Abstract
Positron binding to neutral atoms, which to this day have not been detected experimentally, is thought to be rather weak. According to a few reliable nonrelativistic calculations reported previously, the positron affinity for small atoms, even if it happens to be positive, is predicted to be very small in magnitude, of the order of just few millihartrees $(<0.1\phantom{\rule{0.28em}{0ex}}\mathrm{eV})$. In this work, we used a highly accurate variational expansion in terms of explicitly correlated Gaussians to investigate how relativistic effects may affect the stability of bound states of positrons with atoms. We performed calculations of positronic beryllium, ${e}^{+}[\mathrm{Be}]$, in its ground singlet $S$ and excited triplet $S$ and $P$ states, all of which are bound. According to our findings, neither the inclusion of scalar relativistic nor spin-dependent corrections alters the predictions regarding the existence of the bound states. When leading-order relativistic effects are taken into account, positron affinities change only by 2.2% or less. Notably, this is so even for the triplet $P$ state of positronic beryllium, where the spin-orbit correction is not at all canceled out when the energy difference with the parent system is computed.