Proton-hydrogen reaction in an effectively two-body model
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CLEI Theory
Proton–Hydrogen Reaction in an Effectively Two-Body Model V. V. Pupyshev* Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia Received February 29, 2012
Abstract—A model of total interaction between a proton incident to a hydrogen atom and the proton that is the nucleus of this atom is proposed. This interaction is assumed to be the sum of the short-range nuclear Reid potential and the long-range Thomas–Fermi potential induced by the Coulomb interaction of the electron with the nucleus of the hydrogen atom. The explicit low-energy asymptotic behavior of the cross section for the proton–hydrogen reaction leading to deuteron production is found. It is shown that this cross section increases in inverse proportion to the collision energy for the proton and hydrogen atom in its zero limit. DOI: 10.1134/S1063778813010109
1. INTRODUCTION This article reports on a continuation of the previous investigation performed by the present author and devoted to elastic proton scattering on the hydrogen atom [1]. It is dedicated to the 60th anniversary of the birthday of Professor S.I. Vinitsky. The notation introduced in [1] is retained everywhere below, and use is made of the definitions adopted in well-known monographs quoted in [2–12]. As is well known, the hydrogen atom H is a bound state of two unlikely charged particles: an electron e− and a proton playing the role of the respective nucleus. We denote this proton by p and the proton incident to the hydrogen atom by p. The problem of proton scattering on a hydrogen atom belongs to the class of problems that are the most difficult for qualitative and numerical analyses. Within modern quantum scattering theory for few-body systems [2], investigation of this class of problems has not yet been completed. In particular, the coordinate asymptotic behavior of the wave function for a system of three charged particles is unknown in specific regions of the configuration space that are determined by the direction of the forward scattering of a pair of particles. The explicit asymptotic expressions for the wave function that describes the scattering of a charged particle on the bound state of the remaining two charged particles in the limit of zero collision energy are not known either. The problem of charged-particle scattering on a bound complex formed by three or more charged particles—for example, in a collision of a proton with a heavy atom—have been studied to a still smaller degree. *
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Because of the difficulties listed above, interest in effectively two-body models for a collision between a charged particle and a neutral atom has not faded to date. One such model was proposed in the preceding study performed by the present author [1] and devoted to describing elastic proton scattering on a hydrogen atom. The same model is used in the present study to describe and analyze the situation where the proton– hydrogen (pH) reaction leading to deuteron production is induced by an inelastic proton collision with a hydrogen atom. Sp
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