Physical Review A

Long-range dispersion interactions. III: Method for two homonuclear atoms

Jim Mitroy, J.-Y. Zhang

Published Dec 12, 2007• 20 citations

Abstract

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.

DOI: 10.1103/physreva.76.062703

Related papers

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

J. Y. Zhang, Jim Mitroy

Physical Review AAug 7, 200749 citations

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

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

Physical Review ADec 3, 201210 citations

Third-order perturbation theory for van der Waals interaction coefficients

Li-Yan Tang, Zong-Chao Yan, Ting-Yun Shi +1 more

Physical Review ANov 4, 20115 citations

Long-range interactions between alkali and alkaline-earth atoms

Jun Jiang, Yongjun Cheng, Jim Mitroy

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.

arXiv:1303.1234Journal of Physics B Atomic Molecular and Optical PhysicsJun 10, 201311 citations

Long-range interactions of excited He atoms with the alkaline earth atoms Mg, Ca, and Sr

Jun-Yi Zhang, Jim Mitroy, Z.-C. Yan +3 more

Dispersion coefficients for the long-range interactions of the first four excited states of He, i.e., He(2 (1, 3)S) and He(2 (1, 3)P), with the low-lying states of the alkaline earth atoms Mg, Ca, and Sr are calculated by summing over the reduced matrix elements of multipole transition operators.

The Journal of Chemical PhysicsApr 5, 20131 citation

Properties of alkali-metal atoms and alkaline-earth-metal ions for an accurate estimate of their long-range interactions

Jasmeet Kaur, D. K. Nandy, Bindiya Arora +1 more

Physical Review AJan 8, 201540 citations

Physical Review A

Long-range dispersion interactions. III: Method for two homonuclear atoms

Jim Mitroy, J.-Y. Zhang

Published Dec 12, 2007• 20 citations

Publisher

Abstract

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.

DOI: 10.1103/physreva.76.062703

Related papers

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

J. Y. Zhang, Jim Mitroy

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.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.

Physical Review AAug 7, 200749 citations

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.

Physical Review ADec 3, 201210 citations

Third-order perturbation theory for van der Waals interaction coefficients

Li-Yan Tang, Zong-Chao Yan, Ting-Yun Shi +1 more

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.

Physical Review ANov 4, 20115 citations

Long-range interactions between alkali and alkaline-earth atoms

Jun Jiang, Yongjun Cheng, Jim Mitroy

arXiv:1303.1234Journal of Physics B Atomic Molecular and Optical PhysicsJun 10, 201311 citations

Long-range interactions of excited He atoms with the alkaline earth atoms Mg, Ca, and Sr

Jun-Yi Zhang, Jim Mitroy, Z.-C. Yan +3 more

The Journal of Chemical PhysicsApr 5, 20131 citation

Properties of alkali-metal atoms and alkaline-earth-metal ions for an accurate estimate of their long-range interactions

Jasmeet Kaur, D. K. Nandy, Bindiya Arora +1 more

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 ${\mathrm{Ca}}^{+}$ , ${\mathrm{Ba}}^{+}$ , ${\mathrm{Sr}}^{+}$ , and ${\mathrm{Ra}}^{+}$ 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 $R$ . 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 $R$ are given among all the alkaline ions with Rb.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 ${\mathrm{Ca}}^{+}$, ${\mathrm{Ba}}^{+}$, ${\mathrm{Sr}}^{+}$, and ${\mathrm{Ra}}^{+}$ 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 $R$. 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 $R$ are given among all the alkaline ions with Rb.

Physical Review AJan 8, 201540 citations

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.

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.

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 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.

{\mathrm{Ca}}^{+}

{\mathrm{Ba}}^{+}

{\mathrm{Sr}}^{+}

, and

{\mathrm{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

R

. 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

R

are given among all the alkaline ions with Rb.