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Physical Review A

Energies of metastable 4So states in the alkaline-earth sequence

H. W. van der Hart

Published Feb 1, 1999• 6 citations
Publisher

Abstract

Theoretical binding energies have been obtained for the metastable ${\mathrm{np}}^{3}{}^{4}{S}^{o}$ states in the alkaline-earth sequence using a B-spline configuration-interaction approach. The results agree with available experimental and theoretical data within 5 meV for ${\mathrm{Be}}^{\ensuremath{-}}$ and within 10 meV for ${\mathrm{Mg}}^{\ensuremath{-}}.$ The binding energies of the ${p}^{3}{}^{4}{S}^{o}$ state in ${\mathrm{Mg}}^{\ensuremath{-}},$ ${\mathrm{Ca}}^{\ensuremath{-}},$ and ${\mathrm{Sr}}^{\ensuremath{-}}$ are larger than the one in ${\mathrm{Be}}^{\ensuremath{-}}$ by roughly 250 meV due to the stronger interactions with the ${d}^{2}p$ configurations. For ${\mathrm{Ca}}^{\ensuremath{-}},$ the ${}^{4}{S}^{o}$ binding energy is determined to be 555.5 meV, including a contribution of $\ensuremath{-}70$ meV due to dielectronic core polarization. For ${\mathrm{Sr}}^{\ensuremath{-}}$ the ${}^{4}{S}^{o}$ binding energy is 557.9 meV, including a decrease of only 6 meV due to dielectronic core polarization. This behavior for the ${}^{4}{S}^{o}$ states in ${\mathrm{Ca}}^{\ensuremath{-}}$ and ${\mathrm{Sr}}^{\ensuremath{-}}$ is ascribed to the different neutral-atom states to which the ${}^{4}{S}^{o}$ states are bound.

DOI
10.1103/physreva.59.1125

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This paper presents a combined experimental and theoretical investigation of the binding energy of the metastable ${\mathrm{Ar}}^{\ensuremath{-}}{(3p}^{5}4s4p{}^{4}{S}_{3/2}^{e})$ ion. Utilizing the laser-photodetachment threshold technique combined with state-selective detection of neutral atoms by resonant ionization spectroscopy, we find a binding energy of $32.5\ifmmode\pm\else\textpm\fi{}1.0$ meV with respect to the 3p54s3P2o{3p}^{5}4s{}^{3}{P}_{2}^{o}3p54s3P2o​ state of neutral argon. Our calculations, based on many-body perturbation theory, yield a binding energy of 24.9 meV. As a test of the present computational method, we also include the results of a comparative study of ${\mathrm{Ca}}^{\ensuremath{-}}$.
Energies have been obtained in LS\mathrm{LS}LS coupling for low-lying states in ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$ using a model potential approach including core polarization. An indication has been obtained for the existence of a new quasibound state in ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}},$ 5s4d5p4Fo,5s4d5p{}^{4}{F}^{o},5s4d5p4Fo, bound by 30.0 meV with respect to the 5s5p3Po5s5p{}^{3}{P}^{o}5s5p3Po state. Core polarization is essential for obtaining binding for this state. The quasibound 5s5p24Pe{5s5p}^{2}{}^{4}{P}^{e}5s5p24Pe state is estimated to lie 548.4 meV below the 5s5p3Po5s5p{}^{3}{P}^{o}5s5p3Po state of Sr in good agreement with experiment.
The binding energies of the 4s24p2P{4s}^{2}4p^{2}P4s24p2P ground state in ${\mathrm{Ca}}^{\ensuremath{-}}$ have been determined by means of state-selective photoionization of Ca atoms produced in s-wave photodetachment to be $24.55\ifmmode\pm\else\textpm\fi{}0.10$ meV for the J=1/2J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2J=1/2 and $19.73\ifmmode\pm\else\textpm\fi{}0.10$ meV for the J=3/2J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2J=3/2 component. The sensitivity of the detection technique applied has also made it possible to disprove previous claims for the observation of a metastable ${4s4p}^{2}^{4}P$ state in ${\mathrm{Ca}}^{\ensuremath{-}}$.
Alkaline-earth-metal atoms in their lowest (nsnp)(\mathrm{nsnp})(nsnp) 3P2{}^{3}{P}_{2}3P2​ state are exceptionally long lived and can be trapped magnetically. The nonspherical atomic structure leads to anisotropic long-range interactions between two metastable alkaline-earth-metal atoms. The anisotropy affects the rotational motion of the diatomic system and couples states of different rotational quantum numbers. This paper develops a tensorial decomposition of the most important long-range interaction operators, and a systematic inclusion of molecular rotations, in the presence of an external magnetic field. This analysis illuminates the nature of the coupling between the various degrees of freedom. The consequences are illustrated by application to a system of practical interest: metastable 88Sr.{}^{88}\mathrm{Sr}.88Sr. Using atomic parameters determined in a nearly ab initio calculation, we compute adiabatic potential-energy curves. The anisotropic interatomic interaction, in combination with the applied magnetic field, is demonstrated to induce the formation of a long-range molecular potential well. This curve correlates to two fully polarized, low-field seeking atoms in a rotational s-wave state. The coupling among molecular rotational states controls the existence of the potential well, and its properties vary as a function of magnetic-field strength, thus allowing the scattering length in this state to be tuned. The scattering length of metastable 88Sr{}^{88}\mathrm{Sr}88Sr displays a resonance at a field of 339 G.
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 p1/2{\mathrm{p}}_{1\mathrm{/}2}p1/2​ 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 p1/2{\mathrm{p}}_{1\mathrm{/}2}p1/2​ state is bound by 100 meV, and p3/2{\mathrm{p}}_{3\mathrm{/}2}p3/2​ is a resonance at 16 meV in the continuum.