Clustering of atoms around the positron and positive ions in gaseous He, Ne, and Ar

The clustering of atoms around the positron and positive ions in low-temperature ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, Ne, and Ar gases is calculated by the density-functional method. The gases are described by the van der Waals equation of state. For positron-atom interactions the optical pseudopotential based on scattering-length values is used. In agreement with recent experiments the calculations show that the cluster around the positron is formed only within a certain temperature and density range. Both in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ the model reproduces well the experimental annihilation rates and critical temperatures of the positron-induced clusters. The number of atoms in these clusters is a few hundred and the cluster radius varies from 10 to 20 Å. Also in the case of Ne and Ar the calculations explain qualitatively the few existing experimental results. The clusters around positive ions are formed at any gas temperature and gas density. They contain less than 100 atoms and their size decreases smoothly with increasing temperature.