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Physical Review A

Contribution of various spin configurations to the radiationless decay of PsH

Iraj Masood, S. Zayad Munir, M. Jamil Aslam

Published Mar 25, 2024• 1 citation
Publisher

Abstract

Positronium hydride $(\text{PsH})$ is a weakly bound (molecular) state of two electrons $({e}^{\ensuremath{-}})$, a positron $({e}^{+})$, and a proton $({p}^{+})$. 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 ${p}^{+}$ 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 ${p}^{+}$. 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.

DOI
10.1103/physreva.109.032820

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Positronium hydride (PsH)(\text{PsH})(PsH) is a weakly bound (molecular) state of two electrons (e\ensuremath−)({e}^{\ensuremath{-}})(e\ensuremath−), a positron (e+)({e}^{+})(e+), and a proton (p+)({p}^{+})(p+). Due to the e\ensuremath−\ensuremath−e+{e}^{\ensuremath{-}}\ensuremath{-}{e}^{+}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+{e}^{\ensuremath{-}}\ensuremath{-}{e}^{+}e\ensuremath−\ensuremath−e+ annihilation are absorbed by the remaining e\ensuremath−{e}^{\ensuremath{-}}e\ensuremath− and p+{p}^{+}p+ in PsH, giving us PsH\ensuremath→e\ensuremath−p+\text{PsH}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{p}^{+}PsH\ensuremath→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 PsH\ensuremath→e\ensuremath−p+\text{PsH}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{p}^{+}PsH\ensuremath→e\ensuremath−p+ by exercising all possible spin orientations of PsH and the final states e\ensuremath−{e}^{\ensuremath{-}}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.
The positronium ion (Ps−\mathrm{Ps}^-Ps−), a coulombic three-body bound state of two electrons and a positron, predominantly decays via electron-positron annihilation into electromagnetic final states. While its radiative decay channels have been extensively studied, much less attention has been given to weak processes in this system. In this work, we investigate the rare decay Ps−→e−νμνˉμ\mathrm{Ps}^- \to e^- ν_μ\barν_μPs−→e−νμ​νˉμ​, obtained by replacing the photon in Ps−→e−γ\mathrm{Ps}^- \to e^- γPs−→e−γ with a virtual ZZZ boson. Treating the three-body process as an effective two-body transition, Ps−→e−Z∗(→νμνˉμ)\mathrm{Ps}^- \to e^- Z^*\left(\to ν_μ\barν_μ\right)Ps−→e−Z∗(→νμ​νˉμ​), we compute the decay rate by explicitly evaluating all spin configurations of the initial bound state and final particles. The result agrees with that obtained using the standard spin-summation formalism of quantum field theory. We find that the branching ratio is comparable to that of the weak decay of ortho-positronium, o-Ps→γννˉ\mathrm{o\text{-}Ps} \to γν\barνo-Ps→γννˉ.
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 positronium molecule (Ps2)({\mathrm{Ps}}_{2})(Ps2​) has not been experimentally observed yet because its tiny (4.5 eV) binding energy cannot be detected when the molecule annihilates by emitting two photons with energy of 0.51 MeV each. It is shown in this paper that the electric dipole transition between the recently found L=1L=1L=1 excited state and the L=0L=0L=0 ground state with its characteristic photon energy of 4.94 eV is a clear signature of the existence of the positronium molecule and the possibility of its experimental observation is realistic. The probability of this transition is about 17% of the total decay rate. Another Coulomb four-body system containing positron HPs (the positronium hydride or hydrogen positride), is also included for comparison.
We reexamine the problem of calculating the positions and widths of the lowest-lying resonances in the Ps+H\mathrm{Ps}+\mathrm{H}Ps+H scattering system that consists of two electrons, one positron and one proton. The first of these resonances, for L=0,L=0,L=0, was found by the methods of complex rotation and stabilization, and later described as a Feshbach resonance lying close to a bound state in the closed-channel ${e}^{+}+{\mathrm{H}}^{\ensuremath{-}}$ system. Recently, results for the L=1L=1L=1 and 2 scattering states were published, and it was found, surprisingly, that there is a large shift in the positions of these resonances. In this paper we repeat the analysis for L=1L=1L=1 and find an unexpected explanation for the shift.
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)].
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.