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Journal of Physics A Mathematical and General

Collective rotations of asymmetrically deformed many-body systems

Luc Lathouwers, E Duemens

Published Sep 1, 1982• 8 citations
Publisher

Abstract

The angular momentum projection technique is worked out for systems with an intrinsic asymmetric deformation. These include asymmetric top molecules and triaxial nuclei. A parameterisation of the rotation group is introduced which allows an approximate but analytical evaluation of angular momentum projected matrix elements. Via symmetric orthonormalisation a quantal definition of the moments of inertia is obtained.

DOI
10.1088/0305-4470/15/9/028

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Journal of Mathematical Physics•Nov 1, 1981•2 citations
The angular momentum projection technique is worked out for systems with an intrinsic asymmetric deformation. These include asymmetric top molecules and triaxial nuclei. A parameterisation of the rotation group is introduced which allows an approximate but analytical evaluation of angular momentum projected matrix elements. Via symmetric orthonormalisation a quantal definition of the moments of inertia is obtained.
The authors provide a state-of-the-art overview of projection techniques employed in beyond-mean-field many-body methods. They focus on two symmetries that are of critical importance for the description of nuclear spectroscopy, particle number, and angular momentum. The presentation covers formal aspects of symmetry restoration (group theory) and practical aspects related to numerical implementation. A number of illustrative examples are given, including cranked states in odd-AAA nuclei.
By means of geometric quantization, we discuss the quantum-deformed-symmetric-top model. We show that the quantum-deformed symmetric top and the quantum-standard symmetric top obey the same Heisenberg equations of motion. The quantum-deformed-symmetric-top model possesses quantum group symmetry; thus the quantum group can be dynamical symmetries of the symmetric-top system. The energy levels and wave functions of stationary states of the quantum-deformed-symmetric-top model are obtained exactly by a quantum-group-theoretic approach. Using the exactly solved model, we investigate the rotational spectra of symmetric-top molecules and diatomic molecules when the moment of inertia about the line joining the nuclei is not exactly zero.
Formulas are obtained which give the matrix representation, relative to a product basis, of the projection operator for the total angular momentum of a system. If the individual angular momenta are not too large, the matrix elements depend upon a small number of parameters, independent of the number of angular momenta coupled. Recurrence relations between elements and symmetry properties of elements are derived. These results enable one to perform the vector coupling of a large number of angular momenta in a relatively simple fashion. The connection between the matrix elements and vector coupling coefficients is discussed. Several important special cases are treated in detail.