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Physical Review C

Collective Hamiltonian in linked diagram expansions

Gong-ou Xu, Yang Yi

Published Mar 1, 1990• 5 citations
Publisher

Abstract

A method for obtaining collective Hamiltonians in linked diagram expansions is given. Effects of the Pauli principle have been properly taken into account. An illustration with a two-level pairing force model is given. The derivation of the interacting boson model and truncated quadrupole phonon model Hamiltonians as well as a comparison with the random-phase approximation are discussed.

DOI
10.1103/physrevc.41.1257

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A method for obtaining collective Hamiltonians in linked diagram expansions is given. Effects of the Pauli principle have been properly taken into account. An illustration with a two-level pairing force model is given. The derivation of the interacting boson model and truncated quadrupole phonon model Hamiltonians as well as a comparison with the random-phase approximation are discussed.
The boson expansion method was developed with the purpose of continuously following even nuclear systems near their ground states, from the region of slightly anharmonic vibrations through the transitional region formed by a nonsharp phase transition to a region of permanent distortion characterized by the occurrence of rotational spectra. However, as the boson quantum was defined in the extreme vibrational limit, it was not possible to obtain quantitatively correct spectra in the transitional or deformed region. Believing that the major cause for the lack of success was the disregard of the self- consistent change of the basic degree of freedom, a simple variational method to be used with the boson expansion technique is presented. Its ability to cover the vibration-to-rotation transition is demonstrated by comparison with an exact solution for a four-level model with pairing force. Further the coverage of a quadrupole phase transition is shown for a system interacting via pairing-Plus- quadrupole forces. A successful calculation of static quadrupole moments of Cd and Te isotopes is presented. Finally the approach in general situations with more complicated forces is discussed. (auth)
We discuss a variational approach to collective excitations in a boson formalism based on quasiparticles. Bosons are defined in correspondence with pairs of quasiparticles and boson images of fermion operators are constructed by means of a mapping procedure of Marumori-type. Phonons of the type used within the random phase approximation (RPA) are introduced as Bogoliubov transformations of these bosons. The variables entering into the definition of these phonons as well as of the quasiparticle operators are fixed simultaneously by minimizing the expectation value of the boson Hamiltonian in the vacuum of the phonons. The approach is tested within an exactly solvable two-level model which is characterized by a pairing Hamiltonian. A quite good agreement is found for the energies of the ground state and of the first 0+{0}^{+}0+ excited state. The comparison with the Bardeen-Cooper-Schrieffer method and the quasiparticle RPA as well as with some recent self-consistent RPA-type approaches is discussed.
The usefulness of the quon expansion to treat Pauli principle violations and many-body correlations in many-fermion systems is investigated within two models, namely, the Lipkin and the two level pairing models. The q deformation parameter of the quon algebra is fixed through a dynamical criterion. The spectra obtained are compared with the random-phase approximation (RPA), usual boson expansion, and exact results. The quonic expansion is shown to take into account correlations which are not included either in the second order boson expansion or in the RPA approach.
A new boson expansion theory based on the random phase approximation is presented. The boson expansions are derived here directly in the random phase approximation representation with the help of a technique that combines the use of the Usui operator with that of a new bosonization procedure, called the term-by-term bosonization method. The present boson expansion theory is constructed by retaining a single collective quadrupole random phase approximation component, a truncation that allows for a perturbative treatment of the whole problem. Both Hermitian, as well as non-Hermitian boson expansions, valid for even nuclei, are obtained.