Oscillator strengths between various doublet states of OII ions are calculated in which extensive multi-configuration wave functions are used. The lower levels for the transitions are of the 2p(3) D(2)o and 2p(3) 2po states, and the upper levels are 2p(4), 3s, and 3d states. The results, which are estimated to have errors of less than 10% for individual transitions, agree quite well with the beam foil experiments, as well as with the calculations by use of the non-closed shell many electron theory (NCMET). The agreement with the rocket measurements is also good except for the 538/581 A pair, in which the 538 A line is believed to be blend with the other stronger quartet line. However, a comparison with the recent branching ratio measurement indicates that discrepances between the present calculation and th experiment do exist for certain transistions

Henry, J. W.

Ho, Y. K.

English

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NAGW-48-10
OSCILLATOR STRENGTHS FOR 011 IONS
S%4bmitted to J. Quant. Spectros. Rad. Transf.
(NASA -LR-17415.1) 	 OSC II"- A'ILI Shan NoIdS FCb	 `84-13555
4,ii ICNS PL091CS_ be Fort JLcuiSidLa Stdte
U01v.)	 17 p nL AC1/Mf ACl	 CSCL 20d
Jaci.as
63/72 U13E5
Y. K. Ho and Ronald J.W. Henry
Department of Physics and Astronomy
Louisiana State University
Baton Rouge, Louisiana 70803
April 1983
	 !o
-4 F
^, m
Ln
Prepared for NASA Under Grant No. NAGW-48
AAkr
Oscillator strengths for 011 ions
Y. K. Ho and Ronald J. W. Henry
Department of Physics End Astronomy
Louisiana State University
Baton Rouge, Lc--isiana, 70803
Abstr-a,_t
Oscillator strengths between various doublet states of OII
ions are calculated in which extensive multi-configuration wave
functions are used. The lower levels for the transitions are of
the 2p 3 2 D° and 2p 3 Z P° states, and the upper levels are 2p 4 , =s,
and 3d states. The results, which are estimated to have errors of
less than 10% for individual transitions, agree quite well with
the beam foil experiments, as well as with the calculations by
use of the non--closed shell many electron theory (NCMET). 	 The
agreement with the rocket measurements is also good except for
o
the 538/581 A pair, in which the 538 A line is believed to be
blend with the other stronger quartet line. 	 However, a compari-
son with the recent branching ratio measurement indicates that
discrepances between the present calculation and the experiment
do exist for certain transistions.
i
-2-
(I) Introduction
We report a calculation for the oscillator strengths of the
OII ions between various doublet states by the use of extensive
configuration interaction wave functions. Studies of various
oxygen ions have practical, experimental, and theoretical inter-
ests.	 From the practical side, accurate atomic data are essen-
tial for the interpretations of the physical conditions of astrc-
physical plasmas.	 For example, the recent Voyager flyby of the
Jupiter has revealed bright extreme-ultraviolet (EUV) 	 lines of
oxygen and sulfur ions in the vicinity of the satellite Io n .	 In
addition, some EUV transistions between various doublet states of
011 ions have b?en identified in the day airgrow spectrum. 	 The
spectrum was ocserved in a rocket measurement 2 , 3 .	 From the
experimental side the use of beam foil techniques to determine
the lifetimes of variota ionic states has been quite popular4,5
Other recent experimental investigations on the 011 ions include
the branching ratio measurements 6 , 7 .	 On the theoretical side,
accurate calculationo of the oscillator strengths for 011 ions
are of recent interest.	 Since 011 ions are singly ionized spe=-
ies, strong configuration interactions exist in the calculations
of oscillator strengths.	 Furthermore, since 01I are also open
shell ions,	 variQu e correlation effects must be included for
accurate calculations.	 Previous	 theoretical investigations
include the calculations by use of the non-closed shell many
electron theory (NCMET) a and the first order theory of oscillator
strengths (FOTOS)', which is itself a subset of the full NCMET
theory. The oscillator strengths for these open shell and singly
-3-
-_:1 10 i : — . Nna.a^s -- -- -	 —6 	 _ 	
- - - -	
-	
.— I=.	
.fto..^r:r^ri^^^^s
ionized ions are sensitive to the wave functions used, as well as
to the procedures by which the parameters in the wave functions
are determined (optimized).	 Such sensitivities have been docu-
mented in the literature 10 , 11 , 12 .	 The results for some of the
transitions obtained by these two calculations differ from ea:h
other considerably. It is felt, because of these experimental
Rnd theoretical interests, that an independent extensive calcula-
tion for the oscillator strengths of 011 ions is worthwhile.
This wor? presents such a calculation.	 The wave functions
used are of extensive configuration-interaction type.
	
The pro-
gram CIV3 of Hibbert 13 is used in the present calculation. In
section (II) we will describe the wave functions as well as the
procedures to determine the parameters for the wave functions.
In section (III) we will present our results.	 Comparisons with
other calculations and with experiments will also be giver..
(II) Theory and Calculations
in the program CIV3 of Hibbert 13 , the wave functions are
expressed as linear combinations of configuration-interaction-
type wave functions.
q, =ia, I,	 (1)	 717'4
with I, constructed from one-electron orbitals
-4-
-1
u	 = r
	 P	 (r) Y	 (6,^) X(m ),
	 (2)
nlm	 nl	 lm	 s
In Eq.(2), u is a product of a radial function, a spherical har-
monic and a spin function. The radial functions are linear com-
binations of Slater orbitals
	
k	 I, -E,r
	
P (r) = 2	 C	 r	 e	 (3)
nl	 j=1	 jnl
Wave functions are obtained by solving the eigenvalue prob-
lem
<	 H	 > = S	 E
	 (4
We will discuss later in this article how various parameters for
the orbital wave functions are determined. 	 Once the wave func-
tions for both the upper and lower states are obtained,	 the
absorption oscillator strengths can be calculated. The oscilla-
tor strengths (expressed in atomic units) in the length ar.9
velocity forms are;
of	 _	 2
	
f = 2/3	 -	 < 4' I l k r 14, >1	 (length)	 (5)
L	 g	 i	 k f
i
(LE)-'	 _	 2
	
f = 2/3 	 Irk P I'^ >1
	 (velocity)	 (6)
V	 g	 i	 k f
i
where r and p are
	
the coordinate and momentum operators
-5-
respectively, and of the energy difference between the initial
(^ ) and and final	 states.	 The summations in equations (S)
i	 f
and (6) are summed over the number of electrons. 	 A necessary
(but not sufficient) condition for an accurate calculation for
the oscillator streng"hs is the consistence between the length
and velocity values.
Th= procedure to choose the configurations to represent var-
ious ionic states is the following; Since 011 is an open shell
ion, we include the three major correlation effects in the pres-
ent calculation. These effects are;
(1) internal effects that include the configurations for
which the electrons occupy the Hartree-Fock (H-F) sea, (For exam-
ple, for the 2p 3 z P° state the H-F sea includes the 1s, 2s and 2p
orbitals.	 Therefore, the 2p 5 z P° configuration represents the
internal correlation effect.)
(2) semi-internal effects include the configurations in
which only one electron is outside the H-F sea, and
(3) all-external effects include the configurations in which
two or more electrons are outside the H-F sea.
In this work, however, we limit the all-external effects to
the confi gurations in which no more than two electrons are out-
side the H-F sea. Such an limitation is called the quasi-exter-
nal effect by Sinano9lu8.
For illustrative purposes, we show in table 1 the configura-
tions that are used to represent the 2s2p° Z D state together with
their classifications. For the semi-internal correlation effects
-6-
we include contributions from both the I4=3 shell and the N=4
shell.	 However, for the quasi-external effects only the contri-
butions from the N=3 shell (except for 4f) are included. Also
implicitly, we do have some contributions from higher shells.
Since some of the orbitals do not necessarily have spectroscoF-ic
meanings, the '31' orbital therefore represents the average con-
trib-itions from the higher shells.
The parameters for different orbitals are optimized individu-
ally according to different transitions. For example, for the
transition between the 2p 3 Z D° - zD states, we use the 1s, 2s anc
2p orbitals that are optimized on the 2p 3 z D° state in the singe
configuration H-F approximati-)n. 	 The parameters for these orh, i-
tals have been published by Clementi and Roetti" . 	 The 3s orbi-
tal is then optimized on the 3s zD Excited state, and the 3p and
3d orbitals, etc., are optimized on the 2p° zD excited state.
Therefore, in this case, only the 3s orbital has spectroscoFic
meaning, while others are simply correlation orbitals.
In order to avoid the variational collapse°, 	 care must be
taken for a state that is not the lowest state in a given symme-
try (the total angular momentum, total spin, and Parity). For
example, in the optimization of the 3s orbital for the 2p z 3s zD
state (which has the second lowest energy in its symmetry), the
configuration of the 2s2p° is also included. We then optimise
the 3s on the second lowest energy eigenstate. The Hylleraas-Un-
dheim-MacDonald theorem would guarantee that the calculated
energy be an upper bound to the true energy for the 3s Z D state.
-7-
For the calculations of the ;^d states, we optimized various
orbitals by the following procedure. Since 3d also contributes
to the ground doublet states, we optimize the 36 orbitals on the
average energy of the ground state and the 3d excited state. Thy
4d orbital was then optimized on the 3d excited state.
	 As a
result, the 3d excited state is represented by the combination cf
3d and 4d.	 Here again the individual nd orbital does not have
spectroscopic meanings. Furthermore, in the optimization pro:- .-7 -
duce we also include the 3s and the 2p" states in the expansion..
Since the 36 state has the third lowest energy for a given set of
(n,L,S), we have to include the two lower states to avoid the
poss`bilities of variational collapse.
Most of the transitions reported in this w,)rk are done by the
procedures described above. In other words we first construct a
good representation for the lower state. The upper state is rep-
resented by the extensive configuration-interaction type wave
functions that include the internal, semi-internal and quasi-_::-
ternal effects. In such a procedure we have found the theereti-
cal energy difference agrees quite well with the experimental
observed wave length for most of the transitions reported in this
work. However, for the transition between the Z P O - 2 S states we
have found that the theoretical energy differences between the
upper and lower states are not consistent with the experimental
values. An explanation is suggested as the following; Since the
Z S states are located at higher positions, the orbitals which are
good for the lower 2p 3 z P° state may not be good for the uFp_r
states.	 Therefore we treat the 2p 2 3s z S state as a state with
-8-
an 3s electron attaching to the 2p = I S core of the 0111 ion. As
a result, the orbital parameters for the 1s, 2s and 2p are those
of the 0111 I S state. The 3s orbital is then optimized on the 3s
z S excited state. By doing this we have found that the energy
differences between the lower and upper states are consistent
with the experimental wave lengths.
(III) Results and Discussions
We present our results in table 2 as well as those by Sina-
roglu and coworkers who used the program "ATOM". Such a program
is based on the non-closed shell many electron thecry (NCMET ".
The general agreements between the present calculations and the
f values of the NCMET results are quite good, with the present
L
f and f values being more consistent than those in Ref.	 ( (1).
L	 v
It should t-e mentioned that these two sets of results are
obtained by two different programs,
	
although the methods of
selecting various configurations are very similar. Also, by
judging the differences between the oscillator strengths in thvr
length and velocity forms, we estimate the errors for the pres=nt
calculations are within 10" for the individual transitions.
The comparisions with the FOTOS • calculations are good except
0afor the 673 A and 538 A transitions. In these cases substantial
disagreements have been found. 	 This may reflect the sensitivity
of the optimization procedures (for the various orbital parame-
ters) used in Ref. (9). It should also be mentioned that some of
the transitions reported in this work have been calculated by the
present authors using less extensive wave functions Is .	 Also i.n
-9-
Ref.	 (15) the parameters used to represent various state wao-
functions were optimized for the quartet states. The present
results rend represent improvements over the previous calcula-
tions in Ref. (15).
Comparisions of	 the present results with
	 different Experi-
ments are shown in tables II and III,
	 It is seen that the pr%^s-
ent results agree quite well with	 tho^ie by the beam foil exper..
ments' 6 - "	 (table I'.).	 The comparision with the branching ratio
experiment	 (table	 III)	 is less	 satisfactory for
	
certain tran-
sitions.	 Since the errors for the present calculati-)ns are es-:-
mated to be within
	 10: for the individual transitions,
	 the error
for a given ratio pair is hence of 20:.
	 It is seen that some of
the present results differ from
	 the branching ratio e;:perim*n-.'.
even when	 the combined experimental
	 and theoretical	 errors are
included.	 For example,
	 the discrepancy
	 fnr the 482/515 A rair
shows a factor of two difference.
	 and the 555/601	 A pair shows a
difference of about 60%.
	 Of course
	 we also have good agreement
0
for the 538/581	 A pair.	 Generally	 the present ratios	 (with the
longer	 wavelength as	 the	 denominator)	 are smaller	 than	 the
branching ratio experiments. 	 However.	 the present results seam
to agree better with the EUV airglow rocket measurements.
	 exceFt
0	 0
for the 538/581	 A ratio.
	
The observed
	 538 A line	 (2p"	 2 P - 2F'
E D O	 is believed	 to be blend with the	 538 A	 (3s `P	 - 2p s	ISO)
•	 .
line where the latter has a larger oscillator strength.
This work presents an extensive calculation for the oscilla-
tor strengths for 011 ions between various doublet stated.
	 The
-10-
discrepancies between the theoretical calculations and the
branching ratio experiments indicate that further theoretical and
experimental investigations on such systems are worthwhile. From
the theoretical point of view, improvements of the wave functions
may be made if one also includes (1) tte semi-internal correla-
tion effects coming from the higher shells (higher than N=4), (2)
the external effects for which more than two electrons are out-
side the H-F sea, and (3) the quasi-external contributions comino
from higher shells (higher than N = 3).	 Of course, such impro%, +-
ments ma y have small effects on the oscillator strenoths. It is
hoped, therefore, that the present calculations would stimulate
further experimental investigations, which in turn would provide
a more stringent criterion for the test of various theoretical
calculations.
Ac?ncwledgcr,ents
We are grateful for the comF•uting facilities provided by th--
Louisiana State University Systems Network Computer Center. This
work was supported by NASA grant NACW-48.
A
References
1. D. E. Shemansky and G. R. Smith, J. Geophys, Res. 9j, 9179,
(1981)
2. E. P. Gentieu, P. D. Feldman, and R. R. Meier, Geophys. Res.
Lett. fa, 325, (1979)
3. P. D. Feldman, D. E. Anderson, Jr., R. R. Mf.ier and E. P. Gen-
=ieu, J. Geophys. Res. Qh, ?583, (1981)
4. C. C. Lin, D. J. G. Irwin, J. A. Kernahan, J.	 A.	 I.ivin?st -n,
and E. H. Pinnington, Can. J. Phys., iQ, ?496, (1972)
5. E. H. Pinnington, D. J. G. Irwin, A. E. Livingston, and J.
	
A.
Kernah=n, Can. J. Phys. 12, 1961, (1974)
6. M. D. Morrison, A.B. Chr.stenisen, and A.
	 Cunningham J.
Geophve. Res. 2±, 3589, (1981)
7. M. D. Morrison, A. J. Cunningham and A.B. Christenisen J.
Quart,. Spe=tros. Radiat. Transfer. 29, 137, (19824)
8. 0. S nanoglu J-cX- iCg
 in Currenj Pr sits Vol. 1 , Dew Foil. E±_ -
tros_ooy,ed. S. Bashkin (New York, Springer`, p111 (1976)
9. D. R. Beck and C.
	 A. Nicolaides, Big .M, Foil Soe_tros;`cr,
(Edited by I. A. Sellin and D. J.
	 Pegg ) Vol.	 1, pp 11 5-119,
Plenum Press, New york (1977)
10. W. L. Luken and 0. Sinan,) .31u, Phys. Rev. A 1 1^ . 129=, (1976,
11. C. A. Nicolaides and D. R. Bock, Phys. Rev. A iffi, "30-.
(1978)
12. W. L. Luken and 0. Sinanoglu, Phys. Rev. A 1 , 1313, (1978'
13. A. Hibbert, Compt. Phys. Comm. 9, 141, (1975)
14. E. Clementi and C. P.oetti, Atomic Data. Nucl. Data Tables,
14, 177, (1974)
-12-
15. Y. K. Ho and R. J. W. Henry, Ap. J. 240, 168 (1983)
16. W. H. Smith, J. Bromander, L. J. Curtis, H. G. Berry, and R.
Buchta, Ar,. J. 165, 217, (1971)
17. 1. Martinson, H. G. Berry, W. S. Bickel, and H. Oona, J. Opt.
Soc. Am. 61, 519, (1971)
-13-
TABLE I - Configurations used to represent the 2s2p 4 2 D state
Internal
2s2p4
Semi-internal
2s22p23s
	
2s22p24s
2p43s
	
2p44s
2s22p23d
	
2s22p24d
2p43d
	
2pa4d
2s 2p33p
	
2s2p34f
Quasi-external
2s2p23s2
	
2s2p23s3d
2s2p23p2
	
2s2p23p4f
2s2p23d2
	
2p33s4f
2s2p24f2
	
2s22p3s3p
2p33s3p
	
2s22p3p3d
2p33p3d
	
2s22p3d4f
2p33d4f
	
2s22n3s4f
10
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Oscillator strengths for OII ions

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