The van der Waals coefficients, from ${C}_{11}$ through to ${C}_{16}$ resulting from second-, third-, and fourth-order perturbation theory are estimated for the alkali-metal (Li, Na, K, and Rb) atoms. The dispersion coefficients are also computed for all possible combinations of the alkali-metal atoms and hydrogen. The parameters are determined from sum rules after diagonalizing a semiempirical fixed core Hamiltonian in a large basis. Comparisons of the radial dependence of the ${C}_{n}∕{r}^{n}$ potentials give guidance as to the radial regions in which the various higher-order terms can be neglected. It is seen that including terms up to ${C}_{10}∕{r}^{10}$ results in a dispersion interaction that is accurate to better than 1% whenever the inter-nuclear spacing is larger than $20{a}_{0}$ . This level of accuracy is mainly achieved due to the fortuitous cancellation between the repulsive $({C}_{11},{C}_{13},{C}_{15})$ and attractive $({C}_{12},{C}_{14},{C}_{16})$ dispersion forces.The van der Waals coefficients, from ${C}_{11}$ through to ${C}_{16}$ resulting from second-, third-, and fourth-order perturbation theory are estimated for the alkali-metal (Li, Na, K, and Rb) atoms. The dispersion coefficients are also computed for all possible combinations of the alkali-metal atoms and hydrogen. The parameters are determined from sum rules after diagonalizing a semiempirical fixed core Hamiltonian in a large basis. Comparisons of the radial dependence of the ${C}_{n}∕{r}^{n}$ potentials give guidance as to the radial regions in which the various higher-order terms can be neglected. It is seen that including terms up to ${C}_{10}∕{r}^{10}$ results in a dispersion interaction that is accurate to better than 1% whenever the inter-nuclear spacing is larger than $20{a}_{0}$. This level of accuracy is mainly achieved due to the fortuitous cancellation between the repulsive $({C}_{11},{C}_{13},{C}_{15})$ and attractive $({C}_{12},{C}_{14},{C}_{16})$ dispersion forces.

arXiv:physics/0411174Physical Review AApr 7, 200527 citations

Dimensional reduction in Bose-Einstein-condensed alkali-metal vapors (4 pages)

Luca Salasnich

Physical Review AJan 1, 20040 citations

Dispersion coefficients for the nP - nP asymptote of homonuclear alkali-metal dimers

M. Marinescu

The derivation of the dispersion coefficients for various symmetries of the lower $\mathrm{nP}$ - $\mathrm{nP}$ asymptote of the homonuclear alkali-metal dimers is presented. Using the perturbation theory the dispersion coefficients ${C}_{5}$ are obtained in the first order and the ${C}_{6}$ and ${C}_{8}$ coefficients are obtained in the second order in terms of double sums involving atomic radial matrix elements. The sums are separated in individual contributions of each atom by using a complex integral representation. The atomic matrix elements involving Green's functions are evaluated using the Dalgarno-Lewis method. Numerical results for the ${C}_{5}$ , ${C}_{6}$ , and ${C}_{8}$ dispersion coefficients for Li, Na, K, Rb, and Cs dimers are presented.The derivation of the dispersion coefficients for various symmetries of the lower $\mathrm{nP}$-$\mathrm{nP}$ asymptote of the homonuclear alkali-metal dimers is presented. Using the perturbation theory the dispersion coefficients ${C}_{5}$ are obtained in the first order and the ${C}_{6}$ and ${C}_{8}$ coefficients are obtained in the second order in terms of double sums involving atomic radial matrix elements. The sums are separated in individual contributions of each atom by using a complex integral representation. The atomic matrix elements involving Green's functions are evaluated using the Dalgarno-Lewis method. Numerical results for the ${C}_{5}$, ${C}_{6}$, and ${C}_{8}$ dispersion coefficients for Li, Na, K, Rb, and Cs dimers are presented.

Physical Review ADec 1, 199737 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

The van der Waals coefficients, from

{C}_{11}

through to

{C}_{16}

resulting from second-, third-, and fourth-order perturbation theory are estimated for the alkali-metal (Li, Na, K, and Rb) atoms. The dispersion coefficients are also computed for all possible combinations of the alkali-metal atoms and hydrogen. The parameters are determined from sum rules after diagonalizing a semiempirical fixed core Hamiltonian in a large basis. Comparisons of the radial dependence of the

{C}_{n}∕{r}^{n}

potentials give guidance as to the radial regions in which the various higher-order terms can be neglected. It is seen that including terms up to

{C}_{10}∕{r}^{10}

results in a dispersion interaction that is accurate to better than 1% whenever the inter-nuclear spacing is larger than

20{a}_{0}

. This level of accuracy is mainly achieved due to the fortuitous cancellation between the repulsive

({C}_{11},{C}_{13},{C}_{15})

and attractive

({C}_{12},{C}_{14},{C}_{16})

dispersion forces.

The derivation of the dispersion coefficients for various symmetries of the lower

\mathrm{nP}

\mathrm{nP}

asymptote of the homonuclear alkali-metal dimers is presented. Using the perturbation theory the dispersion coefficients

{C}_{5}

are obtained in the first order and the

{C}_{6}

and

{C}_{8}

coefficients are obtained in the second order in terms of double sums involving atomic radial matrix elements. The sums are separated in individual contributions of each atom by using a complex integral representation. The atomic matrix elements involving Green's functions are evaluated using the Dalgarno-Lewis method. Numerical results for the

{C}_{5}

{C}_{6}

, and

{C}_{8}

dispersion coefficients for Li, Na, K, Rb, and Cs dimers are presented.

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.