## Sponsor

Part of this work was done while J.C.S. was a guest scientist conducting research through the National Research Council —NASA Research Associateship Program. Part of this work was supported by the Division of Chemical Sciences, Office of Energy Research, U.S. Department of Energy.

## Published In

Physical Review A

## Document Type

Article

## Publication Date

12-1991

## Subjects

Positronium – Formation – Mathematical models, Orthogonalization methods, Coulomb functions, Electrons -- Capture

## Abstract

Cross sections for positronium formation by capture from the negative hydrogen ion are given. Orthogonalization corrections to the Coulomb (first-order) Born approximation (CBA) differential and total cross sections are calculated using approximate H- wave functions of both Löwdin [Phys. Rev. *90*, 123 (1953)] and Chandrasekhar [Astrophys. J. *100*, 176 (1944)]. The present calculation of the CBA cross sections using the post interaction for Löwdin’s wave function (LCBAPS) disagrees with the calculation of Choudhury, Mukherjee, and Sural (CMS) [Phys. Rev. A *33*, 2358 (1986)], whereas our results using the prior interaction agree. Thus, where CMS found an order of magnitude post-prior discrepancy in the differential cross sections except at forward angles, and a markedly different shape to the minima, the present post and prior results differ by 1–10 % at 100 eV, and the minima have the same shape and occur within one degree of each other. Chandrasekhar’s ‘‘open-shell’’ wave function, which is superior to Löwdin’s in bound-state problems since it gives a negative binding energy, gives post and prior cross sections that are almost indistinguishable at this energy and are 1/2 to 2/3 as large as the LCBA. Various methods of orthogonalizing the unbound projectile to the possible bound states are considered. It is found that treating the atomic nuclei as if they were isotopic spin projections [Straton and Girardeau, Phys. Rev. A *40*, 2991 (1989)] of a single type of ‘‘nucleon’’ gives cross sections that are an improvement over the CBA.

## DOI

10.1103/PhysRevA.44.7335

## Persistent Identifier

http://archives.pdx.edu/ds/psu/10999

## Citation Details

Straton, Jack C., and Richard J. Drachman. "Formation of positronium in e++ H-collisions." Physical Review A 44.11 (1991): 7335. DOI: http://dx.doi.org/10.1103/PhysRevA.44.7335

## Description

This is the publisher's final PDF. Article appears in Physical Review A (http://pra.aps.org/) and is copyrighted by APS Journals (http://publish.aps.org/)

At the time of publication Jack Straton was employed at Kansas State University.