Improved wave function for positronium hydride

Abstract

An extension of an earlier calculation on positronium hydride PsH is presented. In the earlier work, the wave function was expressed as an exponential term $\exp (-A{r}_1-B{r}_2-C{r}_{1p}-D{r}_{2p})+\exp (-B{r}_1-A{r}_2-D{r}_{1p}-C{r}_{2p})$, times a twelve-term polynomial in the interparticle coordinates: $r_1$, $r_2$, $r_{1p}$, $r_{2p}$, and $r_{12}$ (the electrons are labeled 1 and 2; the positron is labeled as $p$). The coefficients in the polynomial were determined by the variational method. In the present work, the number of terms is increased; the coordinate $r_p$ is included in the polynomial; the wave function is tested for the four cusp conditions; and an annihilation rate and the relaxation of the daughter system are calculated. The new binding energy, 0.794 eV, is greater than the earlier result by 0.137 eV. The annihilation rate is found to be 2.22 ${\mathrm{nsec}}^{-1\mathrm{}}$, with the $1s$ state being the most probable daughter-occupation state. The electron-positron, electron-nucleus, nucleus-positron, and electron-electron cusp values are, respectively, -0.4398, -1.065, -0.0102, and 0.1126. The values of the repulsive cusps definitely show that the wave function has not yet converged to the exact function in all regions of three-particle space. A search for a bound excited state of PUSH with the same symmetry of the ground state was unsuccessful.