges. Electron correlation is included partly in our formalism57• For double excitations our formalism takes care of radial and angular correlations. In view of scarcity of available data, particularly for oscillator strengths and transition probabil ities for

  • 46 INDIAN J CHEM, SEC. A, JAN - MARCH 2000

    Table 3 - Energies (measured from ground state), coulomb repulsions and effective quantum numbers (n') of the doubly excited states of the highly stripped ions below N=2 hydrogenic threshold

    Ions

    MgIO+

    Ap I+

    Si 1 2+

    pD+

    S14+

    States

    2s2p: Jp"

    2s4d: JDe

    2p4d: Jp'

    2s2p: Jp"

    2s5d: JD"

    2p5d: Jp'

    2s2: I S2

    2s5d: JD"

    2p5d: Jp'

    2S2: I S"

    2s5d: JD"

    2p5d: Jp'

    2S2: I S

    2s5d: JD"

    2p5d: lp>

    Energies (a.u) Radial Rad. + Ang.

    1 02.20 1 (f 1 02.463 1 " 1 14.7767e 1 1 5.0388" 1 14.7823" 1 1 5 .0444h 1 20.4647" 1 20.8 1 45" 1 36.9746" 1 37.3244h 1 36.9732" 1 37.3230" 1 40.4592' 1 40.2578' 1 40.9 1 74" 1 40.7 1 60" 1 59.4759" 1 59.9341 h 1 59.480 1 " 1 59.9383h 1 6 1 .73 1 2' 1 6 1 .5 1 59' 1 62.3299" 1 62. 1 1 46h 1 83 .6845" 1 84.2832" 1 83.685(f 1 84.2837" 1 84.5054' 1 84.2808' 1 85 .2757" 1 85.05 1 1 " 209.590(f 2 1 0.3655" 209.595(f 2 1 0.3705"

    'Using HF ground energy of Mukherji A, Pramalla, 2 ( 1 974) 54 "Using expt. ground state energy, Bashkin & Stoner J 0 (Jr) ( 1 975)

    Coulomb repulsions (a.u) Effective Others Radial Rad. + Ang. quant. no

    1 02.3702" 1 .5504 1 .920 1

    0.64 1 4 3 .9722

    0.6483 3.975 1

    1 20.68861 1 .6827 1 .9267

    0.4535 4.9944

    0.4600 4.9932

    140.3949" 2.0708 1 .8705

    0.4965 4.9962

    0.4977 4.9993

    1 6 1 .7435f 2.228 1 2.0 1 44

    0.5 1 7 1 4.9958

    0.5250 4.996 1

    1 84.5859& 2.3673 2. 1 644

    0.5579 4.9883

    0.5585 4.99 1 1

    "Using RHF ground state energy of Koga T et aI., 1 Phys B, 28 ( 1 995) 3 1 1 3. eMartin W C & Zalubas R, 1 phys Chem Ref Data, 1 2 ( 1 983) 378 'Martin W C , Zalubas R & Musgrove A, 1 phys Chern Ref Data, 1 4 ( 1 985) 800 gMartin w e , Zalubas R & Musgrove A, J phys Chern Ref Data, 1 9 ( 1990) 878 l'Martin W C & Zalubas R, J phys Chern Ref Data, 9 ( 1 980) 53 iMartin W C & Zalubas R, J phys Chern Ref Data, 10 ( 198 1) 199

    highly stripped ions, the data generated by us may be very useful for diagnostic purpose and spectra identification of coronal and laboratory sources.

    Acknowledgement The authors are grateful to the Council of Scientific

    and Industrial Research (CSIR) for a research grant under No. 03 (0888)/99/EMR II.

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