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The study of long-range interactions is increasingly becoming essential dueto its various applications in cold atomic physics. These interactions can beconveniently expressed in terms of dispersion coefficients. In the presentwork, theoretical calculations have been carried out to estimate the two-dipole($C_6$) and three-dipole ($C_9$) dispersion coefficients between the group XIIatoms and their ions, \textit{viz.}, Zn, Cd, Hg, Zn$^+$, Cd$^+$, and Hg$^+$. Toobtain these coefficients, the dynamic dipole polarizabilities and reducedmatrix elements required are evaluated using the relativistic methods for boththe considered atoms and ions. Further, using the calculated matrix elements,the oscillator strengths corresponding to leading transitions and static dipolepolarizabilities are determined. These are compared with the available valuesin the literature through which the accuracy of the present calculationsascertains. However, the oscillator strengths for few transitions of Zn, Cd,Hg, Zn$^+$, Cd$^+$, and Hg$^+$, are not reported earlier, and we have providedtheir values in this work. Thereafter, the dispersion $C_6$ and $C_9$coefficients are calculated for various combinations of the group XII elements,and most of these coefficients were not reported earlier in the literature.Furthermore, the combinations for which the other theoretical and experimentalvalues were available for comparison showed good agreement. We, therefore,believe that our results reported for $C_6$ and $C_9$ coefficients for variouscombinations of group XII elements are reliable.

Two-dipole and three-dipole interaction coefficients of GROUP XII elements