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Title: Relationship between Feshbach`s and Green`s function theories of the nucleon-nucleus mean field

Abstract

We clarify the relationship and difference between theories of the optical-model potential which had previously been developed in the framework of Feshbach`s projection operator approach to nuclear reactions and of Green`s function theory, respectively. For definiteness, we consider the nucleon-nucleus system but all results can readily be adapted to the atomic case. The effects of antisymmetrization are properly taken into account. It is shown that one can develop along closely parallel lines the theories of {open_quotes}hole{close_quotes} and {open_quotes}particle{close_quotes} mean fields. The {open_quotes}hole{close_quotes} one-body Hamiltonians describe the single-particle properties of the system formed when one nucleon is taken away from the target ground state, for instance in knockout of pickup processes. The particle one-body Hamiltonians are associated with the system formed when one nucleon is elastically scattered from the ground state, or is added to it by means of stripping reactions. An infinite number of particle, as well as of hole, Hamiltonians are constructed which all yield exactly the same single-particle wave functions. Many {open_quotes}equivalent{close_quotes} one-body Hamiltonians can coexist because these operators have a complicated structure: they are nonlocal, complex, and energy-dependent. They do not have the same analytic properties in the complex energy plane. Their real and imaginary parts fulfillmore » dispersion relations which may be different. It is shown that hole and particle Hamiltonians can also be constructed by decomposing any vector of the Hilbert space into two parts which are not orthogonal to one another, in contrast to Feshbach`s original theory; one interest of this procedure is that the construction and properties of the corresponding hole Hamiltonian can be justified in a mathematically rigorous way. We exhibit the relationship between the hole and particle Hamiltonians and the {open_quotes}mass operator.{close_quotes}« less

Authors:
 [1];  [2]
  1. Istituto Nazionale di Fisica Nucleare, Pavia (Italy)
  2. Universite de Liege, Sart Tilman (Belgium)
Publication Date:
OSTI Identifier:
160039
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 239; Journal Issue: 1; Other Information: PBD: Apr 1995
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; MEAN-FIELD THEORY; GREEN FUNCTION; NUCLEON REACTIONS; NUCLEON-NUCLEON INTERACTIONS; OPTICAL MODELS; HAMILTONIANS; HILBERT SPACE

Citation Formats

Capuzzi, F, and Mahaux, C. Relationship between Feshbach`s and Green`s function theories of the nucleon-nucleus mean field. United States: N. p., 1995. Web. doi:10.1006/aphy.1995.1031.
Capuzzi, F, & Mahaux, C. Relationship between Feshbach`s and Green`s function theories of the nucleon-nucleus mean field. United States. doi:10.1006/aphy.1995.1031.
Capuzzi, F, and Mahaux, C. Sat . "Relationship between Feshbach`s and Green`s function theories of the nucleon-nucleus mean field". United States. doi:10.1006/aphy.1995.1031.
@article{osti_160039,
title = {Relationship between Feshbach`s and Green`s function theories of the nucleon-nucleus mean field},
author = {Capuzzi, F and Mahaux, C},
abstractNote = {We clarify the relationship and difference between theories of the optical-model potential which had previously been developed in the framework of Feshbach`s projection operator approach to nuclear reactions and of Green`s function theory, respectively. For definiteness, we consider the nucleon-nucleus system but all results can readily be adapted to the atomic case. The effects of antisymmetrization are properly taken into account. It is shown that one can develop along closely parallel lines the theories of {open_quotes}hole{close_quotes} and {open_quotes}particle{close_quotes} mean fields. The {open_quotes}hole{close_quotes} one-body Hamiltonians describe the single-particle properties of the system formed when one nucleon is taken away from the target ground state, for instance in knockout of pickup processes. The particle one-body Hamiltonians are associated with the system formed when one nucleon is elastically scattered from the ground state, or is added to it by means of stripping reactions. An infinite number of particle, as well as of hole, Hamiltonians are constructed which all yield exactly the same single-particle wave functions. Many {open_quotes}equivalent{close_quotes} one-body Hamiltonians can coexist because these operators have a complicated structure: they are nonlocal, complex, and energy-dependent. They do not have the same analytic properties in the complex energy plane. Their real and imaginary parts fulfill dispersion relations which may be different. It is shown that hole and particle Hamiltonians can also be constructed by decomposing any vector of the Hilbert space into two parts which are not orthogonal to one another, in contrast to Feshbach`s original theory; one interest of this procedure is that the construction and properties of the corresponding hole Hamiltonian can be justified in a mathematically rigorous way. We exhibit the relationship between the hole and particle Hamiltonians and the {open_quotes}mass operator.{close_quotes}},
doi = {10.1006/aphy.1995.1031},
journal = {Annals of Physics (New York)},
number = 1,
volume = 239,
place = {United States},
year = {1995},
month = {4}
}