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Physical Review A

Autodissociating Rydberg states of positronium hydride

Richard J. Drachman

Published May 1, 1979• 52 citations
Publisher

Abstract

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 $L$ 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 $S$-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.

DOI
10.1103/physreva.19.1900

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Physical Review A•Mar 25, 2024•1 citation
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−1.575E=\ensuremath{-}1.575E=\ensuremath−1.575 Ry. In addition, for each LLL it must have an infinite Rydberg series of excited states whose principal configuration is (e+H\ensuremath−{e}^{+}{\mathrm{H}}^{\ensuremath{-}}e+H\ensuremath−), converging to a limit at E=\ensuremath−1.0555E=\ensuremath{-}1.0555E=\ensuremath−1.0555 Ry, the energy of H\ensuremath−{\mathrm{H}}^{\ensuremath{-}}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+H\ensuremath−{e}^{+}{\mathrm{H}}^{\ensuremath{-}}e+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.
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 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.
The coupled-channel model [Phys. Rev. A {\bf 59}, 363 (1999)] that yields converged low-energy phase shifts, and exact binding and resonance features in Ps-H [Phys. Rev. A {\bf 59}, 2058 (1999)] is applied to study Ps-He+^++ scattering. Similar to PsH, resonances appear in the S-, P-, D-, etc partial waves in the Ps-He+^++ system but in both the singlet and triplet scattering channels. The latter signifies possible Rydberg states of e+e^+e+ around singlet and triplet helium. The S-wave singlet resonance at 2.79 eV agrees to that predicted earlier in e+e^+e+-He entrance channel (energy difference 16.64 eV) at 19.27 eV [Chem. Phys. Lett. {\bf 262}, 460 (1996)].
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.
Calculations are reported for positronium (Ps) scattering by atomic hydrogen (H) in the energy range 0--6.5 eV in a coupled-pseudostate approximation in which excitation and ionization channels of both the Ps and the H are taken into account. The approximation contains an accurate representation of the van der Waals coefficient. Results are presented for phase shifts, scattering lengths, effective ranges, and various cross sections including partial wave, total, and ortho-para conversion cross sections. An analysis of the possible spin transitions is provided and the energy of the positronium hydride (PsH) bound state is determined. Substantial differences are found from earlier work within the frozen target approximation, now clearly confirming the importance of target excitation channels. Good agreement is obtained with recent calculations of S-wave phase shifts and scattering lengths using the stabilization method. Convergence to the exact binding energy for PsH appears to be slow. Resonances corresponding to unstable states of the positron orbiting ${\mathrm{H}}^{\ensuremath{-}}$ are seen in the electronic spin singlet partial waves. The importance of the ${\mathrm{H}}^{\ensuremath{-}}$ formation channel is discussed.
Positronium hydride (PsH)(\text{PsH})(PsH) is a weakly bound (molecular) state of two electrons $({e}^{\ensuremath{-}})$, a positron (e+)({e}^{+})(e+), and a proton (p+)({p}^{+})(p+). Due to the ${e}^{\ensuremath{-}}\ensuremath{-}{e}^{+}$ annihilation, it decays to a number of processes, where the radiationless decay is one of the most important channels. In this decay process, the photons released from the ${e}^{\ensuremath{-}}\ensuremath{-}{e}^{+}$ annihilation are absorbed by the remaining ${e}^{\ensuremath{-}}$ and p+{p}^{+}p+ in PsH, giving us $\text{PsH}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{p}^{+}$. For a particular spin (singlet) configuration of the constituents of PsH, the radiationless decay rate of PsH was determined by Aslam et al. [Phys. Rev. A 104, 052803 (2021)]. In this work, we calculate the decay rate of $\text{PsH}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{p}^{+}$ by exercising all possible spin orientations of PsH and the final states ${e}^{\ensuremath{-}}$ and p+{p}^{+}p+. By summing all the contributions, we verify that the result is the same if we calculate it using the standard fermion spin-sum technique of quantum field theory.