The problem of the bound states of a positron with atoms and apolar molecules is studied with a regularized polarization potential $V=V_{r_c}-\frac{\alpha r^{-4}}{2}$, where $V_{r_c}$ is a repulsive hard-core potential. A continuous relation between the core radius and the target polarizability is identified for alkanes, leading to the observed linear relation between their experimental binding energies and polarizabilities. New values for the binding energies for I and Pt atoms are suggested. Some predictions for related molecules are made, suggesting positron binding to GeH${}_4$ and, possibly, to C${}_2$F${}_6$.

• Received 8 May 2012

DOI:https://doi.org/10.1103/PhysRevA.86.042708