Classical mappings of the symplectic model and their application to the theory of large-amplitude collective motion

Journal Article · Tue Feb 01 04:00:00 EST 1994 · Physical Review, C (Nuclear Physics); (United States)

DOI:https://doi.org/10.1103/PhysRevC.49.840· OSTI ID:5226777

Klein, A; Walet, N R ^[1]

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1. Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States)

We study the algebra Sp([ital n],[ital R]) of the symplectic model, in particular for the cases [ital n]=1,2,3, in a new way. Starting from the Poisson-bracket realization we derive a set of partial differential equations for the generators as functions of classical canonical variables. We obtain a solution to these equations that represents the classical limit of a boson mapping of the algebra. We show further that this mapping plays a fundamental role in the collective description of many-fermion systems whose Hamiltonian may be approximated by polynomials in the associated algebra, as is done in the simplest versions of the symplectic model. The relationship to the collective dynamics is formulated as a theorem that associates the mapping with an exact solution of the time-dependent Hartree approximation. This solution determines a decoupled classical symplectic manifold, thus satisfying the criteria that define an exactly solvable model in the theory of large amplitude collective motion. The models thus obtained also provide a test of methods for constructing an approximately decoupled manifold in fully realistic cases. We show that an algorithm developed in one of our earlier works reproduces the main results of the theorem.

• OSTI ID: 5226777
• Journal Information: Physical Review, C (Nuclear Physics); (United States), Journal Name: Physical Review, C (Nuclear Physics); (United States) Vol. 49:2; ISSN 0556-2813; ISSN PRVCAN
• Country of Publication: United States
• Language: English

Related Subjects

663120* -- Nuclear Structure Models & Methods-- (1992-)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ALGORITHMS
CALCULATION METHODS
COLLECTIVE EXCITATIONS
DIFFERENTIAL EQUATIONS
ENERGY-LEVEL TRANSITIONS
EQUATIONS
EXCITATION
FUNCTIONS
GROUP THEORY
HAMILTONIAN FUNCTION
HARTREE-FOCK METHOD
INTERACTING BOSON MODEL
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
MATHEMATICS
NUCLEAR MODELS
PARTIAL DIFFERENTIAL EQUATIONS
SHELL MODELS
TIME DEPENDENCE