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arXiv:physics/9804023 · Physical Review A

Signature of the existence of the positronium molecule

J. Usukura, Kálmán Varga, Y. Suzuki

Published Sep 1, 1998• 106 citations
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Abstract

The positronium molecule $({\mathrm{Ps}}_{2})$ 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 $L=1$ excited state and the $L=0$ 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.

DOI
10.1103/physreva.58.1918

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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.
Annihilation converts positronium hydride into photons and a hydrogen atom. We calculate the probability that the residual hydrogen atom will relax to each of number of bound states. The results suggest an experiment for detecting positronium hydride in a system in which excited hydrogen atoms do not exist except as the residue after annihilation. The experiment consists of measuring the intensity increase of the Lyman -$\ensuremath{\alpha}$ line upon quenching the 2s2s2s atoms to 2p2p2p atoms. We predict that the intensity will increase by a factor of 35.
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 projection method with explicitly correlated Gaussians is used to demonstrate the existence of two doubly excited states of the positronium molecule (Ps2{\mathrm{Ps}}_{2}Ps2​). One is below the Ps(n=2)+Ps(n=2)\mathrm{Ps}(n=2)\phantom{\rule{4pt}{0ex}}+\phantom{\rule{4pt}{0ex}}\mathrm{Ps}(n=2)Ps(n=2)+Ps(n=2) threshold, with A1{A}_{1}A1​ symmetry, and the other is below the Ps(n=2)+Ps(n=3)\mathrm{Ps}(n=2)+\mathrm{Ps}(n=3)Ps(n=2)+Ps(n=3) threshold, with EEE symmetry. These states exist as resonances in the Ps-Ps continuum. Moreover, the resonance positions and resonance widths of the two states are calculated using the complex rotation method with basis sets obtained via the orthogonalizing pseudoprojector method. The resonance positions obtained using the complex rotation method agree with the results of the orthogonalizing pseudoprojector method. We also investigate the various structural properties of these states as well as the decay probabilities of $2\ensuremath{\gamma}$ emission due to electron-positron annihilation.
The effect of an electric quadrupole moment QQQ is studied for positron-atom bound systems. It is demonstrated that for Q>50Q>50Q>50 a.u. the electric quadrupole potential is sufficiently strong to bind a positron (or an electron) even in the absence of the dipole polarization potential. Such large values of QQQ are not known for atomic ground states; however, they exist in molecules and excited atoms. In the 2s2p3P2o2s2{p}^{3}{P}_{2}^{o}2s2p3P2o​ state of beryllium, the quadrupole contribution makes the difference between a stable bound state and an unstable state, which decays to a Be+\mathrm{Be}{}^{+}Be+ ion and positronium. In the majority of atoms the quadrupole contribution is small and can be neglected.