P-wave shape resonances in positronium ions

Scattering and Its Applications to Various Atomic Processes: Elastic Scattering, Resonances, Photoabsorption, Rydberg States, and Opacity of the Atmosphere of the Sun and Stellar Objects

A scattering process can be a natural process or a process carried out in a laboratory. The scattering of particles from targets has resulted in important discoveries in physics. We discuss various scattering theories of electrons and positrons and their applications to elastic scattering, resonances, photoabsorption, excitation, and solar and stellar atmospheres. Among the most commonly employed approaches are the Kohn variational principle, close-coupling approximation, method of polarized orbitals, R-matrix formulation, and hybrid theory. In every formulation, an attempt is made to include exchange, long-range and short-range correlations, and to make the approach variationally correct. The present formulation, namely, hybrid theory, which is discussed in greater detail compared to other approximations, includes exchange, long-range correlations, and short-range correlations at the same time, and is variationally correct. It was applied to calculate the phase shifts for elastic scattering, the resonance parameters of two-electron systems, photoabsorption in two-electron systems, excitation of atomic hydrogen by an electron and positron impact, and to study the opacity of the Sun’s atmosphere. Calculations of polarizabilities, Rydberg states, and bound states of atoms are also discussed.

Resonances in Systems Involving Positrons

When an incident particle on a target gets attached to the target, the cross-section at that energy could be much larger compared to those at other energies. This is a short-lived state and decays by emitting an electron. Such states can also be formed by the absorption of a photon. Such states are below the higher thresholds and are called autoionization states, doubly excited states, or Feshbach resonances. There is also a possibility of such states to form above the thresholds. Then they are called shape resonances. Resonances are important in the diagnostic of solar and astrophysical plasmas. Some methods of calculating the resonance parameters are described and resonance parameters occurring in various systems are given.

Calculations of Resonance Parameters for the Doubly Excited 1P° States in Ps− Using Exponentially Correlated Wave Functions

Recent observations on resonance states of the positronium negative ion (Ps−) in the laboratory created huge interest in terms of the calculation of the resonance parameters of the simple three-lepton system. We calculate the resonance parameters for the doubly excited 1P° states in Ps− using correlated exponential wave functions based on the complex-coordinate rotation method. The resonance energies and widths for the 1P° Feshbach resonance states in Ps− below the N = 2, 3, 4, 5 Ps thresholds are reported. The 1P° shape resonance above the N = 2, 4 Ps thresholds are also reported. Our predications are in agreement with the available results. Few Feshbach resonance parameters below the N = 4 and 5 Ps thresholds have been reported in the literature. Our predictions will provide useful information for future resonance experiments in Ps−.

Photodetachment of the Positronium Negative Ion with Excitation in the Positronium Atom

Lyman-α radiation ( 2 P → 1 S ) has been seen from astrophysical sources and the sun. The line shape of this transition has been measured recently in Ps atoms both inside and outside a porous silica target. In the photodetachment of Ps−, the residual Ps atom can be left in the 2P state instead of the 1S state giving rise to positronium Lyman radiation at 2432 A0. Photodetachment cross sections of Ps− have been calculated when the Ps atom is left in nP states, n being 2, 3, 4, 5, 6 and 7, using the asymptotic form of the bound-state wave function and a plane wave for the final state wave function, following the approach of Ohmura and Ohmura [Phys. Rev. 1960, 118, 154] in the photodetachment of H−.

Observation of a shape resonance of the positronium negative ion

When an electron binds to its anti-matter counterpart, the positron, it forms the exotic atom positronium (Ps). Ps can further bind to another electron to form the positronium negative ion, Ps⁻ (e⁻e⁺e⁻). Since its constituents are solely point-like particles with the same mass, this system provides an excellent testing ground for the three-body problem in quantum mechanics. While theoretical works on its energy level and dynamics have been performed extensively, experimental investigations of its characteristics have been hampered by the weak ion yield and short annihilation lifetime. Here we report on the laser spectroscopy study of Ps⁻, using a source of efficiently produced ions, generated from the bombardment of slow positrons onto a Na-coated W surface. A strong shape resonance of ¹P^o symmetry has been observed near the Ps (n=2) formation threshold. The resonance energy and width measured are in good agreement with the result of three-body calculations.

The Positronium negative ion is formed by two electrons bound to a positron, and experimental investigations of its states and energy levels are difficult due to its short lifetime. Here, the authors report on laser spectroscopy of positronium using a source of efficiently produced ions.