ON THE QUARTET SPECTRA OF LITHIUM-LIKE IONS

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ON THE QUARTET SPECTRA OF LITHIUM-LIKE IONS

Sven Larsson, Richard Crossley, Tor Ahlenius

To cite this version:

Sven Larsson, Richard Crossley, Tor Ahlenius. ON THE QUARTET SPECTRA OF LITHIUM-LIKE

IONS. Journal de Physique Colloques, 1979, 40 (C1), pp.C1-6-C1-9. �10.1051/jphyscol:1979102�. �jpa-

00218381�

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JOURNAL DE PHYSIQUE CoNoque C1, supplkment au

n

^O2, Tome 40, fkvrier 1979, page C1-6

ON THE QUARTET SPECTRA OF LITHIUM-LIKE IONS

Sven Larsson

Department of Chemistry,University of Bergen,Bergen,Norway and

Dlvlslon of Physical Chemrstry 2,Chemical Centre,Lund Technical University,Lund,Sweden*

Richard Crossley

Department of Mathematics,University of York,York,UK and

Tor Ahlenius

Medlcal Information Centre,Karolinska Institute,Stockholm,Sweden

Abstract: Calculations by the Hylleraas method are reported for 4~ and 4 ~ 0 levels of llthium- llke Ions with nuclear charge Z $ 1 0 . C w r i m n w ~ t h exper~ment is made in the case of Be 11.

The binding energy of the metastable ls2s2p P O state of He IS estimated to exceed 0.0664eV.

RQsum6: Nous reportons de nouveaux calculs sur des niveaux de quartet, ^4~et 4 ~ 0 , d'ions

lith~umoides ( 2 $ 10) en utilisant les coordonndes de Hylleraas. Nous donnons des ~0mparaiSOnS entre nos resultats de Be I1 et les travaux expgrimentaux recents. Nous trouvons que le

niveau ls2s2p 4 ~ 0 de He- est li6 par plus de 0,066 eV.

INTRODUCTION excltatlon methods; recently heavier ions up to

In a recent letter [l] we reported the results Fe XXIV have been investigated through laser plasmas of calculations on some 4 ~ 0 states of doubly-excited C91.

llthlum (LL I**). Tne purpose of these calculations was to lnvestlgate a long-standlng discrepancy between the calculatlons C21 of Holdlen and Geltman

(HG), carr~ed out using the Hylleraas techn~que in which the interelectronic d~stances r appear

=j

explicitly, and unpublished work of Welss (quoted In [2]) by the more conventronal conf~guration inter- action method, and so, hopefully, to resolve problems that had arlsen in the spectr~l analysis based on the HG theory (see, e-g., the review of Berry C31).

It seemed worthwhile to extend our calculations to 4~ and 4 ~ 0 states of ions up to Ne VIII for which attempts at the spectral analysls have been made on the basis of the HG calculatlons. It was not clear whether further actual mlstakes would be found in the HG work (although B w g e and Burge [lo] have confirmed our impression that the HG energy for the 1 ~4~ 2state of Li is too low) but we were ~ ~

confident of being able to produce results of greater accuracy.

Our calculations, using the same Hylleraas technique

The Hylleraas method, as normally applied, but carr~ed to greater lengths, failed to reproduce

automatically gives upper bounds to every energy the energy-lowering found by HG for the second and

level, but for higher levels the accuracy of the thlrd 4 ~ 0 states and lnstead confirmed Weiss's

bounds as energy estimates falls off. We have results. It seems, then, that the HG work was in

indeed succeeded In lowering some of the HG energles error, probably due to an ill-conditioned secular

considerably, bringing about changes in calculated matrix. Calculations by Lunell and Beebe C4,51

wavelengths in some cases of 10% or more. We have also confirmed the accuracy of Werss's work.

observe that poor wave-functions can produce A detalled descriwtion of the method of our calcula-

tions is given elsewhere C61.

Quartet spectra of ions lsoelectronlc to lithium have attracted experimental attention (see the reviews of Berry [3,71,and Martinson [8]), ions as heavy as Ne VIII having been studied both by the conventional beam-foil technique and by electron spectroscopy in conjunction with a variety of

*

Permanent address

accurate transition wavelengths when the errors in the two energies involved happen to cancel, In part~cular when the correlation energxes In the two states are of simllar nature; but they cannot be relied upon so to do. A transition from a tightly bound state to a loosely bound one will be

especially prone to error. In the present work it is very difficult to estimate the accuracy of the results, but the Hylleraas technique should ensure

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979102

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¹

an excellent estimate of electron correlation energy our results agalnst Z identlfy the dominant at least in the lower states. It is therefore to configurations unambiguously except In the case of be expected that our calculated transition energies the ls2s4p and ls2p3s levels of B 111; these Ire will in general exceed the experimental values and very close together and are therefore probably

SO ourcalculated wavelengths will be a little strongly mixed. A natural orbltal analysls [13]

shorter than observations. would be needed to obtaln a quantitative lndicatlon of the configuration mixing in the wave-functions.

CALCULATIONS Our conclusions for the orderlng of the 4~ levels

agree exactly wlth those of Ali and Samanta C141 Calculatlons have been carried out for each

obtained from two-conflguratlon Hartree-Fock lon Li I -Ne VIII for the five lowest states ofeachof

calculat~ons. Ali [15] has also considered the the symmetries 4~ and 4 ~ 0 , using basis sets of

ordering of 4~ and 4 ~ 0 levels.

73 and 97 functions respectively. These basis

sets do not, however, give adequate representat~ons ^Avaluable alternative theoretical approach to of 7s, 5p and higher orbitals so results are not lsoelectronlc studles is by the Z-expansion technique presented here where the dominant configuration (in the present context references [12,16-181)

.

^he

lnvolves one of these. Our results are superior accuracy of the method is very good for such small to those by alternative methods [4,5] apart from systems and the technique can be exploited particu- the recent 200-configuration calculations by larly effectively in a semi-empirical fashion by Bunge and Bunge [lo]; these are restricted, however, use ofexperimental data to estimate expansion to the lowest states of each symmetry of ~1 I only. coefficients.

The baslc Rydberg series of lnterest here are Our results for the 4~ and

4 ~ P

levels appear ls2sns 4~ and ls2snp 4 ~ 0 , running to the ls2s 3s

in tables 1 and 2 respectively, together with the limit. The most important configuration inter- corresponding HG results. Perturlzrsare indicated actions are with series running to the ls2p 3 ~ 0

by brackets. It is particularly striking that the limit: for 4 ~ 0 ls2pnp and for 4 ~ 0 ls2pns and ls2pnd-

HG results are for the perturbersand higher In ~i I, of these levels only ls2p3s 4 ~ 0 lies below

levelsj this provides extra of the the lsZs 3s limit, the identifLcatlon of Berry [ 71 _ofour conf iguration identlf lcatlons.

based on the strength of the ~36182 llne now havlng

further support C111; however the "hydrogenic"ls2p3s- APPLICATION:

Be IIR*

ls2s3p conflguratron mlxing appears to be very

We consider here one example of the applica- small [4,5,121. All the other levels of these

tion of our results to spectral analysis; other perturbing series in Li I wlll autoionise into the

spectra will be discussed elsewhere.

appropriate ls2s~R continuum; thls need not, however,

be a rapid process. The doubly-exclted spectrum of Be I1 is at

The perturbing series play a much stronger rale in the ions. The principal effect of increasing the nuclear charge Z is to bring down the perturbing e levels against the "basic" Rydberg serles; in the non-relatlvlstic llmit Z + mls2p3p 4~ will be

degenerate wlth ls2s3s, and both ls2p3s and ls2p3d 4 ~ 0 will be degenerate with ls2s3p. At the upper end of the Rydberg series the limits ls2s and ls2p will be degenerate; in other words energies will depend only on the principal quantum numbers (hydrogenic degeneracy). Thus as Z increases in each symmetry the energy levels are re-ordeysdthe speed wlth whlch this happens is the most interesting qualitative feature of our calculatlons. The Hylleraas method does not naturally present the wave-function as linear combinations of configurations, but plots of

present the least well studied of the sequence; in particular To et al. El91 have pinted out the experimental problems of locating the 4 ~ 0 levels.

Thls is a problem we are well placed to tackle.

The existing exper~mental analysls is due largely to Hontzeas et al. [20], and we note their comments that much of the analys~s is tentative and In particular the location of the 4 ~ 0 term is in poor agreement with HG.

We obtain for the second (2s3p) and third (2~3s) 4 ~ 0 term energies 0.282 and 0.546 eV lower, respectively, than HG ( ~ n contradistinction to the situation in Li 1[1]). For the former the energy lowering is not sufficient to confirm the location of this level glven by Hontzeas et al. on the basls

0

of a strong line at 1909A identified as 2p24~-

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C1-8 JOURNAL DE PHYSIQUE

Level LI I Be IS B I11 C TV N V 0 VI F VII Ne VIII 1 5.212,59 9.619,49 15.388,88 22.519,93 31.012,37 40.866,09 52.081,Ol 64.657,ll

5.222,OS 9.627,68 25.386,9 22.527,6 32.009,7 40.862,7 52 .076,9 64.652 ,O

Table 1: 4~ binding energies in reduced Hartree units

Entries in square brackets [ ]correspond to perturbing configurations ls2p3p and ls2p4p.

Entries in italic type are results of Holbien and Geltman [2].

Level Li I 1 5.367,83

5.365,89 2 5.186,87

5.223,96

N V 0 VI F VII Ne VIII 33.171,60 43.874,31 56.077,21 69.780,25 33.266,4 43.868,8 56.072,4 69.774,s

Table 2: 4 ~ 0 blndlng energles in reduced Hartree unlts Entrles In brackets correspond to perturbers:[] for ls2p3s a n d o for ls2p3d.

Entrles in ltal~c type are results of Holdren and Geltman [ 2 1 .

Table 3: 4~

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^{4 ~ 0}transltlon wavelengths (2)m Be I1 h(vac) is glven for wavelengths <2000 2; other entrias are A (air).

Entries in brackets ( ) correspond to two-electron jumps.

Entries in itallc type are experimental results; H: Hontzeas et al.[201; M: Mannemkand Martinson [21].

bR: possible blend C211. t: see discussion in text.

+:

wavelength larger than 10,000

2.

He Rydberg taken to be 109,730.6 cm-l.

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2s2p 4 ~ 0 (a two-electron jump). For the 4~ terms we place the 2p3p perturber third with an energy 0.447 eV lower than glven by HG. Our calculatrons conflrm AX1020 and 31802, the 2s3s and 2p3s levels and hence the closed loop 1201 whrch locates the zp24p level; thrs implies a wavelength of 15122 for the 2p2 4~

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^2s2p^{4 ~ 0}transltlon and so blend- ing with the singly-excited Be I1 line at the same wavelength. They do not support the present analysis for hrgher 4~ levels [8]; rather the suggestion [20] that A755 f 22 is the 2s2p

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2s4s transition is verrfied. The transition currently allocated to AX2364 and 27642 we place at 3235 and 42482 respectively; the identlficatrons of Ah2273 and 22962 must be rejected. Our calculated wavelength for the 2s2p 4 ~ 0

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^2p3p^4~transltlon 1s 713.92, rn excellent agreement wrth the observed ~7142;

however the ldentrflcation [20] of thrs line as 2s2p 4 ~ 0

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2s4d %has been supported by Hartree- I

Fock calculatrons by All [15]. Possibly the observed line IS a blend. Table 3 sets out calculated wave-lengths for 4~ - 4 ~ 0 transrtrons together with the observatrons just discussed further ldentifications are tentatrvely advanced from comparison wlth results of work ln progress by '~annervlk and Martrnson C211. We note that, as anticipated,the calculated wavelenqtksare rather shorter than the experimental.

THE ls2s2p 4p0 STATE OF ~ e -

We have also obtained a preliminary result for the electmnaffrnity of He, or more precrsely the binding energy of the metastable ~ e - state ls2s2p 4 ~ 0 agarnst the lowest ~ e - t r i p l e t energy ls2s 3 ~ . We flnd the ~ e - energy to be -2.177672 a.u

. ,

so using Pekerls'svery accurate value for He ls2s 3~ of -2.175230 a.u. 1221 and R(Re) = 109722.3

-

1

cm

,

the electron affrnrty of He IS 0.0664 eV, in very good agreement with Weiss's unpublished value 0.067 eV (the value 0.069 eV quoted by ~ a 2 1 and elsewhere seems to be spurious) [23]. These values may be taken to be lower bounds and therefore appear to exclude theexpermentally derrved value 0.060 ?:

0.006 eV of Smlrnov [24], but are not in conflict wrth the experimental value of Brehm et al. C251, 0.080 t 0.002 eV. We plan to refrne our calcula- tlon and antlcrpate a slgnrfrcant further ralslng of our energy estimate.

Acknowledgements

We are rndebted to Professor R Manne for generously making computer resources available to us and for his hospitalrty in Bergen, to Professor I Martinson for drawrng our attentlon to these problems, for constant rnterest and encouragement, for the communlcatlon of unpublrshed results and for hrs hospitality rn Lund, and to Drs E Holdien and AW Werss for helpful correspondence. The fsrst author acknowledges a research grant from N.F.R., the SGedish Natural Sclence Research Council.

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