Time-delay matrix analysis of resonances: application to the positronium negative ion

Abstract

A procedure to analyse resonances in scattering and photoionization calculations is discussed. It is theoretically connected to a general relation between the trace of the time-delay matrix and the energy derivative of the eigenphase sum. This procedure is especially useful in analysing resonances with strong background contributions, such as shape resonances lying just above the threshold of a new channel with an overcritical dipole field. In this case the background eigenphase sum diverges towards the threshold, and it can easily change the time delay due to an S-matrix pole into a negative time delay, or time advance. As an application, we analyse results of hyperspherical close-coupling calculations of S-, P-, D-, F-, G-and H-wave resonances in the positronium negative ion Ps − near the Ps(n = 2, 3) thresholds. We find examples of a strong background leading to an overall time advance and the dipole oscillation in the cross section above and near a threshold.

Excitons and the Positronium Negative Ion: Comparison of Spectroscopic Properties

“…The photoionization or photodetachment process is a subject of special interest in several areas of physics, such as astrophysics, plasma physics, and atomic physics due to its extreme importance in the atomic structures and correlation effects between atomic electrons [16,17,82,84,85]. The photoionization processes are also of great interest due to their applications in plasma diagnostics.…”

“…For detailed calculations and applications of the photodetachment of the positronium negative ion, interested readers are referred to the articles of Bhatia and Drachman [19], Frolov [17], Igarashi [82,84,85], Michishio et al [8], Nagashima [6], and Ward et al [20]. Here, we outlined the computational details in brief as mentioned in our earlier work [87] and in the works of Bhatia and Drachman [19].…”

Time delay in a multichannel formalism

“…The method of Smith has been applied in atomic physics as well. Authors from this field have considered generalizations involving background contributions and overlapping resonances [8,9]. In some cases, old results from nuclear physics have been rediscovered [10].…”

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

“…After this pioneering work [17] on the resonance states in Ps − , a great number of theoretical calculations on resonance states in Ps − below the N = 2 Ps threshold have been reported in the literature, including the 1 P • Feshbach [7,[18][19][20][21][22] and shape [7,12,22,23] resonance states. Until now, many of these studies used different sophisticated methods or techniques or approaches, such as the technique of direct solution of the three-body scattering problem [24], the stabilization method (SM) [11,21,25,26], the complex-coordinate rotation method (CRM) [11][12][13]25,26], the technique of adiabatic molecular approximation [6], the Kohn variational method [27], the adiabatic treatment in hyperspherical coordinates (ATHC) [18,28,29], and the hyperspherical close-coupling approach (HCCA) [22,[30][31][32].…”