Anharmonicities in vibrational spectra of deformed nuclei discussed in a simple model

Piepenbring, R.; Silvestre‐Brac, B.; Szymański, Z.

doi:10.1016/0375-9474(82)90383-9

Cited by 4 publications

(2 citation statements)

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“…The remaining term is a monopole-monopole interaction that breaks this symmetry in analogy with a quadrupole-quadrupole interaction. A completely different physics for the same mathematics has been achieved by Piepenbring et al (1980Piepenbring et al ( , 1982 by the following mapping of single-particle indices [refer to the definitions associated with Eqs. (4.1) and (4.2)]: splitting, has been discussed within the context of the "mode-mode" coupling theory by Matsuyanagi (1982) as an example of what can be done with the "quantized Bogoliubov transformation. "…”

Section: Schwinger Mapping and Other Resultsmentioning

confidence: 99%

“…VI.D and indeed generalize Matsuyanagi's considerations. More recently (Jammari, Piepenbring, and Silvestre-Brac, 1983), the model of Piepenbring et al (1980Piepenbring et al ( , 1982 described above has been extended to include octupole coupling. This was done by exactly doubling the degeneracy, adding a set of odd-parity levels in a model that is isomorphic to SU(2) X SU(2) X SU(2) X SU(2).…”

Section: Schwinger Mapping and Other Resultsmentioning

confidence: 99%

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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: Schwinger Mapping and Other Resultsmentioning

confidence: 99%

Section: Schwinger Mapping and Other Resultsmentioning

confidence: 99%