Variational method for excited atomic states

An analysis is presented of the extremum properties of energy functionals for the excited states of many-electron systems, in particular, atoms, in the case when there exist low-lying states of the same symmetry as the excited state under consideration. Two theorems are proved concerning the relationship between the upper bound on the eigenvalues corresponding to the excited states and the extremum properties of the energy functional determined by variational test functions which depend on parameters. In this context, different variants of the one-electron approximation used in the excited-state calculations are considered: the method of obtaining self-consistent solutions with one-electron functions orthogonal within the configurations (the Hartree-Fock method for configurations); the frozen atomic core approximation for the excited configuration; the method of nonorthogonal orbitals in the excited configuration; and the approximation of the frozen ionic core. Cases are identified and reasons given for the possible collapse of the excited state energy level to an unjustifiably low value of the energy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 18–33, August, 1990.     

Laser-induced transitions between triply excited hollow states

We present an ab initio calculation of the Li+ photoion yield in the presence of laser coupling between the triply excited 2s(2)2p(2)P(o) and 2s2p(2) (2)D(e) resonances in lithium, the first of which is assumed excited by synchrotron radiation from the ground state. The laser coupling between the triply excited states is shown to lead to a significant and readily measurable modification of the line profile which provides a unique probe of the dipole strength between highly correlated triply excited states.     

Comment on measuring photoionization cross sections of excited atomic states

The results of the measured absolute photoionization cross section from the 7² P excited states of cesium are reported. The following values have been obtained: (6.2±0.5)×10⁻¹⁸ cm² and (8.8±1.6)×10⁻¹⁸ cm² for the levels 7² P _1/2 and 7² P _3/2, respectively.     

类铍离子N3+激发态的能量、振子强度和跃迁几率

利用多组态相互作用方法及Rayleigh-Ritz变分法,计算了类铍N3+ 基态(1s22s21S)和三个激发态(1s22s2p1P0, 1s22s2p3 P0, 1s22p23P)的能量,运用截断变分方法得到能量的改进量,包括了相对论能量和质量极化效应.计算了相关态的振子强度和辐射跃迁率.计算结果与其它理论和实验结果符合得很好.     

Two-photon transitions between discretenS states in atomic He

Summary The two-photon transition probabilities from the ground state 1¹ S and from the metastable states 2¹ S and 2³ S to the lowest excited states are computed in He. A configuration interaction approach is used, and a detailed comparison between the ?length? and the ?velocity? gauges leads to an estimate of 1% accuracy. Correlation effects are found to account for about 20% of the transition probabilities. The life-time of the 2¹ S state is ≅19.6 ms. The two-photon transition probabilities display a dramatic dependence on frequency, characterized by resonances and transparencies. Based on work supported in part by the Gruppo Nazionale di Struttura della Materia of the C.N.R. and by the Frascati Synchrotron Radiation Contract (P.U.L.S.).     

Theoretical oscillator strengths for the NI and OI resonance transitions

We report results from the first many-body calculations of the important oscillator strengths of the resonance lines NI $\text{1s}{}^2\text{2s}{}^2\text{2p}{}^3{}^4\text{S°?is}{}^2\text{2s}{}^2\text{2p}{}^2\text{3s}{}^4\text{P(λ=1200}\text{A}\text{?}\text{), 1s}{}^2\text{p}{}^2\text{3d}{}^4\text{P(λ=953}\text{A}\text{?}\text{)}$ and OI $\text{1s}{}^2\text{2s}{}^2\text{2s}{}^2\text{2p}{}^4{}^3\text{P ?1s}{}^2\text{2s}{}^2\text{2p}{}^3\text{3s}{}^3\text{S°(λ = 1304}\text{A}\text{?}\text{)}$. Our values are: $\text{?(1200)=0·271; ?(1304)=0·047; ?(953)= ·082}$. The first two are in excellent agreement with recent lifetime and absorption measurements and thus the existing discrepancy between theory and experiment is resolved. The third number constitutes the only available result for this transition.     

Experimental investigations of oscillator strengths for ultraviolet transitions in LaII

f-values for ultraviolet transitions from nine excited levels in LaII have been deduced by a combination of lifetime and branching ratio measurements using time-resolved laser spectroscopy and the emission spectrum from a hollow cathode lamp. Part of the present results is compared with previous results. Received 10 February 1999 and Received in final form 22 April 1999     

Energy levels and optical oscillator strengths of inner-shell excited states and photoionizations of the ground and first excited states of C IV ion

Extensive configuration interaction wave functions are determined to calculate the energies of the inner-shell excited states and the oscillator strengths of the optically allowed inner-shell transitions of C IV ion. Photoionization cross-sections of the ground and the first excited states of C IV ion are also obtained by using the R-matrix method. The positions of some inner-shell excited states are redetermined more accurately by analyzing the resonance structures of the photoionization processes. Some of the results are compared with other available theories and experiments. Received 29 September 1999 and Received in final form 8 December 1999     

Differential oscillator strengths and dipole polarizabilities for transitions of the helium sequence

The dipole radial integral for an initial discrete 1s state and a final continuum state has been calculated under the screened hydrogenic model. In this model, single-electron hydrogenic wave functions are employed and the initial and the final states are treated by two different effective-charge parameters. Numerical values of differential oscillator strengths for transitions from 1s 21S to the continuum for the helium sequence ions are obtained. Also calculated are the dipole polarizabilities, which are found to be in excellent agreement with the results of other authors.     

Optical oscillator strengths for atomic nitrogen based upon an analytic IPM model

An analytic atomic independent particle model is used to generate optical oscillator strengths for a variety of transitions in atomic nitrogen. The results generally compare favorably with those obtained from Hartree-Fock-Slater calculations and experiment. Where differences arise, it would appear that the parameter adjustment technique of this IPM model insures a closer representation of the properties of excited atomic states.     

Dipole oscillator strengths for Δn = 0 transitions in highly ionized sulfur

The foil-excitation method has been used to measure f-values for intra L-shell transitions in highly ionized sulfur.     

Discrepancies between theoretical and experimental atomic oscillator strengths of the sodium isoelectronic sequence resonance transition

Discrepancies between theoretical and experimental estimates of the oscillator strengths of the sodium isoelectronic sequence resonance transition are considered in the light of recent multi-configuration Hartree-Fock results. Possible experimental difficulties in the cascading analysis arising from a peculiar pattern of excited-state lifetimes are examined using computer simulations of decay curves.     

The kinetics of electron transitions for donors with excited states

A new theory of the kinetics of non-equilibrium phenomena involving shallow donors with excited levels is presented, applicable to experiments on photoconductivity, impact ionization, current-controlled negative resistance, and the like. For the steady-state case the solution obtained is rigorous. For the transient case a rigorous solution would not in general be feasible, but it is shown that under certain conditions of sample purity it reduces to a trivial modification of the steady-state solution. Numerical results are given for the requisite region of sample purity.     

Electric dipole transitions for highly excited states in helium-like sulphur

We have calculated relativistic energies, weighted oscillator strengths and transition probabilities for electric dipole (E1) transitions among the terms belonging to 1snl (n?9, l?3) configurations in helium-like sulphur. The calculations are based upon the multiconfiguration Hartree-Fock method within the framework of Breit-Pauli relativistic corrections. Our calculated values are also compared with other experimental and theoretical results.     

Radiative lifetimes of excited states and oscillator strengths of spectral lines of some lanthanide atoms and ions (Review)

Journal of Applied Spectroscopy -     

Comparison between analytical and numerical methods as applied to calculations of excited atomic states

This article presents a comparison between two approaches for implementing a variational method when calculating excited states of atoms, namely a numerical approach in which the equations arising from the requirement of an extremum of the variational functional (the Hartree—Fock equations) are solved, and an analytical approach in which the energy functional expressed in terms of analytical test functions is minimized. Both approaches are analyzed from the point of view of the approximations used to ensure that the conditions are satisfied for the complete wave function of the excited state being sought to be orthogonal to all wave functions of lower-lying energy states having the same symmetry. The well-known ATOM package is used for numerically solving the Hartree—Fock equations and the MINMAX package is used for the analytical variational calculations. It is shown that the analytical approach based on the minimax method possesses greater possibilities for taking account of relaxation effects. A comparison is made between single-electron wave functions, the matrix elements, and the energies of dipole transitions for a number of excited states of the Ne atom, as calculated using both approaches. State Pedagogical University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 120–128, July, 1998.