Solution of the scattering T matrix equation in discrete complex momentum space

Journal Article · Thu Mar 01 04:00:00 EST 1984 · Phys. Rev. C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.29.747· OSTI ID:6895920

Rawitscher, G H; Delic, G

The scattering solution to the Lippmann-Schwinger equation is expanded into a set of spherical Bessel functions of complex wave numbers, K/sub j/, with j = 1,2 , . . . , M. The value of each K/sub j/ is determined from the condition that the spherical Bessel function smoothly matches onto an asymptotically outgoing spherical Hankel (or Coulomb) function of the correct physical wave number at a matching point R. The spherical Bessel functions thus determined are Sturmian functions, and they form a complete set in the interval 0 to R. The coefficients of the expansion of the scattering function are determined by matrix inversion of a linear set of algebraic equations, which are equivalent to the solution of the T-matrix equation in complex momentum space. In view of the presence of a matching radius, no singularities are encountered for the Green's functions, and the inclusion of Coulomb potentials offers no computational difficulties. Three numerical examples are performed in order to illustrate the convergence of the elastic scattering matrix S with M. One of these consists of a set of coupled equations which describe the breakup of a deuteron as it scatters from the nucleus on /sup 58/Ni. A value of M of 15 or less is found sufficient to reproduce the exact S matrix element to an accuracy of four figures after the decimal point.

• Research Organization: Department of Physics, University of Connecticut, Storrs, Connecticut 06268
• OSTI ID: 6895920
• Journal Information: Phys. Rev. C; (United States), Journal Name: Phys. Rev. C; (United States) Vol. 29:3; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

645500 -- High Energy Physics-- Scattering Theory-- (-1987)
653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BESSEL FUNCTIONS
COULOMB FIELD
ELECTRIC FIELDS
EQUATIONS
FUNCTIONS
GREEN FUNCTION
INTEGRAL EQUATIONS
LIPPMANN-SCHWINGER EQUATION
MATRICES
MATRIX ELEMENTS
S MATRIX
SCATTERING