Formally exact quantum variational principles for collective motion based on the invariance principle of the Schrödinger equation

Klein, Abraham; Marumori, Toshio; Une, Tsutomu

doi:10.1016/0370-2693(82)90424-5

Cited by 9 publications

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“…The considerations of this section apply on1y to the vibrational regime. The extension to large-amplitude collective motion can be carried out (Klein, Marumori, and Une, (1984), but will not be recorded here because the alternative approach described in the next section has been developed much more thoroughly. D. Reconstruction of the collective Hamiltonian from the intrinsic state The aim here is to formalize the procedures of the previous section, as well as to consider one generalization, necessary in the long run.…”

Section: We May Thus Writementioning

confidence: 99%

Boson realizations of Lie algebras with applications to nuclear physics

1991

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The concept of boson realization (or mapping) of Lie algebras appeared first in nuclear physics in 1962 as the idea of expanding bilinear forms in fermion creation and annihilation operators in Taylor series of boson operators, with the object of converting the study of nuclear vibrational motion into a problem of coupled oscillators. The physical situations of interest are quite diverse, depending, for instance, on whether excitations for fixed-or variable-particle number are being studied, on how total angular momentum is decomposed into orbital and spin parts, and on whether isotopic spin and other intrinsic degrees of freedorn enter. As a consequence, all of the semisimple algebras other than the exceptional ones have proved to be of interest at one time or another, and all are studied in this review. Though the salient historical facts are presented in the introduction, in the body of the review the progression is (generally) from the simplest algebras to the more complex ones. With a sufficiently broad view of the physics requirements, the mathematical problem is the realization of an arbitrary representation of a Lie algebra in a subspace of a suitably chosen Hilbert space of bosons (Heisenberg-Weyl algebra). Indeed, if one includes the study of odd nuclei, one is forced to consider the mappings to spaces that are direct-product spaces of bosons and (quasi)fermions. Though all the methods that have been used for these problems are reviewed, emphasis is placed on a relatively new algebraic method that has emerged over the past decade. Many of the classic results are rederived, and some new results are obtained for odd systems. The major application of these ideas is to the derivation, starting from the shell model, of the phenomenological models of nuclear collective motion, in particular, the geometric model of Bohr and Mottelson and the more recently developed interacting boson model of Arirna and Iachello. A critical discussion of those applications is interwoven with the theoretical developments on which they are based; many other applications are included, some of practical interest, some simply to illustrate the concepts, and some to suggest new lines of inquiry.

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Section: We May Thus Writementioning

confidence: 99%