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arXiv:1303.1234 · Journal of Physics B Atomic Molecular and Optical Physics

Long-range interactions between alkali and alkaline-earth atoms

Jun Jiang, Yongjun Cheng, Jim Mitroy

Published Jun 10, 2013• 11 citations
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Abstract

Dispersion coefficients between the alkali metal atoms (Li-Rb) and alkaline-earth metal atoms (Be-Sr) are evaluated using matrix elements computed from frozen core configuration interaction calculations. Besides dispersion coefficients with both atoms in their respective ground states, dispersion coefficients are also given for the case where one atom is in its ground state and the other atom is in a low lying excited state.

DOI
10.1088/0953-4075/46/12/125004

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arXiv:2008.04341•Aug 10, 2020•0 citations
Dispersion coefficients between the alkali metal atoms (Li-Rb) and alkaline-earth metal atoms (Be-Sr) are evaluated using matrix elements computed from frozen core configuration interaction calculations. Besides dispersion coefficients with both atoms in their respective ground states, dispersion coefficients are also given for the case where one atom is in its ground state and the other atom is in a low lying excited state.
Accurate knowledge of interaction potentials among the alkali-metal 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-metal atoms with the Ca+{\mathrm{Ca}}^{+}Ca+, Ba+{\mathrm{Ba}}^{+}Ba+, Sr+{\mathrm{Sr}}^{+}Sr+, and Ra+{\mathrm{Ra}}^{+}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 representations of the dispersion coefficients versus RRR are given among all the alkaline ions with Rb.
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.
The dispersion coefficients for the long-range interaction of the first four excited states of He, i.e., He(2 1,3{}^{1,3}\phantom{\rule{-0.16em}{0ex}}1,3SSS) and He(2 1,3{}^{1,3}1,3PPP), with the low-lying states of the alkali-metal atoms Li, Na, K, and Rb are calculated by summing over the reduced matrix elements of the multipole transition operators. For the interaction between He and Li the uncertainty of the calculations is 0.1--0.5%. For interactions with other alkali-metal atoms the uncertainty is 1--3% in the coefficient C5{C}_{5}C5​, 1--5% in the coefficient C6{C}_{6}C6​, and 1--10% in the coefficients C8{C}_{8}C8​ and C10{C}_{10}C10​. The dispersion coefficients Cn{C}_{n}Cn​ for the interaction of He(2 1,3{}^{1,3}\phantom{\rule{-0.16em}{0ex}}1,3SSS) and He(2 1,3{}^{1,3}1,3PPP) with the ground-state alkali-metal atoms and for the interaction of He(2 1,3{}^{1,3}\phantom{\rule{-0.16em}{0ex}}1,3SSS) with the alkali-metal atoms in their first 2{}^{2}2PPP states are presented in this Brief Report. The coefficients for other pairs of atomic states are listed in the Supplemental Material.
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.
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.