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Dynamic polarizabilities of Zn and Cd and dispersion coefficients involving group 12 atoms

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10.1063/1.4746155

### Abstract

The refractive index data for Zn and Cd measured by Goebel and Hohm are analyzed with a three-term Maxwell-Sellmeier expression which incorporates the experimental oscillator strengths of the first two dipole transitions. These expressions are extended to imaginary frequencies for the determination of the upper and lower bounds of the dynamic polarizabilities α(*i*ω), from which the van der Waals coefficients of two-body interactions and the non-additive three-body interactions are generated. The determined *C* _{6} values for Zn_{2} (359±8 a.u.) and Cd_{2} (686±10 a.u.) are much larger than those originally estimated by Goebel and Hohm. This is because their one-term approximation of α(ω), which fits the measurements very well in the normal frequency range, greatly underestimates α(*i*ω) when the frequency is extended into the imaginary domain. On the other hand, the present results of heteronuclear interactions verify once again that Tang's one-term approximation of α(*i*ω) leads to accurate combining rules. The two- and three-body interaction coefficients between group 12 atoms (Zn, Cd, Hg) and the alkali, alkaline-earth, rare-gas atoms, and some molecules are estimated with these combining rules.

© 2012 American Institute of Physics

Received 30 May 2012
Accepted 31 July 2012
Published online 28 August 2012

Article outline:

I. INTRODUCTION

II. DYNAMIC (FREQUENCY DEPENDENT) POLARIZABILITY

A. Dynamic polarizabilities and oscillator strength sums

B. Dispersion coefficient and polarizability at imaginary frequency

C. Refractive index and polarizability of real frequency

D. Upper and lower bounds for polarizability at both real and imaginary frequencies

III. DYNAMIC POLARIZABILITY OF THE ZINC ATOM AND DISPERSION COEFFICIENT *C* _{6} FOR THE ZINC DIMER

A. Measurement and analysis of Goebel, Hohm, and Maroulis

B. The three-term fitted α(ω) for the zinc atom and *C* _{6} of the zinc dimer

IV. DYNAMIC POLARIZABILITY OF THE CADMIUM ATOM AND DISPERSION COEFFICIENT *C* _{6} FOR THE CADMIUM DIMER

A. Measurement and analysis of Goebel and Hohm

B. The three-term fitted α(ω) for the cadmium atom and *C* _{6} of the cadmium dimer

V. DISPERSION COEFFICIENTS C_{6} OF HETERONUCLEAR INTERACTIONS INVOLVING GROUP 12 ATOMS

VI. TRIPLE-DIPOLE DISPERSION COEFFICIENTS OF THE THREE-BODY INTERACTIONS

VII. SUMMARY AND DISCUSSION

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2012-08-28

2014-04-16

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