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Nuclear Physics A

Collective variables for the description of rotational motion in many particle systems

Brian H Buck, Lawrence C. Biedenharn, R. Y. Cusson

Published Apr 1, 1979• 102 citations
Publisher
DOI
10.1016/0375-9474(79)90461-5

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With the aid of the correspondence between commutator and Poisson bracket, a set of canonical variables is derived from the Schwinger boson representation for the quantized rotator. By the use of these variables, Euler's equations of motion are given through Hamilton's equations of motion in the case of the rotator. Further, wobbling motion is described in the classical sense. Finally, for the purpose of applying the ATDHB theory to a microscopic description of collective roation, a basic idea is given.
An elementary theory is developed of a classical treatment with the ‘Collective Motion’ of many-particle systems. The fundamental concept of collective motion can be reduced into a certain transformation property of Hamiltonian. Regarded as the dynamical variables, the continuous parameters of such a transformation describe the collective motion of the system, while the individual motions are partly suppressed by the same numbers of subsidiary conditions, or constraints, logically derived in, as the numbers of transformation parameters. Then the general procedure of formulation is illustrated; as an example, the incompressible motion with three modes can be systematically formulated. As another example, the unified treatment is performed also with the vortex motion. The digression in the approximating procedure is also presumed.