Equivalence of post and prior sum rules for inclusive breakup reactions

Journal Article · Thu Aug 01 00:00:00 EDT 1985 · Phys. Rev. C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.32.431· OSTI ID:5598314

Ichimura, M; Austern, N; Vincent, C M

A critical examination of sum rules derived previously by Austern and Vincent (post form) and by Udagawa and Tamura (prior form) demonstrates that agreement between the two approaches is obtained if certain approximations implicit in the Udagawa-Tamura prior-form derivation are avoided. We examine the relation of the two approaches to singularities of the post-form distorted wave Born approximation matrix element and to the procedures for reduction of a many-body theory by use of effective operators in a model space. The two-step heuristic model is seen to be invalid for prior-form inelastic breakup; it is necessary to take account of nuclear excitations during projectile breakup. Careful treatment of the non-Hermiticity of kinetic energy operators with respect to continuum wave functions is required.

• Research Organization: Institute of Physics, University of Tokyo, College of General Education, Komaba 3-8-1, Tokyo 153, Japan
• OSTI ID: 5598314
• Journal Information: Phys. Rev. C; (United States), Journal Name: Phys. Rev. C; (United States) Vol. 32:2; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BORN APPROXIMATION
BREAKUP REACTIONS
DWBA
ENERGY
EQUATIONS
FUNCTIONS
GREEN FUNCTION
HAMILTONIANS
INCLUSIVE INTERACTIONS
INTERACTIONS
KINETIC ENERGY
MATHEMATICAL OPERATORS
MATRIX ELEMENTS
NUCLEAR REACTIONS
OPTICAL MODELS
PARTICLE INTERACTIONS
QUANTUM OPERATORS
SUM RULES
WAVE FUNCTIONS