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Journal of Physics B Atomic Molecular and Optical Physics

Stable negative ions of the heavy alkaline-earth atoms

L Kim, Chris H. Greene

Published Apr 28, 1989• 65 citations
Publisher

Abstract

Strontium, barium and radium are predicted to have stable negative ions of ns2np designation, on the basis of eigenchannel R-matrix calculations performed in LS coupling for the negative ion of each alkaline-earth atom. The calculations also confirm earlier studies indicating that the negative ion of calcium is stable and that corresponding 2P degrees states in beryllium and magnesium are unstable shape resonances. The much larger polarisability of the heavier alkaline earths play a crucial role in binding the additional electron. The analysis uses quantum defect theory in its generalised form appropriate for long-range motion in a dipole polarisation potential.

DOI
10.1088/0953-4075/22/8/001

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Strontium, barium and radium are predicted to have stable negative ions of ns2np designation, on the basis of eigenchannel R-matrix calculations performed in LS coupling for the negative ion of each alkaline-earth atom. The calculations also confirm earlier studies indicating that the negative ion of calcium is stable and that corresponding 2P degrees states in beryllium and magnesium are unstable shape resonances. The much larger polarisability of the heavier alkaline earths play a crucial role in binding the additional electron. The analysis uses quantum defect theory in its generalised form appropriate for long-range motion in a dipole polarisation potential.
Most atomic species—roughly 80% of the periodic table—can form stable negative ions in their gaseous phase. The most notable and easily understood exceptions are the noble gas atoms, the symmetry of whose completely filled electron shells offers no handhold for a would-be extra tenant. The alkaline earths—calcium, strontium, barium and their group IIA cousins—are similarly inhospitable, or so the standard textbooks assure us. Two back-to-back reports in a recent issue of Physical Review Letters have now disabused us of this venerable assurance.
Apropos to the growing interest in the study of long-range interactions which for their applications in cold atom physics, we have performed theoretical calculation for the two-dipole C6C_6C6​ and three-dipole C9C_9C9​ dispersion coefficients involving alkaline-earth atoms with alkaline-earth atoms and alkaline-earth ions. The C6C_6C6​ and C9C_9C9​ coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated C6C_6C6​ coefficients for the considered alkaline-earth atoms among themselves are compared with the previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the C6C_6C6​ coefficients for alkaline-earth atoms with alkaline-earth ions and the C9C_9C9​ coefficients, we have performed separate fitting calculations and compared. Our calculations match in an excellent manner with the fitting calculations. We have also reported the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth ions, i.e., Mg+^++, Ca+^++, Sr+^++, and Ba+^++ as well as the alkaline-earth atoms, i.e., Mg, Ca, Sr, and Ba. These, when compared with the available experimental results, show good agreement.
Three mutually related problems concerning the interaction of an electron with an alkaline-earth atom are examined. (i) The scattering problem: the phaseshifts for p-electron scattering by Ca, Sr and Ba are calculated. (ii) The negative ion problem: the wavefunction and the binding energy are obtained for the outer electron in Ca - 4s 2 4p, Sr - 5s 2 5p and Ba - 6s 2 6p ions. (iii) The photodetachment problem: the photodetachment cross sections are calculated for the outer electron in each of these ions. The most intriguing feature of these problems is the strong correlational potential, attracting the electron to the atom due to the large dipole polarizabilities of Ca, Sr and Ba. The calculations are performed by means of the Dyson equation of the many-body theory.
Apropos of the growing interest in the study of long-range interactions for their applications in cold-atom physics, we perform theoretical calculations for the two-dipole C6{C}_{6}C6​ and three-dipole C9{C}_{9}C9​ dispersion coefficients involving alkaline-earth-metal atoms with alkaline-earth-metal atoms and alkaline-earth-metal ions. The C6{C}_{6}C6​ and C9{C}_{9}C9​ coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated C6{C}_{6}C6​ coefficients for the considered alkaline-earth-metal atoms are compared with previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the C6{C}_{6}C6​ coefficients for alkaline-earth-metal atoms with alkaline-earth-metal ions and the C9{C}_{9}C9​ coefficients we perform separate fitting calculations and compare the results. Our calculations match in an excellent manner with the fitting calculations. We also report the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth-metal ions, i.e., Be+,Mg+,Ca+,Sr+{\mathrm{Be}}^{+}, {\mathrm{Mg}}^{+}, {\mathrm{Ca}}^{+}, {\mathrm{Sr}}^{+}Be+,Mg+,Ca+,Sr+, and Ba+{\mathrm{Ba}}^{+}Ba+, as well as the alkaline-earth-metal atoms, i.e., Be, Mg, Ca, Sr, and Ba. These show good agreement when compared with the available experimental results.
Accurate knowledge of interaction potentials among the alkali atoms and alkaline earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali atoms with the Ca+^++, Ba+^++, Sr+^++, and Ra+^++ alkaline earth ions systematically which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation RRR. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above mentioned systems which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representation of the interaction potentials versus RRR are given among all the considered atoms and ions.