(D)2/(n-m)) 1/2The compilation of energy levels of atoms and ions has been initiated at the National Bureau of Standards in 1946. Three volumes, prepared by Charlotte E. Moore, have been issued in the period 1949-58 (1). The covered elements ranged from hydrogen to lanthanum and from hafnium to actinium. By lack of substantial data, the publication of the fourth volume was delayed. The interpretation of the rare earth spectra made progress in the 60's and early 70's and the volume "Atomic Energy Levels - The Rare Earth Elements" by W.C. Martin, R. Zalubas and L. Hagan (2) covered in 1978 the sequence from lanthanum to lutetium (Z = 57-71)
After 1978, the spectroscopic activities at the National Bureau of Standards were oriented mainly towards multicharged ions and revised compilations were published in a number of elements, actinides being left aside. In the meantime, the interpretation of spectra was continuing for elements beyond actinium in a number of laboratories. In 1982, the compilation of their energy levels was undertaken by the authors with the encouragement of the spectroscopic community and the technical assistance of the Association pour le developpement des Tables de Constantes et Données Numériques.
The time evolution of the production and interpretation of these outermost complex spectra is similar to those of lanthanides. The decisive steps in the techniques were:
- The use of electrodeless discharge tubes (3), these sealed light sources preventing from the contamination by radioactive elements, and of large grating spectrographs. The 9.15 m Paschen-Runge spectrograph at Argonne National Laboratory deserves a special mention, allowing Zeeman patterns to be resolved and wavelengths to be measured from 245 nm to the photographic infrared.
- After 1970, the first Fourier transform spectrometers built at Laboratoire Aimé Cotton (4) were used to record the first and second spectra of Th, Pa, U, Np, Pu, Cm, Bk and Cf in the infrared and, later for some of them, in the visible. At the same time, a chain of programs for atomic structure calculations following the Slater Condon method and Racah algebra was especially written in the same laboratory for the large configurations built on fN cores (5). For these experimental and theoretical reasons, the authors have been involved in the analysis of the first and second spectra of all actinides, their role in Ac and Am being limited to level interpretations. In high resolution extended studies of isotope shifts and hyperfine structures, the Fourier transform spectrometers replaced the Fabry-Perot interferometers which were very useful in the early 60's for starting the analysis of some spectra.
- Since 1980, many actinide spectra have been recorded at Kitt Peak National Observatory by Fourier transform spectrometry. Simultaneously, the revision and improvement of the early analyses has been performed by a reduced number of specialists. Only a part of these results has been published in journals. The references to unpublished works (unp.) are numerous throughout the Tables and prove that the actinide spectroscopy is still well alive.
The aim of the present volume is the compilation of experimental data and, for theoretical backgrounds, the reader should consult the "The Theory of Atomic Structure and Spectra by R.D. Cowan (6) and, for a more fundamental approach to the group theory, "Operator Techniques in Atomic Spectroscopy" by B.R. Judd (7). The bases of atomic structure calculations in the central field approximation had been detailed earlier in "The Theory of Atomic Spectra" by Condon and Shortley (8). Such theoretical studies are usually named Slater-Condon (or parametric) calculations. In this approach, the configurations provide the 0th order of the perturbation theory and they are split into levels by electrostatic and magnetic interactions of their electrons. The radial integrals involved in the matrix elements of the perturbing hamiltonian are treated as adjustable parameters chosen so as to minimise the root mean square deviation of the energies
( (D)2/(n-m)) 1/2
D = Eexp-Eth, n = number of experimental levels, m = number of free parameters.
The low configurations of neutral and singly-charged actinides are characterised by several open subshells resulting in a large number of levels. The binding energies of the 5f and 6d electrons are very close and the configurations overlap. Several terms in the hamiltonian have similar importance and, after diagonalisation, the eigenvectors are far from any coupling limit, i.e. there is no good quantum number except J. For a rigorous theoretical analysis, the hamiltonian should be calculated on the basis of all states of several configurations. In most cases, for computer capacity reasons, this requirement cannot be satisfied and the parametric calculations in the actinides did not get the same achievements as in the transition elements or in the lanthanides.
A model for further interpretations was given by Racah in 1950 on the groups of configurations 5f(6d+7s), (6d+7s)2 and 7p(6d+7s) in ThIII (9), which led to rms deviations of about 1 % of the interpreted energy range. In neutral thorium, the more complicated system 6d27s2+6d37s was analysed by Trees in 1960 (10). In single configuration approximation, Judd has shown in 1962 (11) that intermediate coupling calculations for some 5fN6d configurations can explain the position of the lowest levels and their g-values. The number of theoretical studies increased after 1965 and all these works are referenced (for configurations with more than two electrons) in an historical survey of the theory of complex spectra from the 1930's to January 1985 (12). Only two studies of general interest are recalled here: the 5fN levels of trivalent ions have been predicted by taking into account the interaction with distant configurations by means of effective operators (13;14). A less elaborate study of 5fN7s2 and 5fN7s configurations was useful for identifying some dozens of levels in various elements (15). A diagram of known and predicted energy levels of EsII 5f117s ground configurations is given as an exemple in.
Theoretical interpretations of the hyperfine effects use the eigenvectors of fine structure studies as an intermediate step. The magnetic dipole hyperfine structure was studied theoretically in Pu (16) and Th (17), the latter work including also electric quadrupole hfs studies. The parametric interpretation of the isotope shifts was reviewed by Bauche and Champeau (18). Its unique application to actinides was recently issued for ThI and ThII (19).
As a preliminary step for parametric analyses, selfconsistent field methods have been used to determine radial wavefunctions of the electrons in the actinides and to obtain ab initio values of Slater and spin-orbit radial integrals (20-23)
It is finally expected that the amount of uninterpreted experimental data reported in the Tables will stimulate theoreticians for further improvements.
The attribution of energy levels to configurations is the initial step of their theoretical interpretation. The isotope shift, the intensity of the transitions with previously identified levels, can indicate which may be the dominant configuration before calling the Slater-Condon method for confirmation and quantitative evaluations. Large hyperfine structures which trace unpaired s electrons also contribute to these semi-empirical identifications. The attribution of energy levels to configurations by using pattern recognition techniques has also been attempted in a few cases (24-26). The interpretation of a spectrum is made easier when the lowest levels of the main configurations are known and, therefore, these data have been collected in Table I.
In 1971, Brewer combined all the available spectroscopic identifications with thermodynamic data on lanthanide and actinide metals in order to predict the energy of the lowest levels in configurations involving the valence electrons (5f, 6d, 7s and 7p in actinides). His predictions for neutral atoms (27) and ions (28) have since been confirmed with a few exceptions. For exemple, the energy difference 5f66d7s2 _ 5f7s2 in Am I had been misidentified by Nugent and Van der Sluis (29) as 17858 cm-1, predicted in (27) at 17000 ± 1000 cm-1 and revised to 15200 cm-1 in (30), whereas the present experimental value is 10684 cm-1 (31). Brewer's estimates remain useful and replace the missing experimental data in the Table I, but some LS names attributed by him to the lowest levels of unknown configurations might well be incorrect. The present Table I has been limited to Z = 100, but predictions beyond fermium are given in several publications (27;28;29;30;32;33).
We have added to the same Table I, the ionisation limit of the atom or ion. Most of these values are from semi-empirical (S.E.) determinations by Sugar (34;35) who used the following assumptions:
1) the energy intervals DT between the center of gravity of 5fN7s2 and 5fN7s8s are smoothly dependent on N, and
2) the quantum defect evolution is the same as for lanthanides.
Rydberg series have been observed, with many members and laser stepwise excitation in neutral uranium and neptunium and a few members for Th IV in spontaneous emission. Ionisation limits have been derived from electron impact ionisation experiments in the case of thorium. The results of this method are more difficult to interpret and the spectroscopic values are to be preferred when available.
In the case of uranium, the ionisation limit of the atom and all the ions have been calculated ab initio by means of the Dirac-Fock method.
In 1957, the third volume of Atomic Energy Levels ended with element actinium (Z = 89) and did not include any result for francium (Z = 87). Indeed the spectroscopy of francium started at CERN twenty years later (36) in a joint project of atomic and nuclear physicists. A substantial extension of the first results appeared in 1986-89 (37;38;39;40). The alkali-like Fr I spectrum consists of one optical electron outside the closed subshells of the radon-like core. The optical electrons have the same quantum numbers as those of complex configurations in actinides. By analogy with lower-Z elements (caesium and the lanthanide period), it is expected that some regular trends in electron jumps and spin-orbit splittings as a function of Z will make Fr I a useful reference for further work in the actinides and this is the reason for compiling the 57 known levels in this introduction.
All levels have been determined by laser-spectroscopy on two different isotopes. Below 32466 cm- 1, the levels of 212Fr I are measured by collinear fast beam laser spectroscopy with an accuracy of 0.002 - 0.004 cm-1 (except 15d 2D5/2 with an accuracy of 0.020 cm-1) (37;38;40). Above 32466 cm-1, the laser resonance photoionisation of 221Fr atoms in a hot quasi-enclosed cavity led to 19 levels with uncertainties ranging from 0.080 to 0.300 cm-1 and with unresolved nd 2D fine structures (39). Owing to the fact that the isotope shift in the 7p 2P3/2 - nd,ns transitions mainly originates from the mass effect and is negligible compared to these uncertainties, the measured lines of 221Fr I 7p 2P3/2 - nd,ns are combined with the 212Fr I 7p 2P3/2 level value in order to make a consistent set of levels for the latter isotope. All the values in Table II are for the center of gravity of the hyperfine sublevels (nuclear spin I = 5), except for the excited ns 2S terms, in which only the F = 11/2 hyperfine sublevel is given by the experiment.
The isotope effect explains the difference between the ionisation limit values reported in (39) and (40), the most accurate value, relative to the center of gravity of the 7s 2S1/2 level being 32848.876(±0.007) cm-1 (40) for 212Fr I.
Except for Ac III (41) which was excited in arcs three decades ago, the experimental studies of multicharged ions have been devoted to thorium and uranium, as described in the Tables when energy levels have been derived. Additional informations which were considered as irrelevant for tabulation are surveyed in this Chapter.
Only Ac III, Th III and U III have been observed and partially interpreted s0 far. It is seen in Table III that U III and elements of higher Z have 5fN ground configurations. In doubly-ionized lanthanides the splitting of the ground terms in 4fN is slightly larger than for 4fN6s2 in neutral atoms (2). Similar comparisons in the actinides are hampered by the perturbation of 5fN7s2 by surrounding configurations in the known elements and it cannot be concluded if the removal of the 7s2 subshell leads to the same regularities as for 6s2 in the lanthanides. The predicted splitting of the lowest terms in 5fN is of interest for starting the analysis of these spectra and Carnall and Crosswhite (13) have determined the levels of 5fN configurations with estimated parameters, including those for electrostatic and magnetic effective interactions. Selected results are given in Table III, which makes obvious the breakdown of LS coupling with increasing Z. The only comparison with experiment in U III shows that the theoretical splitting is 4 % too small. No general conclusion is drawn for the rest of the sequence.
Trebly-ionized actinides
Numerous experimental studies of trivalent actinide ions in crystals or in solutions have led to some knowledge of their ground configuration 5fN. These configurations have been calculated by Carnall and Crosswhite (13) and selected low levels are reported in the Tables.
The search for lasers operating at wavelengths shorter than 4.4 nm and the plasma diagnosis in controlled fusion devices have stimulated the spectroscopy of highly-charged ions in the past decade. Nevertheless, the actinides did not benefit much from these activities. The spectra of high-Z ions have similar features which can be investigated in stable elements without facing contamination problems. Neither technecium (Z = 43) nor promethium (Z = 61) nor any actinide, except thorium and uranium, have been investigated so far. It is known from many applications in highly-charged ions that ab initio calculations of atomic structures lead to predicted wavelengths with accuracies (lexp -lth)/lexp of about 10-3 for transitions with a change in principal quantum number n and about 10-2 for Dn = 0 transitions, inasmuchas main configuration mixings and an approximate Lamb shift are considered. The most widely used of the atomic structure codes are based on the multiconfiguration Dirac-Fock method (42;43); the need for extending the QED corrections initially considered in (46) from K and L shells to M and N shells being mentionned in (44). The relativistic parametric potential method (45;46;47) which starts from the central field approximation leads to the same accuracies.
In this paragraph, a brief description of the spectra and energy levels is given by increasing charge of the ions.
- The spectra Th VIII through Th XVI are responsible for a strong emission (5f-5d transitions) centered at 10.5 nm in a plasma produced by laser irradiation (1 J, 25 ns laser pulses) (48). The equivalent peak for uranium (1.5 J, 25 ns laser pulses) is located near 9.5 nm (49) and resonance lines (6p-5d and 5f-5d transitions) of closed-subshell ions U XIII with ground level 5d106s2 1S0 and U XV with ground level 5d10 1S0 are identified in the range 9.38-12.5 nm. The isoelectronic transitions are also present in the ThXI and ThXIII spectra (50) .
- At a stronger excitation (TEXT tokamak plasma with central electron temperature near 1 keV and electron density ne ~1013 cm-3) the spectrum of uranium shows "two well separated spectral features centered at 7 and 8.8 nm and lines originating from ions with simple ground states such as 5s25p6, 5p65d and 5p65d10 superimposed on them" (51). The broad peaks are interpreted in terms of 5p65dk - 5p65dk+1 and 5p65dk - 5p65dk-15f unresolved transition arrays of U XVI - U XXIII, which cannot be distinguished from 5s25pk - 5s25pk-15d, 5s5pk+l transitions of U XXV - U XXX. The spectra of the same uranium ions produced by laser irradiation are observed in the range 2 - 12 nm (52), but according to (51), "the entire domain presents a continuous and rather amorphous structure in which it is difficult to identify individual transitions".
- In the vicinity of closed shells, the spectra of highly-charged ions gain some simplicity. U XXXII has an alkali-like spectrum, the lowest configurations comprising one 5l electron outside closed-shells K, L, M and N. The two lines of the resonance doublet 5p-5s are predicted by the Dirac-Fock method at 8.725 and 17.963 nm (53), but this is not yet supported by observations. The isoelectronic sequence of neodymium corresponds to ions with a single isolated ground level 4f14 1S0 when the hydrogenic rearrangement of the subshells has occured. However the resonance lines corresponding to the excitation of the n = 4 closed subshells have not been observed in any element. Neon-like and nickel-like ions also have a closed-shell ground state and their resonance lines are prominent. It is believed that, in plasma conditions favouring the charge states near U32+, the resonance lines of U XXXIII should be prominent as well. They have been calculated by means of the relativistic parametric potentiel method especially for inclusion here. The four odd configurations with J = l levels resulting from the excitation of 4d104f14 are calculated with configuration mixing effects, which prove to be small (less than 0.3 %) except for two very close levels of 4f135g and 4d95p. Since all intracomplex electrostatic interactions (excitation of 4s24p6) have not been considered, the inaccuracy of the theoretical wavelengths reported in Table IV could been as large as 0.006 nm.
- By stripping the n = 4 shell, the configurations with open 4f, 4d, 4p subshells should lead to a bulk of unresolved transitions similar to the one observed in xenon (54), rare earths (55) and tungsten (56). By empirical extrapolation, the transitions of U XLVIII-U LVI ending on 4p64dk around configurations should occur near 3.1 nm.
- The availability of high power lasers (24 beams of 60 J energy, 450 ps pulse duration each, converging on spherical targets) made it possible to approach the relatively simple sequences of zinc, copper and cobalt, around the closed shell sequence of nickel (57). The five lines of Th LXI, Th LXIII and the 3 lines of U LXII, U LXIII, U LXV, measured with an experimental uncertainty of 0.0015 nm, are listed in Table V.
Copper-like and zinc-like emission peaks are also prominent in the vicinity of resonance lines of nickel-like ions. The average wavelength and full width at half maximum (FWHM) of the unresolved transition arrays (UTA) - the UTA formalism and its applications being reviewed in (58) - have been calculated ab initio and compared with experimental spectra in gold and neighbouring elements (59;60). Pending for the publication of experimental results on thorium and uranium (61), the same approach has been applied to the 3d-4f, 3d-5f, 3d-6f and 3p-4d transitions of copper-like Th LXII, U LXIV and zinc-like Th LXI, U LXIII, which are collected in Table VI with their nickel-like parent transition (62).
- To the best of our knowledge, the spectra of neon-, sodium-, and magnesium-like thorium and uranium have not yet been observed, but the UTA formalism was used in (62) for predicting the average wavelength and full width at half maximum of the n = 3 - n = 2 transitions, as reported Table VII.
- Checks of the fundamental theories - Dirac equation, quantum electrodynamics- in few-electron systems are an incentive for studying the spectra of highly-stripped high-Z ions, in which precision requirements on wavelengths are less severe than for low-Z elements. Helium-like and hydrogen-like uranium have been produced from U92+ bare nuclei at Lawrence Berkeley Laboratory (63) and the transition ls2p 3Po ls2s 3S1 observed at 260±8 eV (64) is in agreement with predictions from the MCDF (65) or 1/Z-expansion (66) methods. The energy level separation among n = 1 and n = 2 levels in H-like U XCII have been determined theoretically (67).
References