Collective subspaces for large amplitude motion and the generator coordinate method

Journal Article · Mon Oct 01 04:00:00 EDT 1979 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.20.1546· OSTI ID:6032805

Reinhard, P; Goeke, K

The collective path vertical-barphi (q) > to be used in a microscopic description of large amplitude collective motion is determined by means of the generator coordinate method. By varying the total energy with respect to vertical-barphi (q) > and performing an adiabatic expansion a hierarchy of equations is obtained which determines uniquely a hierarchy of collective paths with increasing complexity. To zeroth order the vertical-barphi (q) > are Slater determinants, to first order they include 2p-2h correlations. In both cases simple noniterative prescriptions for an explicit construction of the path are derived. For a correlated path their solutions agree at the Hartree-Fock minimum with random phase approximation eigenmodes. The resulting equations for the path are compared with the outcome of related theories, particularly of semiclassical nature. It is remarkable that both sorts of approaches, on one hand the generator coordinate method with correlated states and on the other the quantized adiabatic time dependent Hartree-Fock theory, are virtually identical in the results, although they are of different conceptual origin and use different techniques. It is shown that the use of a correlated path does not cause numerical complications.

• Research Organization: Institut fuer Kernphysik, Kernforschungsanlage Juelich, D-5170 Juelich, West Germany
• OSTI ID: 6032805
• Journal Information: Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 20:4; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653007* -- Nuclear Theory-- Nuclear Models-- (-1987)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
COLLECTIVE MODEL
FIELD THEORIES
GENERATOR-COORDINATE METHOD
HAMILTONIANS
HARTREE-FOCK METHOD
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
NUCLEAR MODELS
PERTURBATION THEORY
QUANTUM OPERATORS
RANDOM PHASE APPROXIMATION
SHELL MODELS
TIME DEPENDENCE