Physical Review A

Fine and hyperfine structure of the Li− spectrum

K. T. Cheng, Jonathan E. Hardis, E. J. Dehm, Donald R. Beck

Published Aug 1, 1984• 14 citations

Abstract

The fine and hyperfine structures of the doubly excited, quintet states of the $^{7}\mathrm{Li}^{\ensuremath{-}}$ ion are of comparable magnitude. This leads to strong second-order hyperfine corrections and to significant distortion of the Land\'e interval rule. We discuss the results of our many-body calculations in this system, and also in the analogous lithium quartet systems for which experimental data exist. We find that the hyperfine matrix elements of these few-electron systems may be adequately computed without detailed consideration of the electron correlations. Fine structure is significantly affected by such correlations. Experimental verification of the ${\mathrm{Li}}^{\ensuremath{-}}$ structure is underway.

DOI: 10.1103/physreva.30.698

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Physical Review A

Fine and hyperfine structure of the Li− spectrum

K. T. Cheng, Jonathan E. Hardis, E. J. Dehm, Donald R. Beck

Published Aug 1, 1984• 14 citations

Publisher

Abstract

The fine and hyperfine structures of the doubly excited, quintet states of the

^{7}\mathrm{Li}^{\ensuremath{-}}

ion are of comparable magnitude. This leads to strong second-order hyperfine corrections and to significant distortion of the Land'e interval rule. We discuss the results of our many-body calculations in this system, and also in the analogous lithium quartet systems for which experimental data exist. We find that the hyperfine matrix elements of these few-electron systems may be adequately computed without detailed consideration of the electron correlations. Fine structure is significantly affected by such correlations. Experimental verification of the

{\mathrm{Li}}^{\ensuremath{-}}

structure is underway.

DOI: 10.1103/physreva.30.698

Related papers

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Atomic many-body theory methods are used to calculate the fine structure of negative ions formed by binding a p electron into an open shell, ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$, and ${\mathrm{Ra}}^{\mathrm{\ensuremath{-}}}$. This binding is due to a strong correlation potential acting between the electron and the neutral atom. Comparison with experimental data shows that the second order many-body perturbation theory calculation overestimates the correlation potential by 10% to 15%. Scaling factors are introduced in the correlation potential to reproduce experimental binding energies of the lower ${\mathrm{p}}_{1\mathrm{/}2}$ components. This procedure yields fine-structure intervals in excellent agreement with experiment for ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$, and ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$, and allows us to predict that in ${\mathrm{Ra}}^{\mathrm{\ensuremath{-}}}$ the ${\mathrm{p}}_{1\mathrm{/}2}$ state is bound by 100 meV, and ${\mathrm{p}}_{3\mathrm{/}2}$ is a resonance at 16 meV in the continuum.Atomic many-body theory methods are used to calculate the fine structure of negative ions formed by binding a p electron into an open shell, ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$, and ${\mathrm{Ra}}^{\mathrm{\ensuremath{-}}}$. This binding is due to a strong correlation potential acting between the electron and the neutral atom. Comparison with experimental data shows that the second order many-body perturbation theory calculation overestimates the correlation potential by 10% to 15%. Scaling factors are introduced in the correlation potential to reproduce experimental binding energies of the lower ${\mathrm{p}}_{1\mathrm{/}2}$ components. This procedure yields fine-structure intervals in excellent agreement with experiment for ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$, and ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$, and allows us to predict that in ${\mathrm{Ra}}^{\mathrm{\ensuremath{-}}}$ the ${\mathrm{p}}_{1\mathrm{/}2}$ state is bound by 100 meV, and ${\mathrm{p}}_{3\mathrm{/}2}$ is a resonance at 16 meV in the continuum.

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Lifetime and hyperfine structure of Li− excited states

Donald R. Beck, Cleanthes A. Nicolaides

The newly discovered excited states of ${\mathrm{Li}}^{\ensuremath{-}}$ are examined from a many-body point of view. Our result for the $^{5}S^{o}$ lifetime includes the contribution of radiative autoionization. This removes one-third of the previous discrepancy between theory (our value = 2.7 ns) and experiment (= 2.3 ns). The first predictions of the hyperfine structures (hfs) of the ${\mathrm{Li}}^{\ensuremath{-}}$ $^{5}S^{o}$ and $^{5}P$ states are made, and the change in the hfs parameters as $p$ electrons are removed is studied.The newly discovered excited states of ${\mathrm{Li}}^{\ensuremath{-}}$ are examined from a many-body point of view. Our result for the $^{5}S^{o}$ lifetime includes the contribution of radiative autoionization. This removes one-third of the previous discrepancy between theory (our value = 2.7 ns) and experiment (= 2.3 ns). The first predictions of the hyperfine structures (hfs) of the ${\mathrm{Li}}^{\ensuremath{-}}$ $^{5}S^{o}$ and $^{5}P$ states are made, and the change in the hfs parameters as $p$ electrons are removed is studied.

Physical Review ANov 1, 198318 citations

Comments on the hyperfine structure of the 4D2 state of rubidium

Ingvar Lindgren, Johannes Lindgren, Ann-Marie Pendrill

In a recent paper Lee, Rodgers, Das, and Sternheimer have reported on the evaluation of the fine and hyperfine structure of the $4^{2}D$ state of the rubidium atom by considering the first-order polarization of the electron core. By means of more extensive calculations we have shown that the first-order results can be quite unreliable for such strongly perturbed systems. By including polarization effects to all orders and the most important correlation effects, we have been able to reproduce the experimental results for this state quite well. The good agreement obtained by Lee et al. for the spin-dipole parameter is in our opinion largely fortuitous.In a recent paper Lee, Rodgers, Das, and Sternheimer have reported on the evaluation of the fine and hyperfine structure of the $4^{2}D$ state of the rubidium atom by considering the first-order polarization of the electron core. By means of more extensive calculations we have shown that the first-order results can be quite unreliable for such strongly perturbed systems. By including polarization effects to all orders and the most important correlation effects, we have been able to reproduce the experimental results for this state quite well. The good agreement obtained by Lee et al. for the spin-dipole parameter is in our opinion largely fortuitous.

Physical Review AMay 1, 197731 citations

Accuracy limits on the description of the lowest S excitation in the Li atom using explicitly correlated Gaussian basis functions

Monika Stanke, Jacek Komasa, Dariusz Kędziera +2 more

We have performed very accurate quantum-mechanical calculations for the two lowest $S$ states of the lithium atom in order to determine the transition energy. In the nonrelativistic part of the calculations performed using the variational method, we explicitly included the nuclear motion. The nonrelativistic wave function was expanded in terms of explicitly correlated Gaussian functions. Next, this wave function was used to calculate the leading ${\ensuremath{\alpha}}^{2}$ relativistic correction ($\ensuremath{\alpha}$ is the fine-structure constant) and the ${\ensuremath{\alpha}}^{3}$ QED correction. We also estimated the ${\ensuremath{\alpha}}^{4}$ QED correction by calculating its dominating component. The results obtained with Gaussians are compared with the most accurate results obtained recently with the Hylleraas-type basis functions.We have performed very accurate quantum-mechanical calculations for the two lowest $S$ states of the lithium atom in order to determine the transition energy. In the nonrelativistic part of the calculations performed using the variational method, we explicitly included the nuclear motion. The nonrelativistic wave function was expanded in terms of explicitly correlated Gaussian functions. Next, this wave function was used to calculate the leading ${\ensuremath{\alpha}}^{2}$ relativistic correction ($\ensuremath{\alpha}$ is the fine-structure constant) and the ${\ensuremath{\alpha}}^{3}$ QED correction. We also estimated the ${\ensuremath{\alpha}}^{4}$ QED correction by calculating its dominating component. The results obtained with Gaussians are compared with the most accurate results obtained recently with the Hylleraas-type basis functions.

Physical Review ANov 14, 200828 citations

The fine and hyperfine structures of the doubly excited, quintet states of the

^{7}\mathrm{Li}^{\ensuremath{-}}

{\mathrm{Li}}^{\ensuremath{-}}

structure is underway.

We perform accurate calculations of energy levels as well as fine and hyperfine splittings of the lowest

^{1,3}P_{J}, ^{3}S_{1}, ^{3}P_{J}^{e}

, and

^{1,3}D_{J}

excited states of the

^{9}\mathrm{Be}

atom using explicitly correlated Gaussian functions, and we report on the breakdown of the standard hyperfine structure theory. Because of the strong hyperfine mixing, which prevents the use of common hyperfine constants, we formulate a description of the fine and hyperfine structure that is valid for an arbitrary coupling strength and may have wide applications in many other atomic systems.

We present and analyze results of the relativistic coupled-cluster calculation of energies, hyperfine constants, and dipole matrix elements for the

2s

2{p}_{1∕2}

, and

2{p}_{3∕2}

states of Li atom. The calculations are complete through the fourth order of many-body perturbation theory for energies and through the fifth order for matrix elements and subsume certain chains of diagrams in all orders. A nearly complete many-body calculation allows us to draw conclusions on the convergence pattern of the coupled-cluster method. Our analysis suggests that the high-order many-body contributions to energies and matrix elements scale proportionally and provide a quantitative ground for semiempirical fits of ab initio matrix elements to experimental energies.

{\mathrm{p}}_{1\mathrm{/}2}

components. This procedure yields fine-structure intervals in excellent agreement with experiment for ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$, and ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$, and allows us to predict that in ${\mathrm{Ra}}^{\mathrm{\ensuremath{-}}}$ the

{\mathrm{p}}_{1\mathrm{/}2}

state is bound by 100 meV, and

{\mathrm{p}}_{3\mathrm{/}2}

is a resonance at 16 meV in the continuum.

The newly discovered excited states of ${\mathrm{Li}}^{\ensuremath{-}}$ are examined from a many-body point of view. Our result for the

^{5}S^{o}

lifetime includes the contribution of radiative autoionization. This removes one-third of the previous discrepancy between theory (our value = 2.7 ns) and experiment (= 2.3 ns). The first predictions of the hyperfine structures (hfs) of the ${\mathrm{Li}}^{\ensuremath{-}}$

^{5}S^{o}

and

^{5}P

states are made, and the change in the hfs parameters as

p

electrons are removed is studied.

In a recent paper Lee, Rodgers, Das, and Sternheimer have reported on the evaluation of the fine and hyperfine structure of the

4^{2}D

state of the rubidium atom by considering the first-order polarization of the electron core. By means of more extensive calculations we have shown that the first-order results can be quite unreliable for such strongly perturbed systems. By including polarization effects to all orders and the most important correlation effects, we have been able to reproduce the experimental results for this state quite well. The good agreement obtained by Lee et al. for the spin-dipole parameter is in our opinion largely fortuitous.

We have performed very accurate quantum-mechanical calculations for the two lowest

S

states of the lithium atom in order to determine the transition energy. In the nonrelativistic part of the calculations performed using the variational method, we explicitly included the nuclear motion. The nonrelativistic wave function was expanded in terms of explicitly correlated Gaussian functions. Next, this wave function was used to calculate the leading ${\ensuremath{\alpha}}^{2}$ relativistic correction ($\ensuremath{\alpha}$ is the fine-structure constant) and the ${\ensuremath{\alpha}}^{3}$ QED correction. We also estimated the ${\ensuremath{\alpha}}^{4}$ QED correction by calculating its dominating component. The results obtained with Gaussians are compared with the most accurate results obtained recently with the Hylleraas-type basis functions.