Centrifugal barrier effects in the high Rydberg states and autoionising resonances of neon

Transcription

1 J. Phys. B: At. Mol. Phys. 17 (1984) Printed in Great Britain Centrifugal barrier effects in the high Rydberg states and autoionising resonances of neon M A Baig and J P Connerade Physikalisches Institut Universitat Bonn, 53 Bonn, Nussallee 12, West Germany and Blackett Laboratory, Imperial College, London SW7 2AZ, England Received 21 December 1983 Abstract. The photoabsorption spectrum of neon in the range A has been investigated at high resolution using synchrotron radiation and a 3 m normal incidence vacuum spectrograph equipped with holographic gratings. All of the five Rydberg series 2p5( P3/,)ns[3]y, nd[fj?, [fly and 2p5(2P,,,)ns[i]y, nd[f]y have been extended to high principal quantum numbers yielding accurate values for the ionisation potentials (2P,/2 = Jt0.2 cm- andzp,/, = Jt0.2 cm-i). Incontrast with thecorresponding features of heavier rare gases, the ns-nd interchannel interactions and autoionisation broadening are shown to be weak. This behaviour is discussed with reference to multichannel quantum defect and Hartree-Fock theory, and is shown to result from centrifugal barrier effects in the nd channels. 1. Introduction Helium is usually regarded as the exception amongst the rare gases, because it is the only one with an s2 outer shell. In a more subtle way, neon is also unique, because it does not precede a transition sequence in the Periodic Table. As will be shown in the present paper, this simple fact has a profound effect on the appearance of the spectrum in the autoionisation range. The p-shell spectra of the rare gases are built on a parent ion with a nearly closed shell. The spin-orbit interaction of the inverted doublet defines the energy range within which autoionisation of the series to the 2P1,2 limit can occur. The resulting spectra are classic examples, both (i), of autoionisation (Beutler 1935, Fano 1961) and (ii), of interchannel interactions in a system with two limits (Lu and Fano 1970) which can be represented by two-dimensional quantum defect plots (Seaton 1966). In addition to the pioneering work quoted above, there have been more recent studies of both (i) and (ii) using improved experimental and theoretical techniques, but these have concentrated on Ar, Kr and Xe. Photoabsorption spectroscopy (Yoshino 1970, Yoshino and Tanaka 1979, Baig et a1 1981a), photoionisation mass spectroscopy (Berkowitz 1979 and references therein), electron-spin-polarisation spectroscopy (Heinzmann 1980, Schafers et a1 1983) and laser spectroscopy (Grandin and Husson 1981, Delsart et a1 1981) have all successfully been applied. Theoretical extensions, based mainly on Seaton s multichannel quantum defect theory (Seaton 1966) have also been reported by many groups (Lu 1971, Lee and /84/ The Institute of Physics 1785

2 1786 MA Baig and J P Connerade Lu 1973, Lee 1974, Geiger 1976, 1977, Johnson and Le Dourneuf 1980, Aymar et a1 1981). Very recently, (i) and (ii) were brought even more closely together in an explicit formula for line profiles of an autoionising series developed by Dubau and Seaton (1984) (see also Seaton 1983), and it was shown that an extended Rydberg sequence of resonances can indeed be represented with just four parameters (Connerade 1983). For neon, the studies have been less extensive, owing mainly to experimental problems. Codling et a1 (1967) performed the first experiment covering the full autoionising range between 200 and 650 A. They worked at the 180 MeV electron synchrotron at the National Bureau of Standards (Washington) with a 3 m grazing incidence spectrograph and a 600 line/" grating. The quoted resolution was about 0.06 A, which is insufficient to extract the line profiles. Subsequently, the resonances were studied by Radler and Berkowitz (1979), who used a 3 m normal incidence monochromator in the second order of a 1200 line/" grating at the Stoughton 240 MeV storage ring, and achieved a resolution of A, which is still insufficient for line profile analysis. More recently, Ganz et a1 (1983) have studied the low-lying autoionisation resonances 2p514s and 2ps12d by two-photon laser excitation and mass-spectrometric ion detection. They achieved a resolution of 4 GHz, which is very high, but were only able to study two resonances. In the present paper, we report a high resolution (i0.004a) spectrum of neon, covering the full range A. All of the five expected Rydberg series have been observed and extended to high principal quantum numbers, yielding accurate values for the ionisation thresholds. Intermediate coupling calculations for p5ns of neon (Baig and Noeldek 1984) show that J,K coupling is the appropriate scheme. Single-configuration calculations using the Froese Fischer (1977) code demonstrate the varying degrees of penetration of the wavefunction of the excited electron into the core as a result of barrier effects in the 2p5nd channel, and our results are discussed in the light of the expected differences of penetration. 2. Experimental The details of our experimental set-up are described in earlier papers (Connerade et a1 1980, Baig et a1 1981a, b). In brief, spectra were recorded (i) in the first order of a 5000 line/" 3 m holographic grating and (ii) in the second order of a 6000 line/" 3 m holographic grating, mounted in an out-of-plane Eagle spectrograph built at Imperial College (Learner 1965). In case (i), maximum sensitivity and, in case (ii), maximum resolution were achieved. The dispersion in case (ii) was 0.27 A mm-', and the photoabsorption continuum above the ionisation limit of Hg I at 1178 A (Baig 1983) was used as a filter for order sorting. Synchrotron radiation emitted by the 500 MeV accelerator at the University of Bonn was focused on the 10 pm entrance slit of the spectrograph by a grazing incidence bent mirror 60 cm long. Commercial grade neon was leaked into the beam line at a pressure of a few pm over a path length of about 6 m. Exposure times ranged from 5 to 20 min on Kodak SWR plates. The spectra were calibrated in wavelength by superposing emission spectra of Cu 11 (Kaufmann and EdlCn 1974) from a hollow cathode run in helium in the first order. A final wavelength calibration was achieved using internal standards of neon and helium lines which are known to four decimal places (Kaufmann and EdlCn 1974). The dispersion

3 J. Phys. B: At. Mol. Phys. 17 (1984) Printed in Great Britain [facing p 17861

4 Autoionising series in neon 1787 curve was fitted by a third-order Tchebichev polynomial to an internal consistency of *0.0004A. The plates were measured on an Abbe comparator with an absolute accuracy of * A. 3. Results and discussion The absorption spectrum of neon in the wavelength range A is shown in figure 1 (plate). All the observed lines can be arranged in five series converging on two limits according to the excitation scheme: and 2s22p6 'so+ 2s22p5(2~3/2) ns[;]? 2s22p5(2~1/2) ns[$]? nd[il? nd[% nd[ll? where three series converge to the 'P3/2 limit and two to the 2P1/2 limit, in accordance with the selection rules for dipole excitation from the ground state. We use the J,K notation (Racah 1942, Cowan and Andrew 1965) for level designation. The members of the series to the limit which lie below the ionisation threshold perturb the series to 2P3,2, while those which lie above the ionisation limit autoionise into the 2p5(2P3/2) Es,Ed continua. Both effects are described within the framework of multi- channel quantum defect theory, as further discussed below. The data exhibit few irregularities of intensities or line spacings. The relatively strong nd[$]? series, previously observed to n = 17 (Codling et a1 1967) has been extended to n = 44, and the next strongest series ns [$I: has been extended from n = 18 to 30. To determine the series limits from the present data, we used the Rydberg formula and required that the quantum defect approach a constant value at high n for the strongest nd series to each limit. This procedure yielded and cm-' respectively for the 2P3/2 and 2P1/2 limits, with an absolute uncertainty of k0.2 cm-'. To compare our results with earlier data, we have also calculated the ionisation potentials using the data of Kaufman and Minhagen (1972) for the 2p5(2P3,2)nf[z]: (n = 4-9) and 2p5(2Pl,,)nf[z]f: (n = 4-8) levels, which are the least perturbed series. A computerised fit by least squares yielded and cm-' in good agreement with our values derived from the nd series. In what follows, we consider the analysis of the interchannel interactions, which we have performed within a multichannel two-limit approach. Before discussing it in detail, it is worth noting the obvious fact (see the spectrum of figure 1 (plate)) that the lines in the autoionising range remain sharp, which implies that the interactions responsible for broadening are weak. More specifically, the 13s[i]y line is only 20 cm-' below the 'P3/2 threshold, and therefore interacts with the higher members of the series converging on the first ionisation limit, whereas higher members of the ns[$]y series interact with the continuum. The change in appearance between 13s and higher members is not noticeable as the ionisation threshold is crossed towards higher energies, which shows that the interchannel interactions are small.

5 1788 M A Baig and J P Connerade We now turn to a discussion of the quantum defect plot illustrated in figure 2, which summarises the information on series perturbations in the energy range below the ionisation limit contained in the present data d I I I, I I I I I $(mod 11 Figure 2. Two-dimensional quantum defect plot of the interchannel interactions between the ns and nd series of Ne I. The graph is displayed according to the technique described by Lu and Fano (1970), based on Seaton s (1966) quantum defect theory. In brief, a Rydberg series together with its adjoining continuum constitute a single channel. In a two-limit system and in the presence of interchannel interactions, discrete states are treated on an equal footing, i.e. no apriori classification is attempted. Thus, the levels are referred to both ionisation potentials and two effective quantum numbers nt and n: are deduced for each level referred to the limits II and 12. The two numbers are functionally related by the expression (Lu and Fano 1970, Brown et al 1976) where A = (12-11)/R. For neon, Iz-Il = cm-, R = cm- and n$ =

6 Autoionising series in neon is the effective quantum number at the first ionisation threshold. One exploits the cyclic property of the Rydberg formula and plots the fractional parts of nr and nt as abscissa and ordinate for all experimentally determined levels of the Rydberg series to II and I2 which lie above Il. The resulting curve (figure 2) establishes the empirical function which describes the periodic nature of the series perturbation. As will be seen below, this curve also contains information about the interchannel interaction above Il. When the autoionising series in Ne, Ar, Kr and Xe are intercompared, two striking differences emerge: (i) the nd resonances in Ar, Kr and Xe exhibit typical, broad Beutler-Fano type asymmetric lineshapes, while the ns resonances are very sharp. In Ne, the situation is different: the ns resonances are broader than the nd resonances and autoionisation is much less conspicuous; (ii) the ns resonances are shifted towards higher energies as one proceeds from Xe to Ne. In Xe, a pair of lines is formed, e.g. by lld and 13s with lld on the lower energy side. In Kr, the same situation prevails for corresponding features (13s and lld), but the splitting decreases. In Ar, the pairs of lines (13s and lld) are nearly degenerate, while in Ne the 13s level crosses over to higher energy than lld and forms a pair with 10d. In effect, the ns series members can be regarded as energy 'markers' which give the potential of the atom without centrifugal effects, and the energies of the nd series members relative to them yield information on centrifugal barrier penetration. Both (i) and (ii) are attributable to centrifugal barrier effects involving the d electron. We have therefore performed ab initio Hartree-Fock calculations to study penetration of the centrifugal barrier as a function of atomic number. Our argument runs as follows: the entire nd series of Xe can be well represented by a four-parameter formula due to Seaton and Dubau (see Connerade 1983), and the widths fall off as l/n"3, which shows that, once the autoionisation profile of a low-lying member in the series is known, the profiles of all the upper members are implicitly determined. It is therefore adequate to consider the spatial overlaps of the wavefunctions for the lowest members in order to build up a consistent picture of the trend from Xe to Ne. In figure 3, we show that the lowest d wavefunctions move inwards and that their overlap with the p5 core increases from Ne to Ar, the most sudden jump being between Ne and Ar. The consequences of the increase in overlap are (i) larger autoionisation probability, as noted above, (ii) a departure from hydrogenicity which is apparent from the quantum defects, and (iii) an increase in transition probability for p+d excitation as one goes from Ne to Xe (see also figure 4). We therefore conclude that all the systematic trends noted above in the data for the rare gases are attributable to centrifugal barrier effects in the p'nd channels. The behaviour of the quantum defects under the influence of barrier penetration was also discussed by Griffin et a1 (1969) for outer-shell excitations, but their study did not involve interchannel coupling effects. For inner-shell excitation, the situation is more complex. This is reflected in the quantum defect plot of figure 1 (plate), which shows very narrow avoided crossings for the ns-nd interchannel interactions of Ne, and therefore implies slow autoionisation rates above the ionisation limit. All five Rydberg series possess nearly constant quantum defects. In tables 1-5, we list the ns and nd Rydberg series of neon, together with effective quantum numbers as measured in the present experiment.

7 1790 M A Baig and J P Connerade Ne 10- Ar Xe rloul Figure 3. Hartree-Fock radial wavefunctions for core-excited Ne, Ar, Kr and Xe. Note how the 3d wavefunction of Ne overlaps much less with the 3s wavefunction and with the 2p core than the corresponding wavefunctions in the heavier rare gases.

8 .A. Autoionising series in neon V Z I - n- - 0 Z -50- U - c 0 n w? - c. t ' -.A. W i " " 1 " " 1'5 2' '0 r Iaul Figure 4. Effective radial potentials for the d electrons in core-excited Ne, Ar, Kr and Xe. The potential for Ne is entirely repulsive near the core, in contrast to the potentials for the other rare gases. The lowest energy d wavefunctions of Ne and Xe are also shown, to emphasise the difference in penetration on the scale of the figure. In table 6, we intercompare quantum defects for the rare gases. As can be seen from this table, the quantum defects of the ns series grow by approximately one unit from one rare gas to the next. For the nd series, the situation is slightly different: filling of the 3d subshell begins only after Ar, beyond which the quantum defect increases by roughly one unit from one rare gas to the next. Between Ne and Ar, however, there is no change in occupation of the d subshell, and the quantum defect changes only by a small fraction of unity. This behaviour is readily understood in terms of quantum defect theory for the situation where a short-range well develops inside the atom, where it has been shown (Connerade 1982) that a phase change of T (equivalent to a change of unity in the quantum defect) occurs every time a new bound state is trapped in the short-range well. If we consider the ns quantum defects

9 1792 M A Baig and J P Connerade Table 1. 2p6 'So- 2p5(2P3,,)ns[$J~. n A(A) v(cm-') n* t t Blend. Table 2. 2p6 'So+ 2p5('P3,,) nd[$]y as 'markers' in the sense described above, the quantum defects, which differ by one unit between the ns and nd series in Ne, become out of step by one further unit beyond Ar because an h er bound state of the d potential well is filled in each of the long periods. We can express the relationship simply as follows. If n, is the number

10 Autoionising series in neon 1793 Table 3. 2p6 'So+ 2p5(2P3,2)nd[t]:. n A (A) v (cm-') n* of occupied s subshells and nd is the number of occupied d subshells, then: 6N = n,- nd- 1 gives the approximate value of the difference between the ns and nd quantum defects in table 5. It is interesting to compare this situation with the recent study by Hill et al (1982) of the evolution of the ns and nd series along the isoelectronic sequence Xe, Cs' and

11 1794 MA Baig and J P Connerade Table 4. 2p6 'So+ 2p5(*P,,,)nd[$]: Ba2+. These authors found that the ns resonance widths are essentially independent of nuclear charge, whereas the widths of the nd resonances increase drastically from Xe to Ba2+. Correspondingly, they also found that the two-dimensional quantum defect plot of the ns-nd interchannel interactions gave very narrow avoided crossings in Ba2+, and they attributed the drastic change to a modification of the balance between the centrifugal and nuclear terms in the effective radial potential. 4. Conclusion The present study has resulted in extensions of the Rydberg series due to excitation of one electron from the 2p subshell of neon. The data have been compared with corresponding data for the other rare gases, and we are able to understand the changes in quantum defects and autoionisation widths by reference to multichannel quantum

12 Autoionising series in neon Table 6. Intercomparison of quantum defects for the ns and nd series of the inert gases. Data from Moore (1971). Identification Ne Ar Kr Xe (2P3/2) ns[tly ? nd[41? (2pl,2) ns[ nd[fl? defect theory and to independent particle ab initio calculations. Centrifugal barrier effects are shown to play a dominant role. Acknowledgments We thank Professor G Noeldeke (University of Bonn) and Professor W R S Garton, FRS (Imperial College) for their continued interest in our work. We are grateful for

13 1796 MA Baig and J P Connerade financial support received from BMFT (Federal Republic of Germany) and from SERC WK). References Aymar M, Robaux O and Thomas C 1981 J. Phys. B: At. Mol. Phys Baig M A 1983 J. Phys. B: At. Mol. Phys Baig M A, Connerade J P and Pantelouris M 1981a EGAS Conf, Heidelbeg vol. SA (Geneva: EPS) p 109 Baig M A, Hormes J, Connerade J P and McGlynn S P 1981b J. Phys. B: At. Mol. Phys. 14 L725 Baig M A and Noeldeke G 1984 to be published Berkowitz J 1979 Photoabsorption, Photoionisation and Photoelectron Spectroscopy (New York: Academic) Brown C M, Tilford S C and Ginter M L 1977 J. Opt Soc. Am Beutler H Phys Codling K, Madden R P and Ederer D L 1967 Phys. Rev Connerade J P 1982 J. Phys. B: At. Mol. Phys. 15 L J. Phys. 3: At. Mol. Phys. 16 L329 Connerade J P, Baig M A, Garton W R S and McGlynn S P 1980 J. Phys. B: At. Mol. Phys. 13 L705 Cowan R D and Andrew K L 1965 J. Opt. Soc. Am Delsart C, Keller J C and Thomas C 1981 J. Phys. B: At. Mol. Phys Dubau J and Seaton M J 1984 J. Phys. B: At. Mol. Phys Fano U 1961 Phys. Rev Phys. Rev. A Froese Fischer C 1977 The Hartree-Fock Method for Atoms (New York: Wiley) Ganz J, Siege1 A, Bossert W, Harth K, Ruf M W, Hotop H, Geiger J and Fink M 1983 J. Phys. B: At. Mol. Phys. 16 L569 Geiger J 1976 Z. Phys. A Z. Phys. A J. Phys B: At. Mol. Phys Grandin J P and Husson X 1981 J. Phys. B: At. Mol. Phys Griffin D C, Andrew K L and Cowan R D 1969 Phys. Rev Heinzmann U 1980 J. Phys. B: A#. Mol. Phys Hill W T, Cheng K T, Johnson W R, Lucatorto T B, McIlrath T J and Sugar J 1982 Phys. Rev. Lett Johnson W R and Le Dourneuf M 1980 J. Phys. B: At. Mol. Phys. 13 L13 Kaufman V and EdlCn B 1974 J. Chem. Refi Data Kaufman V and Minhagen L 1972 J. Opt. Soc. Am Learner R C M 1965 unpublished Lee C M 1974 Phys. Rev. A Lee C M and Lu K T 1973 Phys. Rev. A Lu K T 1971 Phys. Rev. A Lu K T and Fano U 1970 Phys. Rev. A 2 81 Moore C E 1971 Atomic Energy Levels NBS Circular No 35 (Washington, DC: US Govt Printing Office) Racah G 1942 Phys. Rev Radler K and Berkowitz J 1979 J. Chem. Phys Schafers F, Schonhense G and Heinzmann U 1983 Phys. Rev. A Seaton M J 1966 Proc. Phys. Soc Rep. Prog. Phys Yoshino K 1970 J. Opt. Soc. Am Yoshino K and Tanaka Y 1979 J. Opt. Soc. Am