Multiconfiguration Hartree-Fock Method Research Articles

Excitation cross sections for electron scattering fromK+ions

The $B$-spline Breit-Pauli $R$-matrix method is used to investigate electron scattering from singly ionized potassium in the energy range from threshold to $400\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The primary aim of the present work is to resolve discrepancies between the available experimental and theoretical cross sections for excitation of the ${\mathrm{K}}^{+}$ resonance lines. The multiconfiguration Hartree-Fock method with term-dependent nonorthogonal orbitals is employed for an accurate representation of the target wavefunctions. The close-coupling expansion includes 43 bound levels of ${\mathrm{K}}^{+}$ covering all possible terms of the lowest configurations $3{p}^{6}$, $3{p}^{5}4s$, $3{p}^{5}3d$, $3{p}^{5}4p$, $3{p}^{5}5s$, and $3{p}^{5}4d$. Our results confirm that the apparent cross section for the $(60.1+60.8+61.3)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ emission line from the $3{p}^{5}(4s+3d)$ levels in the crossed-beams experiment of Zapesochny et al. {Zh. Eksp. Teor. Fiz. 90, 1972 (1986) [Sov. Phys. JETP 63, 1155 (1986)]} was normalized with an error of about a factor of 4. We also present the cross sections for excitation of the $3{p}^{5}4p$, $3{p}^{5}5s$, and $3{p}^{5}4d$ levels and discuss the cascade contribution from higher excited levels to the $3{p}^{5}4s$ and $3{p}^{5}3d$ levels.

Hartree-Fock studies of the triple differential cross section for electron-impact ionization of the hydrogen atom

We report absolute triple differential cross sections in coplanar ${\ensuremath{\theta}}_{12}=\ensuremath{\pi}$ geometry for the ionization of atomic hydrogen by electron impact at low energies. We used our recently extended multiconfiguration Hartree-Fock method successfully to calculate triple differential cross sections of H for incident energies ${E}_{0}$ of 14.6, 15.6, 17.6, 20, and 25 eV for equal energy sharing of excess energies by the two final state continuum electrons. It has been shown that there is very little difference between the results obtained in the Hartree-Fock and the screening potential approximations implying that in the case of H and ${\ensuremath{\theta}}_{12}=\ensuremath{\pi}$ configuration distortion effects between the two outgoing electrons are small even at low energies. Our results are compared with available absolute and relative experimental data and other existing theoretical calculations and are found to be in very good agreement.

Energies and Lifetimes for Some Excited Levels in La I

We calculated relativistic energies and Lande factors for 5d6s, 5d6s, 5d, 5d6s7s, 4f6s6p, 5d6s6p, 5d6p, and 4f5d6s levels in neutral lanthanum (Z = 57). We also obtained electric dipole transition energies and lifetimes for some excited levels. The calculations are based upon the multiconfiguration Hartree–Fock method within the framework Breit–Pauli relativistic corrections. Moreover, the results obtained were compared with other calculations and experiments.

An ab initio study based on a finite nucleus model for isotope fractionation in the U(III)–U(IV) exchange reaction system

Isotope fractionation in the U(III)-U(IV) reaction system was investigated by a series of atomic relativistic ab initio calculations using the multiconfigurational Dirac-Coulomb Hartree-Fock method. To evaluate the nuclear volume effect on the fractionation, the Fermi statistical distribution function was adopted for nuclear charge density. The isotope fractionation coefficient epsilon resulting from the nuclear volume difference was evaluated from the total electronic energies of U3+ and U4+, based on the theoretical equation proposed by Bigeleisen [J. Am. Chem. Soc. 118, 3676 (1996)]. The calculated fractionation coefficient epsilon in the present work for the isotopic pair 235U and 238U at 293 K is 0.0031, which is quite close to the experimentally observed value of 0.0027. Discussion is extended to the nuclear volume effects on isotopic fractionations in the Pu(III)-Pu(IV) and Eu(II)-Eu(III) exchange systems.

Hartree–Fock results for electron impact ionization of H atoms

The multiconfiguration Hartree–Fock method for bound and continuum wavefunctions has been extended to investigate electron impact ionization of atoms. As a test case, the method is applied to calculate triple differential cross sections for electron impact ionization of H atom at an excess energy of 4 eV for the coplanar θ12 = π geometry. The results are obtained for both equal and unequal energies of the two outgoing electrons in the Hartree–Fock (HF) and screening potential (SP) approximations in order to determine the importance of electron correlation between the two outgoing electrons in the present configuration. At equal energies, both the HF and SP results are found to be very close to each other and are in very good agreement with the relative experimental measurements and other accurate theoretical calculations. At unequal energies, both calculated results also compare well with the relative experimental data over all ranges of θ1 considered by experiment.

Electric dipole transitions for La I ( Z=57)

Wavelengths, weighted oscillator strengths and transition probabilities for electric dipole ( E1) transitions for some excited levels in neutral lanthanum (La I, Z=57) have been calculated using the multiconfiguration Hartree–Fock (MCHF) method within the framework of Breit–Pauli relativistic corrections. Results obtained have been compared with other calculations and experiments. A discussion of these calculations for La I in this study has also been given in view of the MCHF method.

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 1 snl ( 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.

Relativistic all-order and multiconfiguration Hartree-Fock calculations of the4d−4fenergy separation in Li I

We present a calculation of the 4d-4f energy separation in Li I using two advanced techniques in atomic structure theory, namely, the relativistic all-order method and the multiconfiguration Hartree-Fock (MCHF) method. The accuracy of our calculations was investigated by conducting a third-order many-body perturbation theory calculation that allowed us to evaluate the importance of fourth- and higher-order corrections. A large-scale MCHF calculation was performed using the active space method and the core-polarization approximation. The obtained results provide an important test of these methods against each other and are shown to agree with the most accurate available experimental data.

Forbidden transition probabilities of astrophysical interest among low-lying states of V III

Electric and magnetic multipole transitions among low-lying states of doubly ionized vanadium were computed using the multi-configuration Hartree-Fock (MCHF) method with Breit-Pauli (BP) corrections to a non-relativistic Hamiltonian. Energy levels were determined up to and including 3d 2(1 G)4s b 2 G 7/2 and computed energies were found to be in good agreement with experiment and other theories. In addition to Einstein A ki coefficients for some E2 and M1 transitions, lifetime data and selected weighted oscillator strengths are also reported.

Low-energy electron scattering from Ca atoms and photodetachment ofCa−

The B-spline R-matrix method is used to investigate electron scattering from neutral calcium and photodetachment of Ca{sup -} in the low-energy range from threshold to 4 eV. The multiconfiguration Hartree-Fock method with nonorthogonal orbital sets is employed for an accurate representation of the target wave functions. The close-coupling expansion includes 39 bound states of neutral calcium, covering all states from the ground state to 4s8s {sup 1}S. The present calculations yield good agreement with the few available experimental data for both elastic electron scattering and photodetachment of Ca{sup -}. The prominent resonance structure in the low-energy region is analyzed and discussed.

B-spline calculations of oscillator strengths in neutral argon

B-spline box-based multi-channel calculations of transition probabilities in Ar I are reported for energy levels up to n = 12. An individually optimized, term-dependent set of non-orthogonal valence orbitals is used to account for the strong term dependence in the one-electron orbitals. Energy levels and oscillator strengths for transitions from the 3p6 ground-state configuration as well as for transitions between excited states have been computed in the Breit–Pauli approximation. The agreement in the length and velocity gauges of the transition data and the accuracy of the binding energies are used to estimate the accuracy of our results, which are also compared with experimental and other theoretical data. It is shown that the present method can be used for accurate calculations of oscillator strengths for states with intermediate and high n-values, for which it is difficult to apply standard multi-configuration Hartree–Fock methods.

MCHF studies of partial photoionization cross section of atomic fluorine

We present results of a theoretical investigation of the partial and total photoionization cross sections between the 1D and 1S thresholds of atomic fluorine using the multiconfiguration Hartree–Fock method of bound and continuum wavefunctions. The 2p4(1S)ns, md series observed by an experiment through their decay into the allowed 2p4(3P)kl and 2p4(1D)kl ionization channels are carefully identified. The 2s2p6 2S resonance is seen to interact strongly with the nearby 2p4(1S)4s 2S resonance. The results of the partial cross sections are first compared with the experimental observations. The total cross sections are compared with the available experimental and theoretical data. The energy positions of the resonance series 2p4(1S)ns, md as well as 2s2p6 2S excitation are found to be in very good agreement with the experimental observations.

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.

Electron-impact excitation of carbon

The $B$-spline $R$-matrix method is used to investigate the electron-impact excitation of neutral carbon over an energy range from threshold to $60\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. A multiconfiguration Hartree-Fock method with nonorthogonal orbitals is employed to generate an accurate representation of the target wavefunctions. The present close-coupling expansion includes the bound and autoionizing states of neutral carbon derived from the $1{s}^{2}2{s}^{2}2{p}^{2}$, $1{s}^{2}2{s}^{2}2p3\ensuremath{\ell}\phantom{\rule{0.3em}{0ex}}(\ensuremath{\ell}=0,1,2)$, $1{s}^{2}2{s}^{2}2p4s$, $1{s}^{2}2s2{p}^{3}$, and $1{s}^{2}2{p}^{4}$ configurations, plus eight pseudostates to fully account for the polarizability of the ground state of atomic carbon. Cross sections and effective collision strengths are presented for important transitions from the ground state $2{p}^{2}\phantom{\rule{0.3em}{0ex}}^{3}P$, and the metastable $2{p}^{2}\phantom{\rule{0.3em}{0ex}}^{1}D$ and $^{1}S$ states. Our predictions for the cross sections show significant discrepancies with those from previous calculations carried out with the standard $R$-matrix approach in a similar scattering model [Dunseath et al., J. Phys. B 30, 277 (1997)]. These discrepancies are mostly due to the different target descriptions, with the present one giving overall superior agreement with experiment for energy levels and oscillator strengths. The excitation cross sections exhibit prominent resonance structures in the low-energy region. The energy positions, widths, and classifications for the detected resonances are presented.

Theoretical Transition Probabilities and Lifetimes

The beam-foil method and the computation of oscillator strengths with correlated wave functions both had their beginning in the late 1960s. The stimulating interplay between theory and experiment will be reviewed. With the power of todays computers, great progress has been made in computation. The current state of spectrum calculations using the multiconfiguration Hartree–Fock method will be described and the importance of relativistic effects mentioned.

R-matrix calculations of the integral electron-impact excitation cross sections of the ground state of the barium atom

The R-matrix approach has been used to calculate the integral cross sections of excitation of the barium atom by low-energy electrons. The collision strengths have been calculated in the 38-state close coupling approximation, including 16 physical states and 22 pseudostates of the target. The target wave functions have been obtained in terms of the multiconfiguration Hartree-Fock method in the LS coupling scheme. The cross sections calculated exhibit a pronounced resonance structure, which contributes significantly to the total excitation cross sections. The results obtained have been compared to available theoretical and experimental data.

Breit–Pauli energy levels, lifetimes, and transition probabilities for the beryllium-like to neon-like sequences

Energy levels, lifetimes, and transition probabilities for transitions between computed levels are reported for the Be-like ( Z=4,…,12) to Ne-like ( Z=10,…,24) sequences. In most cases, results include all levels up to 2s3d in spectra of Be-like atoms or ions and 2s 22p n 3d, n=0,…,5 in spectra of B-like to Ne-like, respectively. Wavefunctions were determined using the multi-configuration Hartree–Fock method with relativistic effects included through the Breit–Pauli Hamiltonian, omitting only the orbit–orbit interaction. Both allowed (E1) and forbidden (M1, E2, M2) transitions are reported.

MCHF studies of atomic photoionization: autoionization resonances in the partial photoionization cross sections of atomic fluorine

The partial and total photoionization cross sections for 2p sub-shell ionization of fluorine are calculated near the first ionization threshold 2s 22p 4 ( 3P). The electron correlation and polarization effects which are very important for both initial ground, the final ionic states and the final continuum states are taken into account using the multiconfiguration Hartree–Fock method for bound and continuum wave functions. The three series of autoionization resonances observed by experiment between the 3P– 1D threshold, are identified accurately by the theoretical calculation. The calculated energy positions of the autoionization resonances 2p 4( 1D) ns 2D, 2p 4( 1D) md 2P and 2p 4( 1D) md 2D are compared with experimental measurements and are found to be in excellent agreement.

Radiative opacities and configuration interaction effects of hot iron plasma using a detailed term accounting model

We have calculated the radiative opacities of iron plasma in local thermodynamic equilibrium using a detailed term accounting model. The extensive atomic data are obtained by multiconfiguration Hartree-Fock (MCHF) method, with Breit-Pauli relativistic corrections. Extensive configuration interaction (CI) has been included based on LS coupling to obtain energy levels and the bound-bound transition cross sections. A detailed configuration accounting model is applied to evaluate the bound-free absorption cross sections. We simulate two experimental transmission spectra [G. Winhart et al., Phys. Rev. E 53, R1332 (1996); P. T. Springer et al., J. Quant. Spectrosc. Radiat. Transf. 58, 927 (1997)] to verify our calculation model, one is at a temperature of 22 eV and a density of 10(-2) g/cm(3) and the other is at a temperature of 20 eV and a lower density of 10(-4) g/cm(3). It is shown that the strong CI can effectively change the oscillator strengths in contrast to the single configuration HF method. For both of the two simulated transmission spectra good agreement is obtained between the present MCHF results and the experimental data. Spectrally resolved opacities and Planck and Rosseland mean opacities are also calculated. For the isothermal sequence of T=20 eV, when the density decreases from 10(-2) to 10(-5) g/cm(3), the linewidth also decreases so that the iron transition arrays show more discrete line structures and the linewidth becomes very important to the Rosseland mean opacity.

The influence of core–valence electron correlations on the convergence of energylevels and oscillator strengths of ions with an open 3d shell using Fe VIII as anexample

Accurate atomic data, such as fine structure energy levels and oscillator strengthsof different ionization stages of iron ions, are important for astrophysical andlaboratory plasmas. However, some important existing oscillator strengths for ionswith an open 3d shell found in the literature might not be accurate enoughfor practical applications. As an example, the present paper checks theconvergence behaviour of the energy levels and oscillator strengths of Fe VIII bysystematically increasing the 3pn–3dn(n = 1, 2, 3and 6) core–valence electron correlations using the multiconfiguration Hartree–Fockmethod. The results show that one should at least include up to 3p3–3d3core–valence electron correlations to obtain converged results. Large differencesare found between the present oscillator strengths and other theoretical results inthe literature for some strong transitions.