Generating Phase Shifts from Pseudostate Energy Shifts

Abstract

A simple way to generate low energy phase shifts for elastic scattering using bound-state calculations is postulated, validated, and applied to the problem of e -Mg scattering. The essence of the method is to use the energy shift between a small reference calculation and the largest possible calculation of the lowest energy pseudostate to tune a semiempirical optical potential. The ' 1 partial wave for e -Mg scattering is predicted to have a shape resonance at an energy of about 0.13 eV. The value of Z eff at the center of the resonance is about 1500. DOI: 10.1103/PhysRevLett.98.173001 PACS numbers: 31.25.Jf, 03.65.Nk, 34.80.Bm, 34.85.+x One of the most technically demanding problems in quantum physics is the scattering problem, i.e., the prediction of the reaction probabilities when two objects collide [1]. The underlying difficulty lies in the unbounded nature of the wave function. This leads to a variety of computational and analytic complications that are simply absent in bound-state calculations, e.g., the Schwartz singularities that occur in the Kohn variational method for scattering [2,3].One approach to solve scattering problems is to use bound-state methods. There are many examples of such approaches, one of the most popular being the R-matrix methods that use the solutions of the Schrödinger equation in a finite sized cavity to determine the behavior of the wave function in the interaction region [1]. The total wave function is then constructed by splicing the inner wave function onto the asymptotic wave function.However, despite the considerable activity in this area, there are a number of problems that are beyond resolution. The e -atom problem is a notoriously hard numerical problem since the atomic electrons tend to localize around the positron, thus giving a very slowly convergent partial wave expansion of the wave function inside the interaction region (this should not be confused with the partial wave expansion of the asymptotic wave function) [4 -7]. For example, the dimensionality of the equations to be solved to achieve a given accuracy are about 5 times larger for e -H scattering than for e ÿ -H scattering. At present, there are a number of positron collision problems that are simply inaccessible with existing approaches [7].This Letter had its origin in a particular scattering problem, namely, the determination of the near threshold phase shifts for positron scattering from magnesium. The dimensions of the secular equations for bound-state calculations on group II atoms are very large, for example, a configuration interaction (CI) calculation of the e Ca 2 P o state had equations of dimension 874 448 [8]. The idea behind the current method lies closest to the box R-matrix method [9] which is exploited in quantum Monte Carlo (QMC) calculations of scattering [10]. In the QMC calculations, one extracts the phase shift by comparing the zero point energy of a finite size cavity to the energy of the system wave function in the same cavity. In the present method, the phase shift is extracted f...

Recent progress in the description of positron scattering from atoms using the convergent close-coupling theory

“…Given that the validity of the two-centre CCC approach should be energy independent we are unable to explain the discrepancy. [156], the one-centre due to Savage et al [155], and the variational ones due to Mitroy and Bromley [257].…”

“…21. e + -Mg elastic-scattering cross section.The first vertical line is at the Ps-formation threshold, the second one is at the Mg-ionization threshold. The (two-centre) CCC calculations are due to Utamuratov et al [156], the one-centre due to Savage et al [155], and the variational ones due to Mitroy and Bromley [257].…”

Structure and resonances of the e+–He(1s2s3Se) system

“…Feshbach resonances associated with excited states of other atoms have also been identified [16][17][18]. Recently, a lowenergy P-wave shape resonance in positron-Mg scattering has been predicted by calculations [22,23]. Therefore, the analysis of atomic resonances phenomena involving a positron is very interesting.…”

Positron attachment to the He(ns21Se) states

“…However, there has as yet been no unequivocal identification of a resonance in the experimental positron scattering spectrum of any atom [5,9]. The identified resonances are either too narrow, in the case of hydrogen or the alkalis [43,44,46,48], or located in the energy region very close to the threshold [28,42,49,51]. The present resonances are broad (when compared with others) and occur in a system that is amenable to experimentation.…”