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Physical Review C

Microscopic aspects of the pairing rotation and pairing vibration

Yang Yi, Gong-ou Xu

Published Mar 1, 1991• 3 citations
Publisher

Abstract

Microscopic investigation of collective models is illustrated with the study of the multilevel pairing force model. The coherent-state description of pairing excitations through the variation of the pairing field and the classification of generators into collective and noncollective modes are discussed. Numerical calculations are performed for collective pairing rotations and vibrations built on the ground state. The coupling to the noncollective state is studied. Exact results from the Richardson method are given for comparison.

DOI
10.1103/physrevc.43.1225

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Microscopic investigation of collective models is illustrated with the study of the multilevel pairing force model. The coherent-state description of pairing excitations through the variation of the pairing field and the classification of generators into collective and noncollective modes are discussed. Numerical calculations are performed for collective pairing rotations and vibrations built on the ground state. The coupling to the noncollective state is studied. Exact results from the Richardson method are given for comparison.
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Expressions for the ground and excited state energies of a system of nucleons interacting through pairing forces are given as a power series in inverse powers of the number of particles. The expressions are valid for systems with superfluid ground states and either J=0 or L=0 pairing. The first three terms in the expansion are given explicitly, and they exhibit excitations with both vibrational and rotational (in isospin space) character. Analytical and numerical results are given for a model system with a two-level single-particle spectrum.
A numerical procedure is introduced which allows us to extract a collective Hamiltonian, expressed in terms of a collective canonical pair $\stackrel{^}{p}$ and $\stackrel{^}{q}$. The starting point is a microscopic many-body approach, namely the generator coordinate method, and the Weyl formalism permits the description of the collective dynamics in the $p\ensuremath{-}q$ space. As an illustration we compare numerical calculations with exact results, obtained analytically, for the quadratic energy kernel with the Gaussian overlap approximation case and the Goldhaber-Teller dipole model applied to the 4He^{4}\mathrm{He}4He nucleus.NUCLEAR STRUCTURE Numerical derivation of collective Hamiltonians. Generator coordinate method, Weyl procedure. Comparison with analytical results.
In a previous paper the concept of an ideal collective coordinate was introduced as the basis for a phenomenological theory of nuclear collective motion. The application of this idea to the microscopic domain is illustrated by the study of a simple two-level model with monopole-monopole interactions, previously considered by Lipkin and collaborators. The complete scheme of calculation which is presented is seen as an alternative to the boson expansion methods currently in fashion for the study of anharmonic vibrations. The new scheme should, however, be applicable to a more extended range of problems such as the adiabatic limit for vibrations and the general problem of rotation-vibration interactions.
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