Repulsive Interaction Potentials between Rare-Gas Atoms. Homonuclear Two-Center Systems

Abstract

Using a previously derived theoretical expression based on the Thomas-Fermi-Dirac statistical model of the atom, the repulsive interaction energies $U(R)$ between a homonuclear pair of neutral rare-gas atoms have been calculated at internuclear distances $R$ ranging from $0.01{a}_{0}$ to $8.0{a}_{0}$. (${a}_{0}=0.529$ \AA{}.) The present calculations show that agreement with experiment is both closer as well as more extensive than was previously estimated. Specifically, for the He-He interaction, $U(R)$ nearly coincides with other theoretical and experimental results up to $R\ensuremath{\sim}5{a}_{0}$, excepting Amdur's measurements at $R\ensuremath{\lesssim}2{a}_{0}$. Similar and progressively closer accord with experiment is obtained for the Ne-Ne and Ar-Ar interactions. For Kr-Kr and Xe-Xe, agreement is reasonable up to separations of $\ensuremath{\sim}6{a}_{0}$ and $\ensuremath{\sim}7{a}_{0}$, respectively. Curves for the Rn-Rn interaction have also been obtained. Comparison of the experimental data with Bohr's screened Coulomb potential, and with a potential proposed by Firsov, shows that for $R\ensuremath{\gtrsim}1{a}_{0}$, the former decreases far too rapidly with increasing $R$, while for $R\ensuremath{\gtrsim}3{a}_{0}$, the latter falls off much too slowly. For extrapolations towards small $R$, the (12-6) potential is found to rise rapidly to values exceeding the experimental ones by several 100%, whereas the (exp-6) potential or its repulsive part consistently remains within an order of magnitude of the empirical values and often considerably closer. Whether this latter behavior is fortuitous or not is not determined.