- Email: [email protected]
Calculations on quartet levels of 3-electron ions
Nuclear
Instruments
North-Holland.
and Methods
m Physics Research B9 (1985) 509
509
512
Amsterdam
CALCULATIONS
ON QUARTET
N.A. FAIRLEY
LEVELS OF 3-ELECTRON
IONS
* and C. LAUGHLIN
C‘alculations on quartet levels of J-electron ions arc reported. Some ohserved IIWL and
phoromnlsation
cross
scctionz
for
1~252~ 4 I’” lewls of He
1. Introduction
Core-excited quartet levels of 3-electron ions arc of interest from both an experimental and theoretical point of view and have been the subject of many recent studies (see refs. [I -31 and references therein). The terms involved, viz. ls2snl 4L and ls2pri’I’ 4L. lie high in Is’& doublet continua but. due to the selection rules for autoionisation. the majority of levels of ions near the neutral end of the sequence decay primarily by radiative transitions to lower quartet levels. As well as the lowest 1~2.~2~ 4P” lcvcls, which decay by autoionisation to appropriate doublet continua [4]. it would appear that on the autoionisation has an appreciable influence decay of certain ls2pnl 4L (L = I) levels which lie above the 1~2s ‘S threshold (due to the parity selection rule. such levels cannot autoionise via the Coulomb interaction). However. this effect has not yet been investigated theoretically and has been observed only for Li I [S]. The quartet spectra of Li I and Be II have been thoroughly investigated. both experimentally [6.7] and theoretically [2.8--IO]. and are generally well understood. The quartet spectrum of B 111 has received some attention experimentally. by utilising a beam- foil source, but only a relatively small number of assignments have been made [l ,I I] and many of these are now know to be incorrect. Very recently. Chung et al. [3] have studied B III and have identified a number of new lines in the EUV region 270 A to 370 A. Further experimental work is currently being undertaken [12] to help elucidate the B 111 quartet term diagram. The beam--foil method suffers from relatively low spectral resolution [13] and so calculated wavelengths and transition probabilities are a valuable aid in the assignment of observed beam foil lines [14]. We are using a model-potential method in calculations on * Present address: Department of Information and C‘omputer Science. Oklahoma 74078.
State
University.
Stillwater.
Oklahoma
USA.
0168-583X/85/$03.30 (North-Holland
Physics
$2 Elsevier Science Publishers Publishing
Division)
B.V.
in the hum-foil
qxtrum
of horon
are d~scusscd
and 1-i are presented.
quartet levels of 3-electron ions 19.101 and in this paper we report on He-. Li. Be’ and B”. including photoionisation cross sections for the metastable ls2s2p 4P” levels of lie and Li.
2. Method We employ the following model for the 2 excited electrons (labelled 1 and 2) of 1~2sn/~l. and ls2pn’l’ 41. levels of lithium-like ions: [h(l)+h(2)+
l’,(12)]‘f’=
E-l’.
(1)
where h=
-;r
: +I’\,.
(2)
and (:M is a semi-empirical non-local model potential which represents the interaction of the K-shell electron with the other 2 electrons; V,(lZ) is an effective electron-electron repulsion potential (for details see. for example. ref. [9]). Eq. (I) is solved by a configuration-interaction (CI) expansion in terms of eigenfunctions of h. including continuum eigenfunctions which arc necessary to obtain proper convergence [IO]. allowing transition wavelengths. transition probabilities and radiative decay lifetimes to be calculated.
3. Results We first comment on the convergence of the CI expansions for the eigenfunctions \k of eq. (I). The basis functions used in the CI expansions are either (exact) numerical solutions of the l-electron equation h&l = en/%/.
(3)
or variational approximations constructed from linear combinations of trial functions xn, whose radial parts are of the form r”+‘e a’. If N, functions xn, are used to diagonalise the l-electron Hamiltonian h then N, II.
ATOMIC
STRUCTURE
510
N.A. Fairley, C. Laughlin
/ Calculations on quartet levels of 3 - eiectron ions
eigenvalues are obtained, a few of which are positive and so the corresponding eigenfunctions approximate continuum solutions of eq. (3). To illustrate convergence, consider the following truncated expansion for 2s2p 4P0: *(2s2P4P0)
=A
+
f: %&5,,(1)~~,(2) [ n=2 i n=3
+ i
Fig. 1. Convergence of 2s2p 4P0 energy E for B III as a function of the upper limit I of the summations (4) in a configuration-interaction expansion of the wave function: (a) analytical orbitals; (b) numerical orbitals.
47%,flk,(4
1
vh,O)~nPnd(2)
(4)
I
n=3
where A denotes the anti-symmetrising and angularmomentum coupling operators and f I N, for I = 0, 1 and 2. Fig. 1 plots the 2s2p 4P0 energy for B III as the upper limits I in eq. (4) are increased from 3 up to, respectively, N,, NO and N2. The interesting point to note is the steep dip which occurs in the energy around f = 15 when (approximate) analytical representations of the basis functions CP,! are used but which is absent when (exact) numerical basis functions are employed. The fact that the onset of positive energy eigenvalues en, occurs at I = 14 (for this particular calculation) illustrates the importance of continuum basis functions in CI expansions of this type. We have also used the program IMPACT [15] to solve the 3-channel problem (4) exactly (within the limits of the numerical accuracy
of that program) and have obtained a result in close accord with the final converged value in fig. 1. It is of some interest to observe how the positions and compositions of various levels change along the isoelectronic sequence. For example, for Li I the 2p3d 4F0 level lies above the 2’S ionisation limit of Li II and, consequently, it autoionises rapidly via the Coulomb interaction to 2skf ‘F”, for Be II the 2 lowest states of 4Fo symmetry are 2s4f + 2p3d [16] whereas for B III and higher ions 2p3d is the lowest level of 4Fo symmetry. Another interesting example is the interaction of 2pnp 4S levels with 2sns 4S Rydberg levels. For Li I, all 2pnp 4S levels lie above the 23S limit of Li II. For Be II
Table 1 Experimental
denotes
and theoretical
Transition
data for B III quartet
Wavelength
4P 4s ‘D 4D 4D 4D 4P0 4Do 4Po
2s2p 4P”-2s4s -2p3p -2p3p -2p3p 2p2 4P-2p4s 2s2p 4P”-2s3s 2~3s 4S-2p4s -2s3p
4S 4D 4P 4S 4 Pa 4S 4P0 4P0
a1 Ref. [3]_ b, Ref. [Z]. ” Ref. [l].
327.9 328.5 329.3 338.4 367,s 457.7 493.1 499.4 567.2
a) ‘) a) 329.8 ‘) a,ct ‘) =) c, c’ ”
386.8 “** 398.5 =)r* 399.8 ‘),* 408.6 ‘I.* 423.7 ‘),* 524.4”,* 960.7 ‘),* 4084.0=‘,*
an incorrect
assignment.
Model potential
Other calculations
Transition probabii~ty 8 s-l (10 )
326.9 328.8 329.4 338.1 367.5 457.1 492.3 499.1 566.8
327.1 328.7 329.3 338.2 367.5 457.5 491.8 499.7 567.1
=) =) 328 ’0 b, a) =) a) =f a) a) a)
9.38 11.2 5.13 20.0 38.4 119.1 52.4 116.7 23.5
380.0 408.3 399.1 402.2 414.7 518.7 933.7 6099.0
380.1 408.6 398.3 402.4
a) 380.0 b, at ‘) a) 401.3 b,
(A)
Experiment
2s2p 4P”-2p4p -2p4p -2p4p -2s5d -2s4d -2s3d 2p2 4P-2p3d -2p3d -2~3s
lines. An asterisks
519.0 a) 518.7 b, 6086.0 b,
4.05 5.00 17.5 25.8 6.50 34.0 0.002 0.31
Lifetime of upper level (ns) This work
Ref. [3]
0.835 0.662 1.121 0.409 0.227 0.0839 0.184 0.085 0.413
0.875 0.766 1.481 0.424 0.227 0.0845
1.312 1.710 0.534 0.362 0.875 0.294 0.875 21.8
0.085 0.428 1.281 1.738 0.511 0.357 0.299 20.6
N.A. Fuirley, C. Laughlin / Calculations on quartet levels of 3 -electrontons
Fig. 2. Photodetachment cross section LT for the lsZs2p 4Po level of He- as a function of photoelectron energy E: present c~culation; - - ~ Hazi and Reed [21]; 0 Compton et al. [19]; l Hodges et al. [20].
the 2p3p 4S level is the third member of the 4S series, while 2p4p 4S mixes strongly with several 2sns 4S levels in the nei~bourhood of n = 10 and, in fact, there is not a level whose dominant component is 2p4p 4S [17]. For B III, 2p3p 4S is the first excited 4S level and we agree with Chung et al. [3] that the fifth and sixth 4S levels should be classified as 2~6s f 2~4~. Only a relatively small number of lines in the quartet spectrum of B III have been recorded expe~mentally [1,3]. In table 1 we compare our model-potential resufts with experimental and other calculated values. Our calculations confirm some of the assignments given in ref. [l], mainly for VUV lines with wavelengths in the
ii-
511
range 300-600 A, but the majority are not correct. In particular, we disagree with all suggested assignments for lines with wavelengths greater than 2000 A and our calculated positions for 4S levels are not in accord with those deduced by assuming experimental wavelength assignments for 4P0-4S transitions [l] to be correct. Our calculations do, however, support the proposed identifications of new lines reported in ref. [3]. We also agree with the r~lassification of the lines at 398.5, 399.8 and 408.6 A proposed by Chung et al. [3]. The other incorrectly assigned lines quoted in table 1 would not appear to belong to the B III quartet spectrum. It is clear that further experimental work, including lifetime measurements, needs to be done to gain a more comprehensive picture of this spectrum. We have also calculated photoionisation cross sections for the lowest metastable 2s2p 4P0 levels using the programs IMPACT [15] and PHOTUC [18]. To our knowledge the only experimental cross sections available are for the He- ion [19,20] which does not have any other bound states of the form 2snl 4L or Zpn’l’ 4L [21,22]. Fig. 2 presents our calculated photodetachment cross section for He-, together with the experimental cross sections of Compton et al. [19] and Hodges et al. [ZO], and the cross section calculated by Hazi and Reed [21] using a Stieltjes-moment-theory technique. The two theoretical curves agree quite well with each other and with experiment, although they differ somewhat with regard to the value of the maximum in the cross section due to the 4P autodetaching shape resonance just above the 2”P* threshold of He. Watanabe [23] has used hyperspherical-coordinate method to calculate a 4P” + 4P partial cross section in fair agreement with our modelpotential calculation. The cross section for Li I is given in fig. 3 for photon energies below the 23P” threshold of Li II, so that the final continuum state is either 4S or 4D. This cross section is dominated by series of resonances: 2pnp 4D, 2pnp 4S and 2pnf 4D, converging to the 23P0 limit of Li II. The 2p3p 4S and 4D levels of Li I are autoionising, lying 0.4 eV and 0.2 eV, respectively, above the 23S threshold of Li II.
--. \\ \:,----___ --__ ---.___ : 1:::: !
---____’
&-
References
111 K.X. To, E.J. Knystautas,
1U
Electron energy(Ryds1
Fig. 3. Partial and total photoio~sation cross sections for the ls2s2p 4P0 level of Li I; dashed-dotted line 4P0 * 4S partial cross section; dashed line: 4P0 * 4D partial cross section; full line: total cross section.
R. Drouin and H.G. Berry, J. Physique COB. Suppl. 40 (1979) Cl-3. 121 S. Larsson and R. Crossley, Int. J. Quantum Chem. 22 (1982) 836. [31 K.T. Chung, R. Bruch, E. Trabert and P.H. Heckmann, Phys Scripta 29 (1984) 108. 141 M. Levitt, R. Novick and P.D. Feldman, Phys. Rev. A3 (1971) 130. 151 S. Mannervik, Phys. Scripta 22 (1981) 575, WI SM. Bentzen, T. Andersen and 0. Pot&en, J. Phys. B 15 (1982) L71. II. ATOMIC
STRUCTURE
512
N.A. F&fey,
[7] S. Mannervik
[8] [9] [lo] [ll] 1121 [13] 1141 [15]
C. Laughlin
/ Calculations
and H. Cederquist, Phys. Scripta 27 (1983) 175. C.F. Bunge and A.V. Bunge, Phys. Rev. A17 (1978) 822. C. Laughlin, J. Phys. B 16 (1983) 3329. N.A. Fairley and C. Laughlin, J. Phys. B. 17 (1984) 2757. I. Martinson, W.S. Bickel and A. Glme, J. Opt. Sot. Am. 60 (1970) 1213. T. Andersen, private communication (1984). H.G. Berry, Physica Scripta 12 (1975) 5. S.M. Bentzen, T. Andersen and 0. Poutsen, .I. Phys. B. 14 (1981) 3435. M.A. Crees, M.J. Seaton and P.M.H. Wilson, Comp. Phys. Comm. 15 (1978) 23.
on quartet levels of 3 - elecrron ions
[16] [17] [18] [19] [20] [21] [22] [23]
M. Galan and CF. Bunge, Phys. Rev. A23 (1981) 1624. C. Froese-Fischer, Phys. Rev. A26 (1982) 2627. University CoIlege London, unpubIished program. R.N. Compton, G.D. Alton and D.J. Pegg, J. Phys. B 13 (1980) L651. R.V. Hodges, M.J. Coggiola and J.R. Peterson, Phys. Rev. A23 (1981) 59. A.U. Hazi and K. Reed, Phys. Rev. A24 (1981) 2269. CA. Nicolaides, Y. Komninos and D.R. Beck, Phys. Rev. A24 (1981) 1103. S. Watanabe, Phys. Rev. A25 (1982) 2074.
Instruments
North-Holland.
and Methods
m Physics Research B9 (1985) 509
509
512
Amsterdam
CALCULATIONS
ON QUARTET
N.A. FAIRLEY
LEVELS OF 3-ELECTRON
IONS
* and C. LAUGHLIN
C‘alculations on quartet levels of J-electron ions arc reported. Some ohserved IIWL and
phoromnlsation
cross
scctionz
for
1~252~ 4 I’” lewls of He
1. Introduction
Core-excited quartet levels of 3-electron ions arc of interest from both an experimental and theoretical point of view and have been the subject of many recent studies (see refs. [I -31 and references therein). The terms involved, viz. ls2snl 4L and ls2pri’I’ 4L. lie high in Is’& doublet continua but. due to the selection rules for autoionisation. the majority of levels of ions near the neutral end of the sequence decay primarily by radiative transitions to lower quartet levels. As well as the lowest 1~2.~2~ 4P” lcvcls, which decay by autoionisation to appropriate doublet continua [4]. it would appear that on the autoionisation has an appreciable influence decay of certain ls2pnl 4L (L = I) levels which lie above the 1~2s ‘S threshold (due to the parity selection rule. such levels cannot autoionise via the Coulomb interaction). However. this effect has not yet been investigated theoretically and has been observed only for Li I [S]. The quartet spectra of Li I and Be II have been thoroughly investigated. both experimentally [6.7] and theoretically [2.8--IO]. and are generally well understood. The quartet spectrum of B 111 has received some attention experimentally. by utilising a beam- foil source, but only a relatively small number of assignments have been made [l ,I I] and many of these are now know to be incorrect. Very recently. Chung et al. [3] have studied B III and have identified a number of new lines in the EUV region 270 A to 370 A. Further experimental work is currently being undertaken [12] to help elucidate the B 111 quartet term diagram. The beam--foil method suffers from relatively low spectral resolution [13] and so calculated wavelengths and transition probabilities are a valuable aid in the assignment of observed beam foil lines [14]. We are using a model-potential method in calculations on * Present address: Department of Information and C‘omputer Science. Oklahoma 74078.
State
University.
Stillwater.
Oklahoma
USA.
0168-583X/85/$03.30 (North-Holland
Physics
$2 Elsevier Science Publishers Publishing
Division)
B.V.
in the hum-foil
qxtrum
of horon
are d~scusscd
and 1-i are presented.
quartet levels of 3-electron ions 19.101 and in this paper we report on He-. Li. Be’ and B”. including photoionisation cross sections for the metastable ls2s2p 4P” levels of lie and Li.
2. Method We employ the following model for the 2 excited electrons (labelled 1 and 2) of 1~2sn/~l. and ls2pn’l’ 41. levels of lithium-like ions: [h(l)+h(2)+
l’,(12)]‘f’=
E-l’.
(1)
where h=
-;r
: +I’\,.
(2)
and (:M is a semi-empirical non-local model potential which represents the interaction of the K-shell electron with the other 2 electrons; V,(lZ) is an effective electron-electron repulsion potential (for details see. for example. ref. [9]). Eq. (I) is solved by a configuration-interaction (CI) expansion in terms of eigenfunctions of h. including continuum eigenfunctions which arc necessary to obtain proper convergence [IO]. allowing transition wavelengths. transition probabilities and radiative decay lifetimes to be calculated.
3. Results We first comment on the convergence of the CI expansions for the eigenfunctions \k of eq. (I). The basis functions used in the CI expansions are either (exact) numerical solutions of the l-electron equation h&l = en/%/.
(3)
or variational approximations constructed from linear combinations of trial functions xn, whose radial parts are of the form r”+‘e a’. If N, functions xn, are used to diagonalise the l-electron Hamiltonian h then N, II.
ATOMIC
STRUCTURE
510
N.A. Fairley, C. Laughlin
/ Calculations on quartet levels of 3 - eiectron ions
eigenvalues are obtained, a few of which are positive and so the corresponding eigenfunctions approximate continuum solutions of eq. (3). To illustrate convergence, consider the following truncated expansion for 2s2p 4P0: *(2s2P4P0)
=A
+
f: %&5,,(1)~~,(2) [ n=2 i n=3
+ i
Fig. 1. Convergence of 2s2p 4P0 energy E for B III as a function of the upper limit I of the summations (4) in a configuration-interaction expansion of the wave function: (a) analytical orbitals; (b) numerical orbitals.
47%,flk,(4
1
vh,O)~nPnd(2)
(4)
I
n=3
where A denotes the anti-symmetrising and angularmomentum coupling operators and f I N, for I = 0, 1 and 2. Fig. 1 plots the 2s2p 4P0 energy for B III as the upper limits I in eq. (4) are increased from 3 up to, respectively, N,, NO and N2. The interesting point to note is the steep dip which occurs in the energy around f = 15 when (approximate) analytical representations of the basis functions CP,! are used but which is absent when (exact) numerical basis functions are employed. The fact that the onset of positive energy eigenvalues en, occurs at I = 14 (for this particular calculation) illustrates the importance of continuum basis functions in CI expansions of this type. We have also used the program IMPACT [15] to solve the 3-channel problem (4) exactly (within the limits of the numerical accuracy
of that program) and have obtained a result in close accord with the final converged value in fig. 1. It is of some interest to observe how the positions and compositions of various levels change along the isoelectronic sequence. For example, for Li I the 2p3d 4F0 level lies above the 2’S ionisation limit of Li II and, consequently, it autoionises rapidly via the Coulomb interaction to 2skf ‘F”, for Be II the 2 lowest states of 4Fo symmetry are 2s4f + 2p3d [16] whereas for B III and higher ions 2p3d is the lowest level of 4Fo symmetry. Another interesting example is the interaction of 2pnp 4S levels with 2sns 4S Rydberg levels. For Li I, all 2pnp 4S levels lie above the 23S limit of Li II. For Be II
Table 1 Experimental
denotes
and theoretical
Transition
data for B III quartet
Wavelength
4P 4s ‘D 4D 4D 4D 4P0 4Do 4Po
2s2p 4P”-2s4s -2p3p -2p3p -2p3p 2p2 4P-2p4s 2s2p 4P”-2s3s 2~3s 4S-2p4s -2s3p
4S 4D 4P 4S 4 Pa 4S 4P0 4P0
a1 Ref. [3]_ b, Ref. [Z]. ” Ref. [l].
327.9 328.5 329.3 338.4 367,s 457.7 493.1 499.4 567.2
a) ‘) a) 329.8 ‘) a,ct ‘) =) c, c’ ”
386.8 “** 398.5 =)r* 399.8 ‘),* 408.6 ‘I.* 423.7 ‘),* 524.4”,* 960.7 ‘),* 4084.0=‘,*
an incorrect
assignment.
Model potential
Other calculations
Transition probabii~ty 8 s-l (10 )
326.9 328.8 329.4 338.1 367.5 457.1 492.3 499.1 566.8
327.1 328.7 329.3 338.2 367.5 457.5 491.8 499.7 567.1
=) =) 328 ’0 b, a) =) a) =f a) a) a)
9.38 11.2 5.13 20.0 38.4 119.1 52.4 116.7 23.5
380.0 408.3 399.1 402.2 414.7 518.7 933.7 6099.0
380.1 408.6 398.3 402.4
a) 380.0 b, at ‘) a) 401.3 b,
(A)
Experiment
2s2p 4P”-2p4p -2p4p -2p4p -2s5d -2s4d -2s3d 2p2 4P-2p3d -2p3d -2~3s
lines. An asterisks
519.0 a) 518.7 b, 6086.0 b,
4.05 5.00 17.5 25.8 6.50 34.0 0.002 0.31
Lifetime of upper level (ns) This work
Ref. [3]
0.835 0.662 1.121 0.409 0.227 0.0839 0.184 0.085 0.413
0.875 0.766 1.481 0.424 0.227 0.0845
1.312 1.710 0.534 0.362 0.875 0.294 0.875 21.8
0.085 0.428 1.281 1.738 0.511 0.357 0.299 20.6
N.A. Fuirley, C. Laughlin / Calculations on quartet levels of 3 -electrontons
Fig. 2. Photodetachment cross section LT for the lsZs2p 4Po level of He- as a function of photoelectron energy E: present c~culation; - - ~ Hazi and Reed [21]; 0 Compton et al. [19]; l Hodges et al. [20].
the 2p3p 4S level is the third member of the 4S series, while 2p4p 4S mixes strongly with several 2sns 4S levels in the nei~bourhood of n = 10 and, in fact, there is not a level whose dominant component is 2p4p 4S [17]. For B III, 2p3p 4S is the first excited 4S level and we agree with Chung et al. [3] that the fifth and sixth 4S levels should be classified as 2~6s f 2~4~. Only a relatively small number of lines in the quartet spectrum of B III have been recorded expe~mentally [1,3]. In table 1 we compare our model-potential resufts with experimental and other calculated values. Our calculations confirm some of the assignments given in ref. [l], mainly for VUV lines with wavelengths in the
ii-
511
range 300-600 A, but the majority are not correct. In particular, we disagree with all suggested assignments for lines with wavelengths greater than 2000 A and our calculated positions for 4S levels are not in accord with those deduced by assuming experimental wavelength assignments for 4P0-4S transitions [l] to be correct. Our calculations do, however, support the proposed identifications of new lines reported in ref. [3]. We also agree with the r~lassification of the lines at 398.5, 399.8 and 408.6 A proposed by Chung et al. [3]. The other incorrectly assigned lines quoted in table 1 would not appear to belong to the B III quartet spectrum. It is clear that further experimental work, including lifetime measurements, needs to be done to gain a more comprehensive picture of this spectrum. We have also calculated photoionisation cross sections for the lowest metastable 2s2p 4P0 levels using the programs IMPACT [15] and PHOTUC [18]. To our knowledge the only experimental cross sections available are for the He- ion [19,20] which does not have any other bound states of the form 2snl 4L or Zpn’l’ 4L [21,22]. Fig. 2 presents our calculated photodetachment cross section for He-, together with the experimental cross sections of Compton et al. [19] and Hodges et al. [ZO], and the cross section calculated by Hazi and Reed [21] using a Stieltjes-moment-theory technique. The two theoretical curves agree quite well with each other and with experiment, although they differ somewhat with regard to the value of the maximum in the cross section due to the 4P autodetaching shape resonance just above the 2”P* threshold of He. Watanabe [23] has used hyperspherical-coordinate method to calculate a 4P” + 4P partial cross section in fair agreement with our modelpotential calculation. The cross section for Li I is given in fig. 3 for photon energies below the 23P” threshold of Li II, so that the final continuum state is either 4S or 4D. This cross section is dominated by series of resonances: 2pnp 4D, 2pnp 4S and 2pnf 4D, converging to the 23P0 limit of Li II. The 2p3p 4S and 4D levels of Li I are autoionising, lying 0.4 eV and 0.2 eV, respectively, above the 23S threshold of Li II.
--. \\ \:,----___ --__ ---.___ : 1:::: !
---____’
&-
References
111 K.X. To, E.J. Knystautas,
1U
Electron energy(Ryds1
Fig. 3. Partial and total photoio~sation cross sections for the ls2s2p 4P0 level of Li I; dashed-dotted line 4P0 * 4S partial cross section; dashed line: 4P0 * 4D partial cross section; full line: total cross section.
R. Drouin and H.G. Berry, J. Physique COB. Suppl. 40 (1979) Cl-3. 121 S. Larsson and R. Crossley, Int. J. Quantum Chem. 22 (1982) 836. [31 K.T. Chung, R. Bruch, E. Trabert and P.H. Heckmann, Phys Scripta 29 (1984) 108. 141 M. Levitt, R. Novick and P.D. Feldman, Phys. Rev. A3 (1971) 130. 151 S. Mannervik, Phys. Scripta 22 (1981) 575, WI SM. Bentzen, T. Andersen and 0. Pot&en, J. Phys. B 15 (1982) L71. II. ATOMIC
STRUCTURE
512
N.A. F&fey,
[7] S. Mannervik
[8] [9] [lo] [ll] 1121 [13] 1141 [15]
C. Laughlin
/ Calculations
and H. Cederquist, Phys. Scripta 27 (1983) 175. C.F. Bunge and A.V. Bunge, Phys. Rev. A17 (1978) 822. C. Laughlin, J. Phys. B 16 (1983) 3329. N.A. Fairley and C. Laughlin, J. Phys. B. 17 (1984) 2757. I. Martinson, W.S. Bickel and A. Glme, J. Opt. Sot. Am. 60 (1970) 1213. T. Andersen, private communication (1984). H.G. Berry, Physica Scripta 12 (1975) 5. S.M. Bentzen, T. Andersen and 0. Poutsen, .I. Phys. B. 14 (1981) 3435. M.A. Crees, M.J. Seaton and P.M.H. Wilson, Comp. Phys. Comm. 15 (1978) 23.
on quartet levels of 3 - elecrron ions
[16] [17] [18] [19] [20] [21] [22] [23]
M. Galan and CF. Bunge, Phys. Rev. A23 (1981) 1624. C. Froese-Fischer, Phys. Rev. A26 (1982) 2627. University CoIlege London, unpubIished program. R.N. Compton, G.D. Alton and D.J. Pegg, J. Phys. B 13 (1980) L651. R.V. Hodges, M.J. Coggiola and J.R. Peterson, Phys. Rev. A23 (1981) 59. A.U. Hazi and K. Reed, Phys. Rev. A24 (1981) 2269. CA. Nicolaides, Y. Komninos and D.R. Beck, Phys. Rev. A24 (1981) 1103. S. Watanabe, Phys. Rev. A25 (1982) 2074.