Physical Review A

Long-range dispersion interactions. I. Formalism for two heteronuclear atoms

J. Y. Zhang, Jim Mitroy

Published Aug 7, 2007• 49 citations

Abstract

A general procedure for systematically evaluating the long-range dispersion interaction between two heteronuclear atoms in arbitrary states is outlined. The ${C}_{6}$ dispersion parameter can always be written in terms of sum rules involving oscillator strengths only and formulas for a number of symmetry cases are given. The dispersion coefficients for excited alkali-metal atoms interacting with the ground-state H and He are tabulated.

DOI: 10.1103/physreva.76.022705

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Physical Review A

Long-range dispersion interactions. I. Formalism for two heteronuclear atoms

J. Y. Zhang, Jim Mitroy

Published Aug 7, 2007• 49 citations

Publisher

Abstract

A general procedure for systematically evaluating the long-range dispersion interaction between two heteronuclear atoms in arbitrary states is outlined. The

{C}_{6}

dispersion parameter can always be written in terms of sum rules involving oscillator strengths only and formulas for a number of symmetry cases are given. The dispersion coefficients for excited alkali-metal atoms interacting with the ground-state H and He are tabulated.

DOI: 10.1103/physreva.76.022705

Related papers

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

J. Y. Zhang, Li-Yan Tang, T.-Y. Shi +2 more

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.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.

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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 ${C}_{9}/{R}^{9}$ interaction which occurs in the homonuclear case when one atom is in an $S$ state and the other is in a $P$ state. Numerical values of the ${C}_{9}$ coefficient are given for the homonuclear alkali-metal dimers. The size of the ${C}_{9}$ : ${C}_{3}$ dispersion coefficient ratio increases for the heavier alkali-metal atoms. The ${C}_{11}$ and ${C}_{13}$ coefficients between two helium atoms and lithium atoms in their ground states are also given.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 ${C}_{9}/{R}^{9}$ interaction which occurs in the homonuclear case when one atom is in an $S$ state and the other is in a $P$ state. Numerical values of the ${C}_{9}$ coefficient are given for the homonuclear alkali-metal dimers. The size of the ${C}_{9}$:${C}_{3}$ dispersion coefficient ratio increases for the heavier alkali-metal atoms. The ${C}_{11}$ and ${C}_{13}$ coefficients between two helium atoms and lithium atoms in their ground states are also given.

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Mircea Marinescu, Anthony F. Starace

The long-range asymptotic form of the interaction potential surface for three neutral alkali-metal atoms in their ground states may be expressed as an expansion in inverse powers of inter-nuclear distances. The first leading powers are proportional to the dispersion coefficients for pairwise atomic interactions. They are followed by a term responsible for a three body dipole interaction. The authors results consist in evaluation of the three body dipole interaction coefficient between three alkali-metal atoms. The generalization to long-range n atom interaction terms will be discussed qualitatively.The long-range asymptotic form of the interaction potential surface for three neutral alkali-metal atoms in their ground states may be expressed as an expansion in inverse powers of inter-nuclear distances. The first leading powers are proportional to the dispersion coefficients for pairwise atomic interactions. They are followed by a term responsible for a three body dipole interaction. The authors results consist in evaluation of the three body dipole interaction coefficient between three alkali-metal atoms. The generalization to long-range n atom interaction terms will be discussed qualitatively.

Bulletin of the American Physical SocietyMay 1, 19960 citations

A general procedure for systematically evaluating the long-range dispersion interaction between two heteronuclear atoms in arbitrary states is outlined. The

{C}_{6}

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.

{\mathit{C}}_{6}

{\mathit{C}}_{8}

, and

{\mathit{C}}_{10}

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

{\mathit{C}}_{6}

{\mathit{C}}_{8}

, and

{\mathit{C}}_{10}

for homonuclear and heteronuclear alkali-metal diatoms are compared with other calculations.

A procedure for systematically evaluating the long-range dispersion interaction between two homonuclear atoms in arbitrary

LS

coupled states is outlined. The method is then used to generate dispersion coefficients for a number of the low-lying states of the Na and Mg dimers.

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

{C}_{9}/{R}^{9}

interaction which occurs in the homonuclear case when one atom is in an

S

state and the other is in a

P

state. Numerical values of the

{C}_{9}

coefficient are given for the homonuclear alkali-metal dimers. The size of the

{C}_{9}

{C}_{3}

dispersion coefficient ratio increases for the heavier alkali-metal atoms. The

{C}_{11}

and

{C}_{13}

coefficients between two helium atoms and lithium atoms in their ground states are also given.