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Physical Review A

Long-range interactions between excited helium and alkali-metal atoms

J. Y. Zhang, Li-Yan Tang, T.-Y. Shi, Z.-C. Yan, Udo Schwingenschlögl

Published Dec 3, 2012• 10 citations
Publisher

Abstract

The dispersion coefficients for the long-range interaction of the first four excited states of He, i.e., He(2 ${}^{1,3}\phantom{\rule{-0.16em}{0ex}}$$S$) and He(2 ${}^{1,3}$$P$), with the low-lying states of the alkali-metal atoms Li, Na, K, and Rb are calculated by summing over the reduced matrix elements of the multipole transition operators. For the interaction between He and Li the uncertainty of the calculations is 0.1--0.5$%$. For interactions with other alkali-metal atoms the uncertainty is 1--3$%$ in the coefficient ${C}_{5}$, 1--5$%$ in the coefficient ${C}_{6}$, and 1--10$%$ in the coefficients ${C}_{8}$ and ${C}_{10}$. The dispersion coefficients ${C}_{n}$ for the interaction of He(2 ${}^{1,3}\phantom{\rule{-0.16em}{0ex}}$$S$) and He(2 ${}^{1,3}$$P$) with the ground-state alkali-metal atoms and for the interaction of He(2 ${}^{1,3}\phantom{\rule{-0.16em}{0ex}}$$S$) with the alkali-metal atoms in their first ${}^{2}$$P$ states are presented in this Brief Report. The coefficients for other pairs of atomic states are listed in the Supplemental Material.

DOI
10.1103/physreva.86.064701

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The dispersion coefficients for the long-range interaction of the first four excited states of He, i.e., He(2 {}^{1,3}\phantom{\rule{-0.16em}{0ex}}$$S) and He(2 {}^{1,3}$$P), 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}\phantom{\rule{-0.16em}{0ex}}$$S) and He(2 {}^{1,3}$$P) with the ground-state alkali-metal atoms and for the interaction of He(2 {}^{1,3}\phantom{\rule{-0.16em}{0ex}}$$S) with the alkali-metal atoms in their first {}^{2}$$P states are presented in this Brief Report. The coefficients for other pairs of atomic states are listed in the Supplemental Material.
Knowledge of the long-range interaction between atoms and molecules is of fundamental importance for low-energy and low-temperature collisions. The electronic interaction between the charge distributions of two ground-state alkali-metal atoms can be expanded in inverse powers of R, the internuclear distance. The coefficients C6{\mathit{C}}_{6}C6​, C8{\mathit{C}}_{8}C8​, and C10{\mathit{C}}_{10}C10​ of, respectively, the ${\mathit{R}}^{\mathrm{\ensuremath{-}}6}$, ${\mathit{R}}^{\mathrm{\ensuremath{-}}8}$, and ${\mathit{R}}^{\mathrm{\ensuremath{-}}10}$ terms are calculated by integrating the products of the dynamic electric multipole polarizabilities of the individual atoms at imaginary frequencies, which are in turn obtained by solving two coupled inhomogeneous differential equations. Precise one-electron model potentials are developed to represent the motion of the valence electron in the field of the closed alkali-metal positive-ion core. The numerical results for the static multipole polarizabilities for the alkali-metal atoms and the coefficients C6{\mathit{C}}_{6}C6​, C8{\mathit{C}}_{8}C8​, and C10{\mathit{C}}_{10}C10​ for homonuclear and heteronuclear alkali-metal diatoms are compared with other calculations.
The third-order expression for the dispersion interaction between two atoms is written as a sum over lists of transition matrix elements. Particular attention is given to the C9/R9{C}_{9}/{R}^{9}C9​/R9 interaction which occurs in the homonuclear case when one atom is in an SSS state and the other is in a PPP state. Numerical values of the C9{C}_{9}C9​ coefficient are given for the homonuclear alkali-metal dimers. The size of the C9{C}_{9}C9​:C3{C}_{3}C3​ dispersion coefficient ratio increases for the heavier alkali-metal atoms. The C11{C}_{11}C11​ and C13{C}_{13}C13​ coefficients between two helium atoms and lithium atoms in their ground states are also given.
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.