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Physical Review A

Ground state andS-wave autodissociating resonant states of positronium hydride

Zong-Chao Yan, Y. K. Ho

Published Apr 1, 1999• 72 citations
Publisher

Abstract

The fully correlated calculations in Hylleraas coordinates for the nonrelativistic ground-state energy and the first three S-wave resonances of positronium hydride are reported. For the resonances, the positions and widths are determined using the method of complex-coordinate rotation. Our results significantly improve previous work. For example, the ground-state energy is about five parts in ${10}^{9}$ in accuracy, the lowest variational upper bound reported to date. A comparison with other previous work is made.

DOI
10.1103/physreva.59.2697

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The fully correlated calculations in Hylleraas coordinates for the nonrelativistic ground-state energy and the first three S-wave resonances of positronium hydride are reported. For the resonances, the positions and widths are determined using the method of complex-coordinate rotation. Our results significantly improve previous work. For example, the ground-state energy is about five parts in 109{10}^{9}109 in accuracy, the lowest variational upper bound reported to date. A comparison with other previous work is made.
A doubly excited autodissociating resonant state in positronium hydride has been discovered, which is situated in a Rydberg series converging to the ${\mathrm{H}}^{\ensuremath{-}}(2{s}^{2})+{e}^{+}$ threshold. Previous research has noted a scarcity of such highly excited resonant states, particularly those with a doubly excited nature. The exploration of these states was made possible by employing a projection operator method supported by the stochastic variational method. Accurate calculations of the resonant positions and widths were performed using the complex coordinate rotation method with explicitly correlated Gaussians as basis functions. Our analysis has revealed the intrinsic structural characteristics of these highly excited states. The probability density distribution demonstrates that most resonant states of positronium hydride tend to favor either a ${\mathrm{H}}^{\ensuremath{-}}+{e}^{+}$ or ${\mathrm{Ps}}^{\ensuremath{-}}+{\mathrm{H}}^{+}$ configuration. However, two doubly excited resonant states exhibit a unique characteristic involving both the ${\mathrm{H}}^{\ensuremath{-}}+{e}^{+}$ and ${\mathrm{Ps}}^{\ensuremath{-}}+{\mathrm{H}}^{+}$ configurations. By integrating the probability density distribution with a quantum defect formula, highly excited resonances can be accurately assigned to either the ${\mathrm{H}}^{\ensuremath{-}}(2{s}^{2})+{e}^{+}$ or ${\mathrm{Ps}}^{\ensuremath{-}}(1{s}^{2})+{\mathrm{H}}^{+}$ Rydberg series, thereby reducing discrepancies compared to earlier classifications.
The "molecule" positronium hydride (PsH), consisting of one atom each of positronium and hydrogen, has one well-known particle-stable state of total energy $E=\ensuremath{-}1.575$ Ry. In addition, for each LLL it must have an infinite Rydberg series of excited states whose principal configuration is (${e}^{+}{\mathrm{H}}^{\ensuremath{-}}$), converging to a limit at $E=\ensuremath{-}1.0555$ Ry, the energy of ${\mathrm{H}}^{\ensuremath{-}}$. All of these excited states are energetically able to dissociate into ground-state Ps + H, and the higher-lying states can also decay with emission of excited Ps and ground-state H. These Rydberg states should appear as resonances in Ps + H scattering. In this paper I compute the lowest SSS-wave resonance parameters, using an optical-potential formalism based on the (${e}^{+}{\mathrm{H}}^{\ensuremath{-}}$) configuration. The results are in rough agreement with those previously obtained using Kohn variational or complex-rotation techniques with highly correlated trial functions. The physical description of the PsH excited states is thus clarified.
The method of complex-coordinate rotation is applied to investigate autoionization states of positronium molecules. Using elaborate Hylleraas-type wave functions in which all six interparticle coordinates are used, resonance parameters for six S-wave resonant states are determined. It is believed that three of them belong to a Rydberg series in which the two positrons form a singlet spin state, and the other three resonances belong to the triplet spin state for the two positrons. All these two Rydberg series are converging on the ground state of the ${\mathrm{Ps}}^{\mathrm{\ensuremath{-}}}$ threshold.
The leading-order relativistic corrections to the ground-state energy of the positronium molecule (Ps2)({\mathrm{Ps}}_{2})(Ps2​) have been computed within the framework of perturbation theory. As the zero-order wave function we used a highly accurate nonrelativistic variational expansion in terms of 6000 explicitly correlated Gaussians that yielded the lowest variational upper bound for this system to date. We also report some expectation values representing the properties of Ps2{\mathrm{Ps}}_{2}Ps2​.