Application of the dyson boson mapping to the analysis of the phase transition at N = 88–90

Tsukuma, Hidehiko; Thorn, H.; Takada, Kenjiro

doi:10.1016/0375-9474(87)90345-9

Cited by 23 publications

(7 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The more usual situation is the one in which the problem cannot be solved without some truncation of the Hilbert space. The cleanest examples of this occur in the recent works of Takada and his associates (Takada, 1985;Takada and Tazaki, 1986;Takada and YaInada, 1987;Tsukuma, Thorn, and Takada, 1987). Here one of the above methods (Takada, 1986) has been applied successfully, in that it has been established that the bases used in the above calculations, which are severely limited in size, are entirely nonspurious.…”

Section: E Some Resultsmentioning

confidence: 99%

“…The one acknowledged failure (Tsukuma, Thorn, and Takada, 1987) is an attempt to describe the famous phase transition in the Sm isotopes, taking into account the coupling between the most collective 2+ Tamm-Dancoff boson and a set of noncollective bosons, in which the included basis states contain at most one of these nonco1lective excitations. Without the latter, theory and experiment are widely divergent.…”

Section: E Some Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Boson realizations of Lie algebras with applications to nuclear physics

1991

View full text Add to dashboard Cite

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.

show abstract

Section: E Some Resultsmentioning

confidence: 99%

Section: E Some Resultsmentioning

confidence: 99%

Boson realizations of Lie algebras with applications to nuclear physics

1991

View full text Add to dashboard Cite

show abstract

“…The latter method has also given reason for the use of the ideal boson state vectors, which do not consider the effects of the Pauli exclusion principle at all [6,12]. These boson expansion methods have contributed to the elucidation of the large-amplitude collective motions such as the shape transition of nuclei in the transitional region [8,15,16]. In addition, there is another attempt to derive NOLCEXP from dynamical nuclear field theory [17].…”

Section: Introductionmentioning

confidence: 99%

“…NOLCEXP partially adopted this approximation [12], and DBET entirely [14]. The Tamm-Dancoff approximation [15] or similar approximations [8,16] determine the excitation modes of the Tamm-Dancoff type phonons. They are small-amplitude-oscillation approximations, and therefore only the collective excitation modes selected by these methods are not sufficient for reproducing the shape transition of the nucleus in the transitional region.…”

Section: Introductionmentioning

confidence: 99%

Norm operator method for boson expansions

Taniguchi¹

2022

Preprint

View full text Add to dashboard Cite

We propose a new boson expansion theory that reveals and solves the problems of the conventional boson expansion methods that have tried to elucidate nuclear collective motion. The limitation of the number of phonon excitations in addition to phonon excitation modes results in proper boson expansions and allows the use of ideal boson state vectors. The norm operator plays a crucial role and makes it possible to perform boson expansions without the closedalgebra approximation. The treatment of the norm operator determines whether the type of mapping is Hermitian or not, while the boson expansions become infinite expansions regardless of the types of mapping. The closed-algebra approximation makes small parameter expansions impossible and the ideal boson state vectors, having no effect of the Pauli exclusion principle, contain spurious components.

show abstract

“…If this formula works well, we no longer need to solve the right and left eigenvalue problems so that the efforts of the numerical calculation is greatly reduced and besides we can take the advantage of the finiteness of expansion. With the help of the Hermitian treatment, D-type BET has been applied to many nuclei in the various range of the nuclear chart [23]- [30].…”

Section: §1 Introductionmentioning

confidence: 99%

On the Approximation in the Hermitian Treatment of Dyson Boson Expansion Theory

Kajiyama

Taniguchi

Miyanishi

1999

Progress of Theoretical Physics

View full text Add to dashboard Cite

We discuss the Hermitian treatment of the Dyson-type boson expansion theory. We show that the basic assumption of the conventional treatment does not hold in general and that the method is only approximately valid. The exception is the case in which the multi-phonon states are mutually orthogonal, which is not expected in realistic nuclear systems. We also show that the approximation is of the same order as that of the truncation of the expansion usually done in the Hermitian-type boson expansion theory. §1. IntroductionThe boson expansion theory (BET) 1) -3) has been widely used as a many-body technique to analyze anharmonic effects in nuclear collective motion beyond the random phase approximation. This theory is a systematic method to transform the eigenvalue problem in fermion space into that in boson space. With this method, an arbitrary fermion pair operator is expressed as an expansion of the boson operators, which enables us to calculate the wave functions more easily.However, the BET is not a complete theory and contains some problems to be solved. First, one must apply the theory to the limited subspace of the original fermion space, which we call the truncated fermion subspace. Otherwise, the boson space on which the transcribed boson operators act contains an unphysical part having no one-to-one correspondence to the original fermion space. One cannot give the exact prescription how the limited fermion subspace should be selected in general. Second, for reasons closely related to the above problem, one must adopt the so-called closed algebra approximation. 1) The validity of this approximation is not clear, although it is indispensable for the BET. Third, the convergence of the expansion for the non-collective mode is not assured. * )Concerning the last point, the Dyson-type (D-type) BET 6) -11) has a distinctive feature compared with the others such as the Holstein-Primakoff-type (HP-type) BET. 12) -17) In the D-type BET, the fermion space is mapped to the physical boson subspace by the special biunitary transformation so that a transformed pair operator * ) To solve these problems we proposed an alternative mapping theory in which only the collective modes were mapped into the boson modes. However, the purpose of the present paper is not to discuss this issue. The interested reader may refer to Refs. 4) and 5).

show abstract

Application of the dyson boson mapping to the analysis of the phase transition at N = 88–90

Cited by 23 publications

References 10 publications

Boson realizations of Lie algebras with applications to nuclear physics

Boson realizations of Lie algebras with applications to nuclear physics

Norm operator method for boson expansions

On the Approximation in the Hermitian Treatment of Dyson Boson Expansion Theory

Contact Info

Product

Resources

About