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Physical Review A

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


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.


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