One of the most significant developments in computational atomic and molecular physics in recent years has been the introduction of B-spline basis sets in calculations of atomic and molecular structure and dynamics. B-splines were introduced in applied mathematics more than 50 years ago, but it has been in the 1990s, with the advent of powerful computers, that the number of applications has grown exponentially. In this review we present the main properties of B-splines and discuss why they are useful to solve different problems in atomic and molecular physics. We provide an extensive reference list of theoretical works that have made use of B-spline basis sets up to 2000. Among these, we have focused on those applications that have led to the discovery of new interesting phenomena and pointed out the reasons behind the success of the approach.
We present a revised analysis of the spectrum of singly ionized xenon, Xe II. This spectrum has been reanalyzed on the basis of the wavelength material published by Drs J. C. Boyce and C. J. Humphreys. The latter has kindly placed the original wavelength list covering the wavelength range 10 220-390 Å at our disposal. We report 161 energy levels which have been identified on the basis of classifications of 950 lines. We report the first f and g levels in Xe II. Also a number of g-factors have been determined for the first time and we give in total 75 g-factors. We have carried out least-squares fits to the even configurations and report the resulting parameter values and eigenvector compositions. A least-squares fit to the 5p46p configuration is also reported. The levels have been named in jK and for many levels also in LS coupling. The former is the better coupling scheme for Xe II. We present an analysis of the 5s photoelectron satellite spectrum of Xe based on our calculated eigenvector compositions and calculations of transition probabilities for ground state transitions as well as lifetimes for the 6p levels. The latter are compared to recent experimental measurements. A list of wavelengths for observed laser transitions showing the present classifications and a discussion of the determination of the ionization potential of Xe II concludes the paper.
We have calculated energy levels and radiative transition probabilities in the ground configurations of the sulfur and selenium isoelectronic sequences up to molybdenum and silver, respectively. Transition probabilities have been obtained for M1 and E2 "forbidden lines" within the p4 configurations using electrostatic and spin-orbit integrals for the interactions within this configuration deduced by a fitting procedure to the available experimental energy levels or by graphical inter(extra)polation of Slater parameters along the sequence when the energy levels are unknown. Some of the most important configuration interaction and relativistic effects have been included explicitly using the HFR self-consistent method due to Cowan and Griffin. For most of the ions in the selenium sequence, transition probabilities are reported for the first time. The effects of including configurations with 4f electrons explicitly have been studied for both the 3p3 and 3p4 configurations.
Abstract. We present extensive configuration itenction (CI) calculations of oscillator strengths, transition probabilities and lifaimes of upper levels ofall transitions in Ar 11 between the levels of 3s236.3s3p6. 3p43d. 3p44s and 3p44p states. The calculations incorporate the major correlation effects and in addition allow for the orbital Functions (pticularly 3p) to be effectively different for different slates. Some discrepancies with experimental energies remain. pmicularly those of levels with a 3p' 'S care. Prior to the calculation of the oscillator strengths. we 'hne-tune' &e o mefficients using experimental enerpies. Specifically, the final cl coefficients are determined following small adjustments to the diagonal Hamiltonian matrix elements so that the calculated eigenvalue difkrences agree with the corresponding experimental energy separations. This work describes in detail our previous calculations of quattet levels and extends the calcularions to other symmetries. Comparison with recent, highly accurate casxde-free experimens shows close accord in all but a small number of transitions.
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