Microscopic study on the shape phase transition in the sm isotopes:

Yamada, Kazuya; Takada, Kenjiro; Tsukuma, Hidehiko

doi:10.1016/0375-9474(89)90174-7

Cited by 5 publications

(4 citation statements)

References 10 publications

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“…In three out of four initial applications the agreement with experiment is "promising, " but (to be discussed) there is one acknowledged failure. This has led to a second round of work Yamada, Takada, and Tsukuma, 1989), intended to cure some of the acknowledged deficiencies of the previous eff'orts. Below we give a brief account of these works.…”

Section: E Some Resultsmentioning

confidence: 99%

“…We refer the reader to these papers for details. This formation has been applied to Sm Yamada, Takada, and Tsukuma, 1989). Noncollective modes with J =0,2, 4 were included.…”

Section: E Some Resultsmentioning

confidence: 99%

“…From Takada and Tazaki, 1986. The energy levels found by Yamada, Takada, and Tsukuma (1989) for Sm and ' Sm by a succession of approximations are compared with experiment in Figs. 15 and 16.…”

Section: E Some 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: E Some Resultsmentioning

confidence: 99%

“…We refer the reader to these papers for details. This formation has been applied to Sm Yamada, Takada, and Tsukuma, 1989). Noncollective modes with J =0,2, 4 were included.…”

Section: E Some Resultsmentioning

confidence: 99%

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Boson realizations of Lie algebras with applications to nuclear physics

1991

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“…The need to consider these phonons in calculations for two phonon triplet (L = 0, 2, 4) energies was discussed in [6]. In [7], in addition to the renormalization of the boson Hamilto nian parameters, the parameters of the E2 transition operator were renormalized, resulting in a reasonable description of the properties of collective states in the Sm isotope chain including both transition and deformed nuclei.…”

Section: Introductionmentioning

confidence: 99%