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Physical Review Letters

Resonant Photodetachment of the Positronium Negative Ion

J. Botero, Chris H. Greene

Published Mar 31, 1986• 72 citations
Publisher

Abstract

An adiabatic treatment in hyperspherical coordinates is used to predict the existence of resonant structures in ${\mathrm{Ps}}^{\ensuremath{-}}$ (Ps denotes positronium) photodetachment. This highly correlated system displays a weak series of narrow Feshbach resonances lying just below the $\mathrm{Ps}(n=2)$ threshold, while a single strong shape resonance dominates the photodetachment spectrum above this threshold as in ${\mathrm{H}}^{\ensuremath{-}}$. Use of a "prediagonalized" representation of hyperspherical harmonics dramatically improves the convergence of the adiabatic calculation.

DOI
10.1103/physrevlett.56.1366

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In an effort to unravel the dependence of the dynamics of three-bound-particle systems on the relative masses of the particles, an adiabatic treatment in hyperspherical coordinates is used to study the ground state and some doubly excited states of Ps('-) (positronium negative ion) and other three-particle systems, including H('-) and M('-) (muonium negative ion). Two different methods for the solution of the adiabatic eigenvalue equation are presented; one uses a "prediagonalized" basis of hyperspherical harmonics, and the other uses an asymptotic basis which consists of hydrogenic functions for the positronium. Potential curves for Ps('-) and M('-) in the ('1)S('e), ('1)P('o), ('3)P('e), ('3)P('o) and ('1)D('e) states and for H('-) in the ('1)P('o) states are presented. A method for calculating the probability density as a function of the hyperspherical coordinates (R,(alpha),(theta)(,12)) is introduced and used for the P states of Ps('-). This helps to understand the different symmetries and to distinguish among them. A remarkable linear dependence of the binding energy of the ground state and of the doubly excited states on the reduced mass of the atom, discovered in this study, is presented and discussed.

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An adiabatic treatment in hyperspherical coordinates is used to predict the existence of resonant structures in Ps\ensuremath−{\mathrm{Ps}}^{\ensuremath{-}}Ps\ensuremath− (Ps denotes positronium) photodetachment. This highly correlated system displays a weak series of narrow Feshbach resonances lying just below the Ps(n=2)\mathrm{Ps}(n=2)Ps(n=2) threshold, while a single strong shape resonance dominates the photodetachment spectrum above this threshold as in H\ensuremath−{\mathrm{H}}^{\ensuremath{-}}H\ensuremath−. Use of a "prediagonalized" representation of hyperspherical harmonics dramatically improves the convergence of the adiabatic calculation.
In an effort to unravel the dependence of the dynamics of three-bound-particle systems on the relative masses of the particles, an adiabatic treatment in hyperspherical coordinates is used to study the ground state and some doubly excited states of Ps('-) (positronium negative ion) and other three-particle systems, including H('-) and M('-) (muonium negative ion). Two different methods for the solution of the adiabatic eigenvalue equation are presented; one uses a "prediagonalized" basis of hyperspherical harmonics, and the other uses an asymptotic basis which consists of hydrogenic functions for the positronium. Potential curves for Ps('-) and M('-) in the ('1)S('e), ('1)P('o), ('3)P('e), ('3)P('o) and ('1)D('e) states and for H('-) in the ('1)P('o) states are presented. A method for calculating the probability density as a function of the hyperspherical coordinates (R,(alpha),(theta)(,12)) is introduced and used for the P states of Ps('-). This helps to understand the different symmetries and to distinguish among them. A remarkable linear dependence of the binding energy of the ground state and of the doubly excited states on the reduced mass of the atom, discovered in this study, is presented and discussed.
A highly accurate calculation is supplemented by an adiabatic approximation to explore the resonance spectrum of positronium ${\mathrm{Ps}}^{\mathrm{\ensuremath{-}}}$. Surprisingly, the spectrum can be understood and classified with H2+{\mathrm{H}}_{2}^{+}H2+​ quantum numbers by treating the interelectronic axis of ${\mathrm{Ps}}^{\mathrm{\ensuremath{-}}}$ as an adiabatic parameter. We report and interpret the existence of 1^{1}1S shape resonances, a phenomenon so far unknown in three-body Coulomb systems. The new results on ${\mathrm{Ps}}^{\mathrm{\ensuremath{-}}}$ combined with previous results for ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ suggest the existence of a resonance spectrum and its similarity for all ABA Coulomb systems with charges \ensuremath{\Vert}ZA{\mathit{Z}}_{\mathit{A}}ZA​/ZB{\mathit{Z}}_{\mathit{B}}ZB​\ensuremath{\Vert}=1 and masses mA{\mathit{m}}_{\mathit{A}}mA​/mB{\mathit{m}}_{\mathit{B}}mB​\ensuremath{\ge}1.
Low-energy positron scattering from singlet and triplet metastable He(1s2s1s2s1s2s) is investigated using the RRR-matrix propagation method in hyperspherical coordinates. Elastic and positronium-formation cross sections are reported, and near-threshold resonance structures are analyzed in terms of eigenphase sums and the time-delay matrix. For the triplet target, the calculated cross sections are in agreement with available convergent-close-coupling results and display the expected threshold behavior. Beyond the known SSS-wave features, Feshbach resonance series in higher partial waves extending up to highly excited atomic thresholds are systematically identified. The time-delay matrix further uncovers hidden resonances that produce obvious structures in the positronium-formation cross sections.
The photoionization cross section for the positronium (Ps) negative ion, Ps−, at the lowest n = 2 Feshbach resonance, estimated by neglecting the influences of the weakly bound outer electron, is σF = 1.4 × 10−12 cm2, about 3 × 103 times the existing lower limit calculated by Igarashi and co-workers (New J. Phys. 2, 17 (2000)). Although the estimated cross section is 200 times smaller than the analogous cross section for photoexcitation of the Ps Lyman-α transition, including the effect of the broad line width of the resonance shows it will be feasible to observe this resonance to obtain precision information about the three body Ps− system.
We have calculated SSS-wave resonances in the positron-lithium system using the stabilization method in the framework of hyperspherical coordinates. Resonances below the Li (n=4)(n=4)(n=4) thresholds have been investigated. We have located the previously known SSS-wave resonances by Roy and Ho [J. Phys. B 35, 2149 (2002)] and observed relatively good agreement for the resonance positions. In addition, one Feshbach resonance associated with the Ps (n=2)(n=2)(n=2) threshold is also identified.