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Physical Review A

Resonances in positronium hydride

Joseph Di Rienzi, Richard J. Drachman

Published Feb 26, 2002• 19 citations
Publisher

Abstract

We reexamine the problem of calculating the positions and widths of the lowest-lying resonances in the $\mathrm{Ps}+\mathrm{H}$ scattering system that consists of two electrons, one positron and one proton. The first of these resonances, for $L=0,$ 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 $L=1$ 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 $L=1$ and find an unexpected explanation for the shift.

DOI
10.1103/physreva.65.032721

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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++H\ensuremath−{e}^{+}+{\mathrm{H}}^{\ensuremath{-}}e++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.
Seiler, Oberoi, and Callaway first located resonances in the positron-hydrogen system below the n=2n=2n=2 inelastic threshold, using the algebraic close-coupling method without including the open positronium channel. Several other calculations including both open channels have failed to find any resonances. In an attempt to clarify the situation, a calculation has been performed which is an extension of the work of Seiler, Oberoi, and Callaway. A wave function including the 1s1s1s, 2s2s2s, and 2p2p2p eigenstates of hydrogen and the 1s−\stackrel{-}{1s}1s− ground state of positronium was used in a calculation that is a simplification of the usual close-coupling technique and that resembles the optical-potential method. In this approximation it is found that the lowest resonance of Seiler, Oberoi, and Callaway is destroyed by opening the 1s−\stackrel{-}{1s}1s− channel. It is concluded that any resonances which may occur in this system must lie closer to the n=2n=2n=2 threshold than do the corresponding electron-hydrogen resonances.
We have investigated the elastic scattering of positronium atoms by hydrogen atoms below the excitation threshold at 5.1 eV, limiting the investigation to the spin-zero (singlet) state of the two electrons. Nonresonant SSS-wave phase shifts have been obtained from normalizable trial functions by extracting the center-of-mass wave function and examining its spatial behavior. An effective-range expansion is fitted to the phase shifts and the previously obtained positronium-hydride bound-state energy to yield a scattering length $a\ensuremath{\cong}5.3{a}_{0}$ compared with Fraser's corrected exchange result, a=7.28a0a=7.28{a}_{0}a=7.28a0​ (a0{a}_{0}a0​ is the Bohr radius). The stabilization method suggests that a resonance occurs at a scattering energy of 4.5 eV, about 0.6 eV below the excitation threshold. Using the complex rotation method, we have obtained evidence confirming the existence of the resonance and an estimate of its width of about 6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ eV.
We were previously successful in representing a series of low-lying Ps+H\mathrm{Ps}+\mathrm{H}Ps+H scattering resonances as due to quasibound Coulomb states in the closed-channel ${e}^{+}+{\mathrm{H}}^{\ensuremath{-}}$ system. Here we investigate the analogous Coulomb states of ${\mathrm{Ps}}^{\ensuremath{-}}+{\mathrm{H}}^{+}$, which are also accessible from the Ps+H\mathrm{Ps}+\mathrm{H}Ps+H scattering system, but at considerably higher collision energies. We locate several such states and suggest that they may be scattering resonances, but because there are many open-channel thresholds lying below they may have large widths and shifts.
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.
We have performed a three-body calculation for investigation of S-wave resonances in the positron–helium scattering in the hyperspherical coordinates. B-splines are used to obtain accurate hyperspherical potential curves and channel functions. An adiabatical hyperspherical approach is used to predict semi-quantitatively the position of the resonances. A multichannel calculation with the stabilization method is also used to extract accurately the positions and widths of resonances. We find four resonances associated with the He + –Ps( n = 2) channel. The resonance parameters for the lowest two resonances are in reasonable agreement with the calculations of Kar and Ho ( 2004 J. Phys. B: At. Mol. Opt. Phys. 37 3177 ), and two more new resonances below the Ps( n = 2) threshold are identified.