Physical Review A

Low-lying D1 states of Be I

Charlotte Froese Fischer

Published Nov 1, 1984• 23 citations

Abstract

The composition of the three lowest $^{1}D$ states of BeI has been investigated using the multiconfiguration Hartree-Fock method. Though the $2{p}^{2}$ configuration lies above the $2s4d$ configuration in the Hartree-Fock approximation, correlation in the localized $2{p}^{2}$ configuration and its interaction with the higher-lying Rydberg series, including the continuum, are such that the $2{p}^{2}$ state is depressed to the extent that the lowest $^{1}D$ state is predominately $2{p}^{2}$, the second largely $2s3d$, and the third almost entirely $2s4d$.

DOI: 10.1103/physreva.30.2741

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Physical Review A

Low-lying D1 states of Be I

Charlotte Froese Fischer

Published Nov 1, 1984• 23 citations

Publisher

Abstract

The composition of the three lowest

^{1}D

states of BeI has been investigated using the multiconfiguration Hartree-Fock method. Though the

2{p}^{2}

configuration lies above the

2s4d

configuration in the Hartree-Fock approximation, correlation in the localized

2{p}^{2}

configuration and its interaction with the higher-lying Rydberg series, including the continuum, are such that the

2{p}^{2}

state is depressed to the extent that the lowest

^{1}D

state is predominately

2{p}^{2}

, the second largely

2s3d

, and the third almost entirely

2s4d

DOI: 10.1103/physreva.30.2741

Related papers

Multiconfiguration Hartree-Fock calculations of low-lying excited 2 Sstates in lithium

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The hyperfine interaction constants, specific-mass-shift parameters, and total energies for the 3s ${\mathrm{}}^{2}$ S and 4s ${\mathrm{}}^{2}$ S states in lithium were calculated using the multiconfiguration Hartree-Fock method. The configuration expansions were obtained with the active space method, where configuration state functions are generated by excitations from the reference configuration to an active set of orbitals. The active set was increased in a systematic way, allowing the convergence of the studied parameters to be monitored. The obtained nonrelativistic energies are close to the lowest-upper-bound estimates from Hylleraas calculations. Whereas the convergence rate of the hyperfine interaction constants with respect to the increasing basis in the Hylleraas calculations degrades appreciably for higher states in the Rydberg series, no such effect could be seen for the multiconfiguration Hartree-Fock calculations. The uncertainties of the calculated hyperfine interaction constants are estimated to be less than three parts in a thousand for both of the studied states. The value for the 3s ${\mathrm{}}^{2}$ S state is in excellent agreement with results from relativistic many-body perturbation theory calculations, but is well outside the error bars from a recent precision measurement using Stark spectroscopy.The hyperfine interaction constants, specific-mass-shift parameters, and total energies for the 3s${\mathrm{}}^{2}$S and 4s${\mathrm{}}^{2}$S states in lithium were calculated using the multiconfiguration Hartree-Fock method. The configuration expansions were obtained with the active space method, where configuration state functions are generated by excitations from the reference configuration to an active set of orbitals. The active set was increased in a systematic way, allowing the convergence of the studied parameters to be monitored. The obtained nonrelativistic energies are close to the lowest-upper-bound estimates from Hylleraas calculations. Whereas the convergence rate of the hyperfine interaction constants with respect to the increasing basis in the Hylleraas calculations degrades appreciably for higher states in the Rydberg series, no such effect could be seen for the multiconfiguration Hartree-Fock calculations. The uncertainties of the calculated hyperfine interaction constants are estimated to be less than three parts in a thousand for both of the studied states. The value for the 3s${\mathrm{}}^{2}$S state is in excellent agreement with results from relativistic many-body perturbation theory calculations, but is well outside the error bars from a recent precision measurement using Stark spectroscopy.

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arXiv:cond-mat/0509530Physical Review ADec 29, 200540 citations

The composition of the three lowest

^{1}D

states of BeI has been investigated using the multiconfiguration Hartree-Fock method. Though the

2{p}^{2}

configuration lies above the

2s4d

configuration in the Hartree-Fock approximation, correlation in the localized

2{p}^{2}

configuration and its interaction with the higher-lying Rydberg series, including the continuum, are such that the

2{p}^{2}

state is depressed to the extent that the lowest

^{1}D

state is predominately

2{p}^{2}

, the second largely

2s3d

, and the third almost entirely

2s4d

The hyperfine interaction constants, specific-mass-shift parameters, and total energies for the 3s

{\mathrm{}}^{2}

S and 4s

{\mathrm{}}^{2}

S states in lithium were calculated using the multiconfiguration Hartree-Fock method. The configuration expansions were obtained with the active space method, where configuration state functions are generated by excitations from the reference configuration to an active set of orbitals. The active set was increased in a systematic way, allowing the convergence of the studied parameters to be monitored. The obtained nonrelativistic energies are close to the lowest-upper-bound estimates from Hylleraas calculations. Whereas the convergence rate of the hyperfine interaction constants with respect to the increasing basis in the Hylleraas calculations degrades appreciably for higher states in the Rydberg series, no such effect could be seen for the multiconfiguration Hartree-Fock calculations. The uncertainties of the calculated hyperfine interaction constants are estimated to be less than three parts in a thousand for both of the studied states. The value for the 3s

{\mathrm{}}^{2}

S state is in excellent agreement with results from relativistic many-body perturbation theory calculations, but is well outside the error bars from a recent precision measurement using Stark spectroscopy.

^{2}

P\ifmmode^\circ\else\textdegree\fi{} states of ${\mathrm{Be}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$, and ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$, along with results of some small-scale multiconfiguration investigations of the Mg resonance. An instability originating in difficulty satisfying orthogonality constraints prevents a full multiconfiguration treatment of this resonance. Single-configuration dilated Hartree-Fock calculations predict

^{2}

P\ifmmode^\circ\else\textdegree\fi{} shape resonances for all these systems, though recent extensive calculations show the Ca, Sr, and Ba ions to be bound. Nonetheless, we think it is significant that the dilated numerical method can easily carry out fully variational computations on these heavy atoms, and our results, in conjunction with those of other studies, shed light on the importance of electron correlation in its effect upon the resonance parameters and its variation with progressively heavier alkaline-earth atoms. We also establish the feasibility of accounting for important correlation effects through the use of multiconfiguration approximations, though we have not attempted an accurate calculation in this work. Our Be, Mg, and Ca results agree well with previously published single-configuration dilated basis-set calculations, but no such calculations have been carried out for Sr or Ba. Finally, we investigate the dilational stability of the numerical method since this has been an important consideration in basis-set calculations. A simple exercise based on Cauchy's theorem shows that analyticity of the Hartree-Fock radial wave functions implies that the energy and other physical quantities are independent of the dilation parameter, and a high degree of such independence is demonstrated in our numerical results.