TY - JOUR

T1 - Mathematical analysis of a simple model related to the stripping reaction

AU - Lieb, Elliott

AU - Koppe, Heinz

PY - 1959/12/1

Y1 - 1959/12/1

N2 - A scattering process in which an incoming bound particle can split up into its component parts when its total energy is above a threshold is of considerable interest physically (deuteron stripping, etc.) and mathematically (analytic properties of the S-matrix, etc.). For such complicated problems it is obviously convenient to have a simple, analytically soluble model for reference, but although many models have been suggested in the past none have proved analytically tractable. In this paper we propose and completely solve a one-dimensional model which, although it is not very physical, has all the desired characteristics. The problem is not mathematically trivial, however, and leads to a Wiener-Hopf integral equation.

AB - A scattering process in which an incoming bound particle can split up into its component parts when its total energy is above a threshold is of considerable interest physically (deuteron stripping, etc.) and mathematically (analytic properties of the S-matrix, etc.). For such complicated problems it is obviously convenient to have a simple, analytically soluble model for reference, but although many models have been suggested in the past none have proved analytically tractable. In this paper we propose and completely solve a one-dimensional model which, although it is not very physical, has all the desired characteristics. The problem is not mathematically trivial, however, and leads to a Wiener-Hopf integral equation.

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U2 - 10.1103/PhysRev.116.367

DO - 10.1103/PhysRev.116.367

M3 - Article

AN - SCOPUS:36149014380

SN - 0031-899X

VL - 116

SP - 367

EP - 371

JO - Physical Review

JF - Physical Review

IS - 2

ER -