^{1,2,a)}, Jun-Yi Zhang

^{3}, Zong-Chao Yan

^{4}, Ting-Yun Shi

^{1}and J. Mitroy

^{3}

### Abstract

The long-range dispersion coefficients for the ground and excited states of Li, , and interacting with the He, Ne, Ar, Kr, and Xe atoms in their ground states are determined. The variational Hylleraas method is used to determine the necessary lists of multipole matrix elements for He, Li, , and , while pseudo-oscillator strength distributions are used for the heavier rare gases. Some single electron calculations using a semiempirical Hamiltonian are also performed for Li and and found to give dispersion coefficients in good agreement with the Hylleraas calculations. Polarizabilities are given for some of the Li and states and the recommended polarizability including both finite-mass and relativistic effects was 0.192 486 a.u. The impact of finite-mass effects upon the dispersion coefficients has been given for some selected interatomic interactions.

This work was supported by NSFC of China under Grant No. 10974224 and by the National Basic Research Program of China under Grant No. 2010CB832803. Z.-C.Y. was supported by NSERC of Canada and by the computing facilities of ACEnet, SHARCnet, WestGrid, and in part by the CAS/SAFEA International Partnership Program for Creative Research Teams. J.M. and J.-Y.Z. would like to thank the Wuhan Institute of Physics and Mathematics for its hospitality during their visits. The work of J.M. was supported in part by the Australian Research Council Discovery Project (Grant No. DP-1092620).

I. INTRODUCTION

II. LONG-RANGE POLARIZATION AND DISPERSION INTERACTIONS

III. ATOMIC STRUCTURE DESCRIPTIONS

A. The Hylleraas method

B. The semiempirical approach

C. Li structure

D. structure

E. structure

F. Wave functions and transition operators for the rare gases

IV. RESULTS AND DISCUSSION

A. -rare gas dispersion coefficients

B. Li-rare gas dispersion coefficients: Excited Li states

C. -rare gas dispersion coefficients

D. -rare gas dispersion coefficients

V. CONCLUSION

### Key Topics

- Polarizability
- 26.0
- Dispersion
- 25.0
- Non adiabatic reactions
- 9.0
- Polarization
- 9.0
- Quadrupoles
- 9.0

## Tables

Comparisons of the binding energies (in a.u.) of Li in and states. The experimental valence binding energies are taken from the National Institute of Standards and Technology database (Ref. 69). The -weighted average is used for states with . The ground-state energies for the and ions are −7.279 913 412 669 305 9(1) and −7.279 321 519 738 427 6(1) a.u., respectively. The numbers in parentheses give the computational uncertainties in the energies.

Comparisons of the binding energies (in a.u.) of Li in and states. The experimental valence binding energies are taken from the National Institute of Standards and Technology database (Ref. 69). The -weighted average is used for states with . The ground-state energies for the and ions are −7.279 913 412 669 305 9(1) and −7.279 321 519 738 427 6(1) a.u., respectively. The numbers in parentheses give the computational uncertainties in the energies.

The polarizabilities for and in their and states (in a.u.). The numbers in parentheses give the computational uncertainties in the polarizabilities.

The polarizabilities for and in their and states (in a.u.). The numbers in parentheses give the computational uncertainties in the polarizabilities.

Ground-state polarizabilities for and (in a.u.). The number in parentheses gives the computational uncertainty in the polarizability.

Ground-state polarizabilities for and (in a.u.). The number in parentheses gives the computational uncertainty in the polarizability.

The polarizabilities of the rare gases in their ground states (in a.u.). All values for helium listed in the table are derived from infinite-mass Hylleraas calculations. The polarizabilities for the heaver rare gases are computed from pseudo-oscillator strength distributions as discussed in the text. Polarizabilities from other Hylleraas calculations (Refs. 15 and 67) are also listed. The number in parentheses represents the computational uncertainty.

The polarizabilities of the rare gases in their ground states (in a.u.). All values for helium listed in the table are derived from infinite-mass Hylleraas calculations. The polarizabilities for the heaver rare gases are computed from pseudo-oscillator strength distributions as discussed in the text. Polarizabilities from other Hylleraas calculations (Refs. 15 and 67) are also listed. The number in parentheses represents the computational uncertainty.

The long-range dispersion coefficients , , and (in a.u.) for the state interacting with the RG atoms. Hylleraas values are given for both and . The CICP values (implicitly for ) are taken from Refs. 17 and 68. The number in parentheses represents the computational uncertainty.

The long-range dispersion coefficients , , and (in a.u.) for the state interacting with the RG atoms. Hylleraas values are given for both and . The CICP values (implicitly for ) are taken from Refs. 17 and 68. The number in parentheses represents the computational uncertainty.

The , , and (in a.u.) dispersion coefficients for the interaction. The column denotes the magnetic quantum number of the excited state. The CICP values for Ne, Ar, Kr, and Xe were taken from Ref. 17. The number in parentheses represents the computational uncertainty.

The , , and (in a.u.) dispersion coefficients for the interaction. The column denotes the magnetic quantum number of the excited state. The CICP values for Ne, Ar, Kr, and Xe were taken from Ref. 17. The number in parentheses represents the computational uncertainty.

The long-range dispersion coefficients , , and (in a.u.) for the interaction. The CICP values for RG atoms heavier than He are taken from Ref. 17. For system, the computation uncertainties are given in the parentheses.

The long-range dispersion coefficients , , and (in a.u.) for the interaction. The CICP values for RG atoms heavier than He are taken from Ref. 17. For system, the computation uncertainties are given in the parentheses.

The , , and (in a.u.) dispersion coefficients for the interaction. The column denotes the magnetic quantum numbers of the excited state particles. The CICP dispersion coefficients have not been previously published. The number in parentheses represents the computational uncertainty.

The , , and (in a.u.) dispersion coefficients for the interaction. The column denotes the magnetic quantum numbers of the excited state particles. The CICP dispersion coefficients have not been previously published. The number in parentheses represents the computational uncertainty.

The , , and (in a.u.) dispersion coefficients for the interaction. The column denotes the magnetic quantum numbers of the excited state particles. The CICP dispersion coefficients for RG atoms heavier than helium are taken from Ref. 17. The number in parentheses represents the computational uncertainty.

The , , and (in a.u.) dispersion coefficients for the interaction. The column denotes the magnetic quantum numbers of the excited state particles. The CICP dispersion coefficients for RG atoms heavier than helium are taken from Ref. 17. The number in parentheses represents the computational uncertainty.

The long-range dispersion coefficients , , and (in a.u.) for the state interacting with the RG atoms. Hylleraas calculations are reported in the rows identified as and . For interactions, the computational uncertainties are given in the parentheses.

The long-range dispersion coefficients , , and (in a.u.) for the state interacting with the RG atoms. Hylleraas calculations are reported in the rows identified as and . For interactions, the computational uncertainties are given in the parentheses.

The long-range dispersion coefficients , , and (in a.u.) for the interactions. The column denotes the magnetic quantum numbers of the excited state particles. For interactions, the computational uncertainties are given in the parentheses.

The long-range dispersion coefficients , , and (in a.u.) for the interactions. The column denotes the magnetic quantum numbers of the excited state particles. For interactions, the computational uncertainties are given in the parentheses.

The long-range dispersion coefficients , , and (in a.u.) for the interaction. Dispersion coefficients computed in Refs. 27, 41, and 42 implicitly assume an infinite mass for . For interactions, the computational uncertainties are given in the parentheses.

The long-range dispersion coefficients , , and (in a.u.) for the interaction. Dispersion coefficients computed in Refs. 27, 41, and 42 implicitly assume an infinite mass for . For interactions, the computational uncertainties are given in the parentheses.

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