Multiconfiguration Hartree-Fock Approximation Research Articles

M1 and E2 transitions in the ground-state configuration of atomic manganese

Using the multiconfiguration Hartree–Fock approximation within the framework of the Breit–Pauli Hamiltonian (MCHF+BP) and the relativistic Hartree–Fock (HFR) approximation, we have calculated the forbidden transition (M1 and E2) parameters such as transition energies, logarithmic weighted oscillator strengths and transition probabilities between the fine-structure levels in the ground-state configuration of 3d54s2 for atomic manganese (Mn I, Z = 25). A discussion of these calculations for manganese using MCHF+BP and HFR methods is given here.

On the line intensity ratios of prominent Si II, Si III, and Si IV multiplets

Line intensities of singly, doubly and triply ionized silicon (Si II, Si III, and Si IV, respectively) belonging to the prominent higher multiplets, are of interest in laboratory and astrophysical plasma diagnostics. We measured these line intensities in the emission spectra of pulsed helium discharge. The Si II line intensity ratios in the 3 s3 p 22 D–3 s 24 p 2 P o , 3 s 23 d 2 D–3 s 24 f 2 F o , and 3 s 24 p 2 P o –3 s 24 d 2 D transitions, the Si III line intensity ratios in the 3 s3 d 3 D–3 s4 p 3 P o , 3 s4 p 3 P o –3 s4 d 3 D, 3 s4 p 3 P o –3 s5 s 3 S, 3 s4 s 3 S–3 s4 p 3 P o , and 3 s4 f 3 F o –3 s5 g 3 G transitions, and the Si IV line intensity ratios in the 4 p 2 P o –4 d 2 D and 4 p 2 P o –5 s 2 S transitions were obtained in a helium plasma at an electron temperature of about 17,000 ± 2000 K. Line shapes were recorded using a spectrograph and an ICCD camera as a highly-sensitive detection system. The silicon atoms were evaporated from a Pyrex discharge tube designed for the purpose. They represent impurities in the optically thin helium plasma at the silicon ionic wavelengths investigated. The line intensity ratios obtained were compared with those available in the literature, and with values calculated on the basis of available transition probabilities. The experimental data corresponded well with line intensity ratios calculated using the transition probabilities obtained from a Multi Configuration Hartree–Fock approximation for Si III and Si IV spectra. We recommend corrections of some Si II transition probabilities.

Large scale multi-configuration Hartree-Fock calculation of the hyperfine structure of the ground state of vanadium

Abstract The hyperfine structure of the ground state of vanadium, 51VI, is calculated in the nonrelativistic framework of the multi-configuration Hartree-Fock approximation. A configuration state function limiting algorithm is used to make the calculations feasible and to study the influence of core, valence and core-valence correlations in detail. The obtained configuration state function space captures the most important orbital correlations within 2%. Further correlations are included through configuration interaction calculation. The atomic state functions are used to evaluate the magnetic dipole hyperfine factor A and the electric quadrupole factor B. It turns out that the ab initio calculation can not capture the core polarization of the 2s shell. It introduces an error that is higher than the Hartree-Fock approximation. However, the detailed correlations being observed suggest the introduction of a wrong correlation orbital due to the algorithm being used. Neglecting this orbital leads to good agreement with 2% deviation from the experimental values for the A factors.

Extension of the single-channel MCHF method to include multichannels

The multiconfiguration Hartree–Fock (MCHF) method for single open channel has been extended to include multi-open channels. The coupled integro-differential equations satisfied by the radial wavefunctions of the multi-open channels associated with the scattering of electrons by atoms and ions at low energies are solved completely numerically self-consistently in the MCHF approximation to obtain the required linearly independent solutions. The asymptotic scattering parameters obtained from these solutions are used to calculate cross sections. The electron correlation and polarization effects which are very important for scattering of electrons at low energies can be obtained completely ab initio through the configuration interaction procedure. The extended method is now capable of performing calculations for both elastic and inelastic scattering processes. As a test case, we have calculated contributions to both elastic and inelastic cross sections for scattering of electrons from hydrogen and helium atoms as well as ionized helium at a few low energies for few partial waves including a few open channels. Our results are compared with similar data obtained by other existing approximate methods and are found to be in excellent agreement confirming a successful extension.

Relativistic energies and transition probabilities for some highly excited levels in singly ionized indium

For some excited levels (n⩽8), the energies, wavelengths, oscillator strengths and transition probabilities calculations in singly ionized indium have been calculated within the framework of multiconfiguration Hartree–Fock approximation with relativistic corrections (Breit–Pauli Hamiltonian). The wavefunctions and some relativistic corrections have been obtained using MCHF–BP atomic package. Comparisons with other calculations and experiments are presented.

Bowen Fluorescence, Stark Broadening, and Transition Probabilities in the O iii Spectrum

The intensity ratios of the 344.405, 342.863, and 343.057 nm spectral lines of doubly ionized oxygen (O III), which originate from the 2p3d 3P levels, have been investigated in optically thin laboratory plasmas in pure oxygen and helium-oxygen mixture at 42,000 and 47,000 K electron temperatures and at electron densities in the range 1022-1023 m-3. Two of them (344.405 and 342.863 nm) belong to the primary cascade in the astrophysically important Bowen fluorescence mechanism. On the basis of the I(344.405 nm)/I(342.863 nm), I(344.405 nm)/I(343.057 nm), and I(343.057 nm)/I(322.863 nm) O III line intensity ratios, in pure oxygen and helium-oxygen plasmas, we have found that the 343.057 nm O III spectral line also shows fluorescence tendency caused by the Bowen mechanism not evident up to now. The transition probability values (Einstein's A-values) of these transitions are obtained by means of the relative line intensity ratio (RLIR) method using, for the first time, the O III spectral lines in emission spectra. We have found that our experimental transition probabilities agree well with calculated A data based on the multiconfiguration Hartree-Fock approximation (MCHF) including the Breit-Pauli potential. Besides, the A-values of the 342.736 and 344.036 nm lines, belonging to the forbidden 3s-4d O III transitions, are also obtained. They are the first measured data. Stark broadening parameters [line width (W) and shift (d)] of the mentioned O III lines have also been measured. They are the first published data.

Large electron correlation effects in the nondipole asymmetry parameters near photoionization thresholds

The nondipole corrections to the dipole approximation for the angular distribution of photoelectrons are calculated for Ar $3s$ subshell in the Hartree-Fock (HF) approximation for photoelectron energies ranging from threshold to 2 keV. The effects of electron correlation which are very important have been taken into account using the multiconfiguration HF approximation. It is found that near the threshold from 0 to 50 eV photoelectron energy, the nondipole parameters show oscillatory structure due to large electron correlation effects. The results are compared with existing theoretical and experimental data.

Photoabsorption and photoionization of titanium from excited states

Photoabsorption and photoionization cross sections are reported from 3d24s4pD32o, 3d24s4pG33,4o and 3d34pF55o initial states of titanium, reaching final-state energies from −500 to 8000 cm−1 relative to the first ionization threshold 3d24s4F3/2. The nearly ab initio calculations use the eigenchannel R-matrix method, the multichannel quantum-defect theory, and the LS → jj relativistic recoupling frame transformation. The last two steps use experimental energies of Ti+ levels. Radial orbitals needed to calculate short-range interaction parameters are obtained in a multiconfiguration Hartree–Fock approximation that directly generates natural orbitals for the target states. This method bypasses an intermediate step followed in earlier eigenchannel R-matrix studies, in which a set of primitive orbitals was used. Theoretical cross sections are compared with experimental data, in particular near the two lowest ionization thresholds 3d24s4F and 3d3 4F. Our results, which at these energies are accurate to within errors of ∼0.03 in the quantum defects, account for most of the experimental features. Predictions are also made for the spectra at higher energies, where overlapping Rydberg series seriously complicate the photoabsorption pattern.

Autoionization studies of the 1s2s2p 4P5/2 levels in He-, Li I, and Be II.

Autoionization rates of the 1s2s2p $^{4}$${\mathit{P}}_{5/2}$ level are computed for ${\mathrm{He}}^{\mathrm{\ensuremath{-}}}$, Li i, and Be ii, using the golden-rule formalism in the multiconfiguration Hartree-Fock approximation. The main objective is to clarify ambiguities concerning the metastable $^{4}$${\mathit{P}}_{5/2}$ component in ${\mathrm{He}}^{\mathrm{\ensuremath{-}}}$, whose lifetimes differ significantly in various works. The present calculations reveal a much shorter lifetime, 345 \ensuremath{\mu}s, than predicted in earlier theoretical works. Our result for ${\mathrm{He}}^{\mathrm{\ensuremath{-}}}$ is in perfect agreement with recent measurements, and for Li i and Be ii we agree well with other theoretical predictions.

Photoionization of magnesium

Photoionization from the 3s subshell of magnesium is investigated in the energy region near threshold where several resonances have been observed. Theoretical cross sections are reported. The latter have been computed using the multi-configuration Hartree–Fock approximation extended to include a continuum function. Results are compared with other theories and experiment.

Allowed and Forbidden n = 2?2 Transitions of the Elements Kr and Mo

Relativistic intermediate-coupling wavefunctions are used to evaluate transition energies, line strengths and transition probabilities for all allowed and forbidden n = 2-2 transitions for krypton and molybdenum beryllium-like ions. Our results are in very good agreement with those calculated using the relativistic multi-configuration Hartree-Fock approximation. These calculations were carried out under the same physical assumption that the dominant correlation effect is the n = 2 intra-shell correlation. We also discuss the importance of relativistic effects on the radial functions, the relativistic intermediate-coupling scheme in the variational process, the importance of radiative corrections for transition energies between states with different occupation of the 2s shell, and the relative importance of intra- versus inter-shell correlation effects.

Electron impact excitation of Si X

Excitation cross sections of Si9+ by electron impact have been computed, for comparison, in different approximations and in different target descriptions using a computer package developed at University College London. Collision strengths have been calculated for fine-structure transitions between the ground configuration term 2s22p 2P0 and the excited configurations 2s2p2 4P, 2D, 2S, 2P and 2p3 4S degrees , 2D degrees , 2P degrees of Si9+ using the eight-state close-coupling approximation and distorted-wave approximation for the energy range 6.0 to 70.0 Ryd. Configuration interaction and spin-orbit interaction within the configurations 2s2p2, 2p3, 2s2p3d, 2p23d, 2s3d2 and 2s23d have been taken into account. Wavefunctions for the target states and hence the oscillator strengths are calculated by using the multiconfiguration Hartree-Fock approximation with the four orbitals 1s, 2s, 2p, 3d and the above mentioned three odd and four even configurations. Collision strengths have also been calculated by a five-state close-coupling approximation between the configurations 2s22P 2P degrees and 2s2p2 4P, 2D, 2S, 2P allowing configuration interaction between 2s2P 2P degrees , and 2p3 2P degrees configuration and spin-orbit interaction within the 2s2p2 configuration. The authors' results indicate that the use of an elaborate target description and a more accurate treatment of the collision problem may change some cross sections by more than 25%. The results are compared with earlier work. This problem has important applications in plasma diagnostics and in the interpretation of the extreme ultraviolet solar emission spectrum.

Indirect nuclear spin-spin coupling constants within the coupled multiconfiguration hartree-fock approximation

The multiconfigurational coupled Hartree-Fock expression for the Fermi contact contribution to the indirect nuclear spin-spin coupling constants is derived Numerical calculations on H2 and FH indicate that the nuclear spin-spin coupling is very difficult to describe in finite basis set calculations.

Oscillator strengths for2S-2P transitions in the copper sequence

Theoretical results based on the multiconfiguration Hartree-Fock approximation are reported for 4s2S-4p2P transitions of the Cu sequence. A partially extended Hartree-Fock model was used in which at last 3d orbital was not constrained to be the same as the rest. Some core-polarization effects were also included. Non-relativistic and approximate relativistic f values are reported and compared with observation.

Investigation of the excitation spectrum of an exact nuclear model by the MCHF approximation

Abstract The multiconfiguration Hartree-Fock (MCHF) method is applied to the exactly solvable model of Lipkin, Meshkov and Glick. The energy spectrum is investigated for truncation of the Hartree-Fock basis states in the weak, intermediate and strong coupling regions. There is a good agreement between the computed low lying states and the exact ones, in the weak and intermediate coupling regions. But the low lying spectrum is strongly modified in the strong coupling region. An explanation is given for this behavior. The ground state energy is found to be very well reproduced in all the three regions.

Oscillator strengths of some Ba lines, calculated in MCHF approximation

Several states of neutral Ba were calculated in the non-relativistic multi-configuration Hartree Fock approximation. Energies and mixing parameters were found. Oscillator strengths for dipole transitions are given and compared with values in the literature. The transition probability of the infrared line 61P0-51D at 15000 AA is negligible compared to that of the resonance line 61P0-61S. The quadrupole transition probability of 51D-61S at 8775 AA is about 2 s-1.

The effect of correlation on the excitation probability Kr 4p 6→Rb+ 4p 5 5p following β-decay

Using a multi-configuration Hartree-Fock (MCHF) approximation for the stationary states, the effect of correlation on the excitation probability, Kr 4p61S→ Rb+ 4p5 5p1S is studied. It is shown that the MCHF approximation equivalent to a nonorthogonal Hartree-Fock approximation, is the most important correction to the Hartree-Fock total wave function, and that the remaining correlation, though significant, has a much smaller effect.

Oscillator strengths for 3 dn4 s → 3 dn4 p transitions in the iron series

The observed oscillator strengths for the 3 d n 4 s → 3 d n 4 p transitions in the iron series show anomalous behaviour for Cr and Mn : the former is exceedingly small whereas the latter is unusually large. Theoretical Hartree-Fock gf-values are reported and a considerable discrepancy with experimental values is noted for Cr. The effect of the interaction of 3 d n 4 p with 3 d n−1 4 s4 p is studied using a fixed core, multi-configuration Hartree-Fock approximation. This interaction does not improve significantly the agreement with observed values.