-
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,
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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.
References
Fancett 8 C, Z Phy D, Supply to Vol 2 1 , S 1 ( 1 99 1 ). 2
Feldman U, Phys SeT; 24 ( 198 1 ) 68 1 . 3 Doschek G A et at. Ap 1,
1 96 ( 1 975) L 83. 4 Nakazaki S, Sakimoto K & Itikawa Y, Phy
SeT, 47 ( 1 993) 359 :
Culhane J L et ai, Sol Phys, 1 36, 89 ( 1 99 1 ). 5 Trabbert E,
Z Phys A. 3 19, 25 ( 1 984); Phys SeT, 48 ( 1 993) 699. 6 Engstrom
L, Phys SeT; 40 ( 1 989) 1 7. 7 Irvings, R E, Maniak S T, Beldeck D
J, Bengtsson P & Curtis L
J, Phy SeT, 5 1 ( 1 995) 35 1 .
-
SAHA et at. : EXCITED STATES OF HIGHLY STRIPPED IONS 47
8 Madden R P & Codling K, Phys Rev Lett, 1 0 ( 1 963) 5 1 6,
Ap J 1 4 1 ( 1965) 364.
9 Woodruff P R & Samson J A R, Phys Rev A , 25 ( 1982) 848.
1 0 Domke M et ai, Phys Rev Lett, 66 ( 1 99 1 ) 1 306. 1 1 Linde, D
W, Ferrett T A, Heinman P A, Shirley D, Phys Rev A,
36 ( 1987) 2 1 1 2. 1 2 Stolterfoht M, Ridder D, Ziem P, Phys
Lett, 42A ( 1 972) 240. 1 3 Chetioui A et ai, J Phys B, 23 ( 1 990)
3659. 14 Cowan R D, The theory of atomic structure and spectra
(Univ
California Press, Berkeley), 1 98 1 . 1 5 Grevesse N , Phys Scr,
T 47 ( 1 993) 1 33 . 16 Avgoustoglou, E, Johnson W R, Liu Z W &
Sapirstein J, Phys
Rev A , 5 1 ( 1 995) 1 1 96. 17 Hilbert A & Scott M P, J
Phys B, 27( 1 994) 1 3 1 5 . 1 8 Tully J A, Seaton M J &
Beninfgton K A, J Phys B, 23 ( 1 990)
38 1 1 . 1 9 Morton D C, Phys SCT; T47 ( 1 993) 1 83. 20 Das A K
& MukheIjee P K, Ap J, 505 ( 1 998) 1009. 2 1 Das A K, Ghosh T
K, Ray D, Mukherjee T K & MukheIjee P K,
Phys SCT; ( 1 998). 22 Das A K, Ghosh T K, Ray D, Mukherjee T K
& Mukherjee P K,
Ap J, 508 ( 1 998). 23 Keenan F P, Kingston A E & Mc Kenzie
D L, Ap J, 29 1 ( 1 985)
855. 24 Stavrakas T A & Lee W R, J Phys B, 1 5 ( 1 982)
1939. 25 Bitter et al M, Phys Rev A, 32 ( 1 985) 30 1 1 . 26 Ray D
& Mukherjee P K , E P J, D2 ( 1 998) 39, J Phys B, 3 1
( 1 998) 3479. 27 Biemont E & Zieppen C J, Phys Scr T, 65 (
1996) 1 92. 28 Mendoza C, Phys Scr T, 65 ( 1996) 1 98. 29 Kato T,
Phys Scr T, 73 ( 1 997) 98. 30 Martin W C & Zalubas R, J phys
Chem Ref Data, 8 ( 1979) 86 1 ;
9 ( 1980)53; 1 0 ( 1 98 1 ) 1 9 1 ; 1 2 ( 1983)376. 3 1 Martin W
C, Za1u1as R & Musgrove A, J phys Chem Ref Data,
14 ( 1985) 798; 14( 1985)798. 32 Sugar J & Corl iss C, J
phys Chem Ref Data 1 4, Suppl 2 ( 1 985)
47 1 .
3 3 Sugar J & Musgrove A, J phys Chem Ref, 1 9 ( 1990) 527,
24 ( 1 995) 1 083.
34 Shirai et at. T, J phys Chem Ref Data, 37 ( 1 987) 235; 19 (
1 990) 927; 20 ( 1 99 1 ) I ; 2 1 ( 1 992) 23.
35 Lamouveux M & Radojevic Y, J Phys B, 1 5( 1 982) 1 34 1 .
36 Hibbert A & Scott M P, J Phys B, 27 ( 1 994) 1 3 1 5. 37
Ka1dor U & Haque A, Chem Phys Lett, 1 28 ( 1 986) 45. 38 Shorer
P, Phys Rev A, 20 ( 1979) 642. 39 Callaway J, Phys Rev A, 26 (
1982) 1 99. 40 Anania Lipski R & Conneely M J, At Data Nuc Data
Tables, 20
( 1977) 1 27. 4 1 Macias A, Martin F, Riera A & Yanez M,
Phys Rev A , 36 ( 1 987)
4 1 87. 42 Copper J W, Fano U & Pratts F, Phys Rev Lett, 10
( 1 963) 5 1 8 . 43 Hennick D R & Sinanogla 0, Phys Rev A, 1 1
( 1 975) 97. 44 Kundu B & Mukherjee P K, Can J Phys, 63 ( 1
985) 1 278; AI' J
298 ( 1 985) 844. 45 Ray D, Kundu B & Mukherjee P K, J Phys
B, 2 1 ( 1 988) 3 1 9 1 . 46 Lowdin P 0 & Mukherjee P K , Chem
Phys Lett, 1 4 ( 1 972) 1 . 47 Langhoff P W, Epstein S T &
Karplus M, Rev Mod Phys, 44
( 1 972) 602. 48 Mukherjee P K & Moitra R K, J Phys B, 1 1 (
1 978) 28 1 3. 49 Ray D, Kundu B , Mukherjee P K, Ohtsuki K &
Ohno K, Phys
Lett A , 1 36 ( 1 989) 423. 50 Fano U & Copper J W, Rev Mod
Phys, 40 ( 1 968) 44 1 . 5 1 Roy H P, Gupta A & Mukherjee P K,
lnt J quant Chem, 9 ( 1 975)
75. 52 Ray D & Mukherjee P K, J Phys B, 24 ( 1 99 1 ) 1 24 1
. 5 3 Das A K & MukheIjee P K , Z Phys D , 28( 1 993) 97. 54
MukheIjee P K, Z Phys D, 39( 1 997) 1 95. 55 Das A K, Mukherjee P K
& Thakkar A J, Eur Phys J, D6 (1 999)
45 1 . 5 6 Lipski L , Anani R & Conneely M J , At Data Nucl
Data Tables.
20 ( 1 977) 1 27. 57 Mc Curdy C W, rescigno T N, Yeager D L
& Mc Koy Y, Meth
ods of electronic structure theory, edited by H F Schaefer III
(Plenum N Y), 1 977.