Finestructure transitions in doubly excited three-electron Mg9+

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PHYSICS LETTERS

27 December 1982

FINESTRUCTURE TRANSITIONS IN DOUBLY EXCITED THREE-ELECTRON Mg9~ F. TRABERT, H. HELLMANN, P.H. HECKMANN, S. BASHKIN 1 Experimentalphvsik I!!, Ruhr-Universitàt, Postfach 102148, D-4630 Bochum 1, Fed. Rep. Germany

and H.A. KLEIN and J.D. SILVER Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX] 3PU, UK Received 20 September 1982

The transitions 1s2s2p4P0_1s2p2 4P in Li-like Mg9~ions have been investigated in beam—foil experiments at Bochum and Oxford. The linestructure intervals have been determined with a precision better than 3%, and the term multiplet separation has been determined to correspond to X = (58.604 ±0.005) nm. The finestructure results are compared with several calculations.

2 4P 23/25/2 and 1s2p 112312512 states form the lowest-lying high-spin multiplets in doubly excited three-electron ions. Spin—orbit, spin— other-orbit and spin—spin interactions contribute to the finestructure splittings of these 4 multiplets (so) and Z 3with (ss, powers of the nuclear charge as Z soo). The multiplet separation only increases approximately linearly with Z. Thus for spectroscopic studies with a certain precision it should be best to study the finestructure by making measurements in elements with the highest possible nuclear charge. However, the states of the upper (ls2p2 4P)multiplet may decay not only by UV decay to the ls2s2p4P0 multiplet (decay rate ozZ), but also by spin-changing X-ray decay to the low-lying 1s22p doublet levels, or by autoionization. The probability for the latter processes increases with high powers of Z, thus weakening the UV decay branch with increasing nuclear charge and shortening the lifetimes of the levels of interest down to values which are close to the limits of experimental accessibility. Experimental work on such ions up to Z = 10 has The ls2s2p4P~

1

Permanent address: Department of Physics, University of Arizona, Tucson, AZ 85721, USA.

76

been published [1,2] and is in progress [3,4]. Early work [11 showed discrepancies between experimental results and then available theoretical data, these discrepancies were considerably reduced by a better approximation of the Breit operator [5]. the Thebody present experiment was undertaken to extend of experimental data to a high nuclear charge; limitations being UV yield and lifetimes involved [6], and blends with known spectral lines (in various diffraction orders) in the wavelength range of interest. The theoretical calculations available [5—9] predict the 4~O4~ finestructure transitions to lie close to the 1s22s 2S 22p 2~~2 3/2 resonance transitions in 112—1sLi-like Mg~,but at shorter wavelengths. singly excited These lines are in the same ionization state as the lines of interest, and as the wavelengths of the resonance lines are well known [10], they make most suitable calibration lines. In a previous study of the EUV spectrum of foilexcited magnesium [11], the range of interest for this experiment has been covered, and several lines in this range could not be identified. With the same spectroscopic set-up at the Bochum 4 MV Dynamitron tandem accelerator laboratory the spectral region indicated by the various theoretical predictions has now been investigated with much higher integrated beam current 0 031-9163/82/0000—0000/$02.75 © 1982 North-Holland

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than in the earlier survey. A beam of up to 0.8 pA MgH ions drawn from a Middleton-type sputter source was accelerated to yield about 200 nA of Mg4~at 15 MeV. The ions were passed through a 10 pg/cm2 carbon foil and at this energy 18% of the particles should emerge in the q = 9+ charge states of interest [12]. The extreme ultraviolet radiation emitted at right angles from the excited ion beam was analyzed by a 2.2 m McPherson 247 grazing incidence monochromator equipped with a 600 2/mm gold-coated ruled grating and a channeltron detector. The wavelength range studied is far beyond the blaze wavelength Xb 12.7 nm of the grating, and the solid angle of acceptance sustained by the spectrometer is only f/78. Thus the spectrometer efficiency was low and this, combined with the low beam current, resulted in a weak signal. The long data collection time led to a considerable background in the spectra, although the dark count rate of the detector was low (~lcount/2 mm). For the first search, a large slit width (150 pm) was chosen, which gave a line width (FWHM) of 0.12 nm; sufficient to separate most of the spectral components but not good enough for precise experiments. The only unidentified lines in the spectra obtained were close to the range of the predictions for the ‘IPO_4P transitions by Cheng et al. [5], but appeared at slightly longer wavelengths. The foil position was varied to investigate the temporal behaviour of these lines, and the results were consistent with our preliminary identification. A later spectrum, recorded with a slit width of 80 pm (FWHM 0.06 nm) and the spectrometer viewing the ion beam at the foil is shown in fig. 1. The calibration lines (the 2s—2p resonance lines of Mg X) on the right hand part of the spectrum may be clearly seen. Some of the lines in the enhanced central section of the spectrum shown coincide with second diffraction order images of 3—4 transitions in Mg VIII [11]. With the range of search narrowed after the Blochum observations, a Hilger E766 1 m normal incidence monochromator (f/lU) at Oxford (see ref. [13]) was used to obtain higher spectral resolution and make better wavelength measurements of the 4~0_4~ transitions. The Oxford 10 MV folded tandem accelerator with its higher terminal voltage capability made it possible to run the sputter ion source with oxygen, to extract MgO ions from the source and yet to obtain Mghl+

27 December 1982 100

Mg

19MeV

Bochurn

Spectrum smoothed

e2 eB

ci

_________________________

56

58 60 Wavelength/nm

_______

62

Fig. 1. Spectrum of Mg at 19 MeV beam energy recorded at Bochum. The strong lines on the right hand side are from the Mg X 2s—2p resonance transitions and serve as calibration lines. The line at X = 56.14 nm is the 3rd diffraction order image of Mg X 3d—4f [10,11]. The markers indicate changes of normalization (i.e. integrated beam current per channel). In the central region the normalization was 48 pC/channel.

(q = 4,5) ion beams of 30 and 40 MeV with currents up to 400 nA. At both energies the Li-like charge state fraction after passing through the foil (C 10 pg/ cm2) is close to its maximum at about 42% or 36% [12], respectively. The spectrometer was equipped with a 1200 2/mm Os-coated grating blazed for Xb 150 nm. The spectral range of interest was investigated in second diffraction order and thus close to the blaze wavelength. The strength of 1st diffraction order lines in the region scanned was reduced by the lower efficiency of the channeltron for light of longer wavelengths. The instrument has been calibrated with a hollow cathode lamp. Details of the procedure can be found in ref. [14]. The displacement of the grating sine bar was monitored on-line using a Heidenhain moire fringe length gauge. A periodic error between the motor drive and the position read out of amplitude 6 pm was observed (see also ref. [13]), corresponding to an error of ±0.005 nm in wavelength. The wavelength determination refers to a linear scale as given by the length gauge readings, remaining small nonlinearities of the calibration curve are allowed for in the error estimates. For the observation of the fast ion beam, the spectrometer was refocused [15] by moving the grating towards the ion beam. With slits 120 pm wide a line width (FWHM) in first order of 0.11 nm was achieved. Since the observation was made in second diffraction order, this corresponds to twice as high a resolving power as in first diffraction order and is similar to the 77

Volume 93A, number 2 t000

Mg

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30MeV

27 December 1982

Oxtord

~ 3~

1001

i~5~1 ~

~°°

Mg 30 MeV I

I

~

Wove~gth/nm

Fig. 2. Sum of spectra ofMg at 30 MeV beam energy recorded at Oxford. The Mg X lines of interest appear in second diffraction order. A change of normalization is indicated.

Oxford

OL~~ 57

58

59

Fig. 3. Part of a spectrum of Mg at 30 MeV beam energy recorded at Oxford. The wavelength scale has been altered to represent first diffraction order wavelengths. Top markers identify 4P°—24Pfinestructure transitions. The normalizathe Mg tion wasX 62pC/channel.

resolution obtained in the Bochum experiment. A disadvantage of observation in second diffraction order is the appearance of unwanted spectral lines in various diffraction orders (here first or third), some of which blend with expected components in the Mg9~transition array under study. Examples of the spectra recorded at Oxford are shown in figs. 2 and 3. The wavelengths and line identifications are given in table 1. Better conditions at Oxford, mainly the acceptance

angle of the spectrometer, the more suitable grating and the optimum beam energy resulted in a signal rate of the spectra taken at Oxford which was higher by almost two orders of magnitude. Two spectra were recorded both at 3U and 4U MeV beam energy. Due to the low yield of the finestructure transitions it was not possible to position the exciter

Table I Identification of the observed lines of magnesium in the Oxford spectra. Wavelength x (nm) (1st order)

Diffraction orderm

Classification

Commept

115.26 28.82 34.42 57.762 ±0.008

1 4 3 2

Mg Mg Mg Mg

blended broad

58.093 ±0.005 58.435 ±0.005 58.680 ±0.015 58.7 10 ±0.015 59.070 ±0.015 118.14 29.56 59.375 ±0.005 40.43 40.487 60.9787

2 2 2 2 2 1 4 2 3 i 3 2

VIII 5—6 VIII 3—4 XI 5—7 X 4P~, 4P 4P~ 2—4P 5,2 Mg X 4P~ 12—4P 312 Mg X 4P~—4P 2— 312 Mg X4P?, 4P 512 Mg X 2— 112 Mg X P312~~2 MgVIlI5—6 Mg VIII 4P~, 3_4 4P Mg X 2— 312 Mg X 4—52~i/2 Mg —2p2P~, X 2s 2

broad calibra-

61.500±0.005 61.603 ±0.005

21 2

Mg XI 5—6

broad

Mg X 6—7 2S Mg X2P~ 2s 112 —2p 2

broad

62.4952

78

~} 2

60

WaveLength / nm

blend -d broad

tion [101

calibralion [101

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foil with respect to the spectrometer using the lines of interest. Instead the long-lived Mg X 2s—2p transitions had to be used, resulting in slightly different foil positions for the 4 spectral scans. The lifetimes of the 4P levels range 5 to 169 ps [6], resulting in aloss of intensity of from the short-lived components. The errors of the wavelength determination result from several sources: The uncertainty of the wavelengths of the calibration lines [10] is very small cornpared to the level of accuracy of this experiment and has been neglected. The accuracy of the wavelength reference scale is then determined by the precision of the localization of the reference lines. The reproducibility of the relative positions of the long-lived calibration lines was excellent. It was limited not by statistics but by the nonperfect description of the line shape by a gaussian or other simple curves, The precision of the wavelength determination of the weak components of the Mg X p0_4p multiplet was statistics limited. In case of line blendings the error has been estimated conservatively to reflect the uncertainty of the intensity distribution in a broader line profile. The error estimates given in table 1 also reflect the reproducibility of the spectral lines, The finestructure intervals and the term separation have been deduced by least-squares fitting to the individual spectra. The averaged results are given in table 2, together with values obtained from an interpolation of predictions by Cheng et al. [5] which

Table 2 Multiplet separation ~TCG of centers of gravity (see ref. [5J) and finestructure intervals ~T. The data related to ref. [51 result from an interpolation along the isoelectronic sequence. The data related to ref. [91are calculated from ref. [91using the experimental Mg X 2s—2p term difference [101. ___________-

Interval

Term difference (cm_i) This work

Theory

4p04p

170637 ±16 58.604 ±0.005 nm

~58.03 nm [5] 58.7 nm [91

1010 ±20

980

are close to the experimental values. Very similar fs splittings result from the Z expansion data of Vainshtein and Safronova [9] when combined with the experimental term values of the Mg X 2p 2P~t 4~O4~ of 23/2 levels [10]. [7] Theasmean term separation Goldsmith derived from the level positions is closer to the experimental results than the one interpolated from the calculation by Cheng et al. The fs splitting obtained by Goldsmith, however, is significantly smaller than indicated by the other calculations and matches the experimental values less well. The multiplet separation, i.e. the term value difference of the centers of gravity of the 2 4p0 and 2 4P level multiplets, has been determined to correspond to a wavelength of X = (58.604 ±0.005) nm. The ab initio calculations [5,7] deviate from this value by about L~X 0.5 to 0.6 nm, corresponding to a term difference error of about 1 500 cm—1. Among the contributions to the 4~O4~ term difference which have not been included in the available calculations [5,7] are QED effects. For example, the 2s—-2p Lamb shift difference for an ion with Z = 11 (Mg X* with the nucleus screened by the one ls electron) amounts to 229 cm—1 [16], and the present experimental precision corresponds to about 7% of this Lamb shift contribution. The omission of the Lamb shift in the presently available calculations ought to result in an underestimate of the mean transition wavelength by about 0.05 nm. The deviation of the theoretical values from the experimental one, however, is larger by an order of magnitude and indicates shortcomings in the non-Lamb shift part of the calculations. We conclude that present theoretical calculations are not yet precise enough to be tested for QED contributions whereas the present experimental accuracy would already allow to do this. Further experimental work at Oxford will try and improve the accuracy of the wavelength measurement. At Bochum an improved spectrometer is under construction which will be used to investigate the lifetimes of the 1s2p2 4P levels. These lifetimes are sensitive to higher-order coupling interactions and relate i.a. to autoionization rates. It should also be possible to extend the present work to aluminium and possibly sili.

________

[51

27 December 1982

.

.

.

.

4P~, 4~i/2~4~3/2

2—~P~,2

2708 ±20 1824±35

~~3,2—~5,2 ___________

1995 ±25

2670 [5] 1820 [5] -

1960 [5] __________

con. The provision of ion beams and other assistance by the accelerator crews at Bochum and Oxford is grate79

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fully acknowledged. Mr. T. Thacker diligently helped with the data transfer. Messrs. R. Hucke, B. Muller, H.R. MUller and G. Schneider assisted in the Bochum runs. Two of us received travel support, by the Deutsche Forschungsgemeinschaft (E.T.) and by the Alexander-von.Humboldt-Stiftung and NATO (S.B.), respectively. We acknowledge valuable discussions on theoretical aspects with J. Hata and I.P. Grant who are working on an improved calculation of the term structure including QED effects. References [I] A.E. Livingston and HG. Berry, Phys. Rev. A17 (1978) 1966. [21 E.J. Knystautas, and R. Drouin, in: Beam—toil spectroscopy, Vol. 1, eds. Sellin and Pegg (Plenum,New York, 1976) p. 393. 131 I. Martinson, private communication.

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14]

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AL. Livingston and H.G. Berry, private communicalion.

[5 J (1978) K.T. Cheng, L359.J.P. Desclaux and Y.-K. Kim, J. Phys. Bl I [6] T.W. Tunnell and C.P. Bhalla,Phys. Lett. 67A (1978) 119. [7] S. Goldsmith, J. Phys. B7 (1974) 2315. [81 B.C. Fawcett, priv~atecommunication. [91 L.A. Vainshtein and UI. Safronova, Atom. Data Nucl. Data Tables 21(1978) 49. 1101 B. EdlCn,Phys. Scripta 19 (1979) 255.

Ill]

E. Triibert and PH. Heckrnann, Phys. Scr. 21(1980) 146.

1121 R.O. Sayer, Rev. de Phys. AppI. 12(1977)1543. [13] l.A. Armour, E.G. Myers, J.D. Silver and E. Träbert, Phys. Lett. 75A (1979) 45. [14] HA. Klein, S. Bashkin, B.P.Duval, F. Moscatelli,J.D. Silver, H.F. Beyer and F. Folkmann, J. Phys. B, lobe publislied. [15] .1.0. Stoner Jr. and J.A. Leavitt, Appl. Phys. LetI. 18 (1971) 477. 116] G.W. Erickson, J. Phys. Chem. Ref. Data 6(1977) 831.