Justification of local potentials in coupled channel problems

Journal Article · Sat Mar 01 04:00:00 EST 1980 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.21.919· OSTI ID:5679108

Fliessbach, T

It is often stated that for reactions between two nuclei, the exchange terms lead to serious nonlocalities in the potential. The resonating group function u/sub E/ indeed obeys a strongly nonlocal equation. However, u/sub E/ is not a wave function and it is impossible to approximate its equation by a Schroedinger equation with a local potential. As stated by several authors, one has to consider ..cap omega../sub E/= (1-K)/sup 1/2/ u/sub E/ instead of u/sub E/ where 1-K is the norm kernel. In this paper, these statements are verified in a simple model in which the Hamiltonian and norm kernels are given analytically for both u and ..cap omega... We then investigate the corresponding equations for several (in general, coupled) channels and the possibility of using local potentials in these equations. Alpha decay into more than one channel is discussed as an example.

• Research Organization: Physik-Department der Technischen Universitaet Muenchen, 8046 Garching, Germany
• OSTI ID: 5679108
• Journal Information: Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 21:3; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ALPHA DECAY
BOUNDARY CONDITIONS
COUPLED CHANNEL THEORY
DECAY
DIFFERENTIAL EQUATIONS
ENERGY LEVELS
EQUATIONS
EXCHANGE INTERACTIONS
FRAGMENTATION
FUNCTIONS
HAMILTONIANS
HILL-WHEELER THEORY
INTERACTIONS
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
NONLOCAL POTENTIAL
POTENTIALS
QUANTUM OPERATORS
SCHROEDINGER EQUATION
WAVE EQUATIONS
WAVE FUNCTIONS