A New Formulation of a Many-Level Shell Model: A Method of Constructing Orthonormal Basis States Analytically

Takada, Kenjiro; Sato, Motom; Yasumoto, Shigeru

doi:10.1143/ptp.104.173

Cited by 5 publications

(3 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The formulation and explicit expression of the new type of cfp, which is a quite different concept from usual single-boson (or -fermion) cfps, have been given in our recent paper Ref. 30). We choose this multi-phonon subspace {|nΓ βIK } as the collective fermion subspace (CFS), and we map this subspace to a corresponding collective boson subspace (CBS).…”

Section: Fermion Pair Operators and Corresponding Boson Operatorsmentioning

confidence: 99%

Non-Unitary Boson Mapping and Its Application to Nuclear Collective Motions

Takada

2001

Prog. Theor. Phys. Suppl.

View full text Add to dashboard Cite

First, the general theory of boson mapping for even-number many-fermion systems is surveyed. In order to overcome the confusion concerning the so-called unphysical or spurious states in the boson mapping, the correct concept of the unphysical states is precisely given in a clear-cut way. Next, a method to apply the boson mapping to a truncated many-fermion Hilbert space consisting of collective phonons is proposed, by putting special emphasis on the Dyson-type non-unitary boson mapping. On the basis of this method, it becomes possible for the first time to apply the Dyson-type boson mapping to analyses of collective motions in realistic nuclei. This method is also extended to be applicable to odd-number-fermion systems.As known well, the Dyson-type boson mapping is a non-unitary transformation and it gives a non-Hermitian boson Hamiltonian. It is not easy (but not impossible) to solve the eigenstates of the non-Hermitian Hamiltonian. A Hermitian treatment of this nonHermitian eigenvalue problem is discussed and it is shown that this treatment is a very good approximation. Using this Hermitian treatment, we can obtain the normal-ordered Holstein-Primakoff-type boson expansion in the multi-collective-phonon subspace. Thereby the convergence of the boson expansion can be tested. Some examples of application of the Dyson-type non-unitary boson mapping to simplified models and realistic nuclei are also shown, and we can see that it is quite useful for analysis of the collective motions in realistic nuclei.In contrast to the above-mentioned ordinary type of boson mapping, which may be called a "static" boson mapping, the Dyson-type non-unitary selfconsistent-collective-coordinate method is discussed. The latter is, so to speak, a "dynamical" boson mapping, which is a dynamical extension of the ordinary boson mapping to be capable to include the coupling effects from the non-collective degrees of freedom selfconsistently.Thus all of the Dyson-type non-unitary boson mapping from A to Z is summarized in this paper. §1. IntroductionSince the jj-coupling shell model of Mayer and Jensen was established, 1) the structure of a nucleus has been understood in terms of a single-particle mean field and residual interactions. On the other hand, Bohr and Mottelson proposed the collective model, 2) in which the single-particle mean field fluctuates time-dependently and brings the nuclear collective motions. Since these proposals, the microscopic structure of the collective motions has been one of the most important problems in the nuclear theory; namely, they have intended to describe the collective motions in terms of the degrees of freedom of single particles moving inside the nuclear mean field. One of the early and successful trials was the quasiparticle RPA (random-phase approximation) proposed by Marumori, 3) Arvieu and Vénéroni, 4) and Baranger. 5) This intended to microscopically describe the nuclear vibrational motions by using a correlated pair of quasiparticle operators, which is often called "phonon", and

show abstract

Section: Fermion Pair Operators and Corresponding Boson Operatorsmentioning

confidence: 99%

Non-Unitary Boson Mapping and Its Application to Nuclear Collective Motions

Takada

2001

Prog. Theor. Phys. Suppl.

View full text Add to dashboard Cite

show abstract

“…To exemplify our method, we shall use a few realistic examples of nuclear shell model calculations. All results in this article are based on the shell model code by the Kyushu group [9][10][11]. The shell model basis states of this code are constructed by using the coefficients of fractional parentage discussed in Ref.…”

mentioning

confidence: 99%

“…The shell model basis states of this code are constructed by using the coefficients of fractional parentage discussed in Ref. [11]. In this paper we take the USD interactions of Ref.…”

mentioning

confidence: 99%

Lowest eigenvalue of the nuclear shell model Hamiltonian

Shen

Zhao

2010

Phys. Rev. C

View full text Add to dashboard Cite

In this paper we investigate regular patterns of matrix elements of the nuclear shell model Hamiltonian $H$, by sorting the diagonal matrix elements from the smaller to larger values. By using simple plots of non-zero matrix elements and lowest eigenvalues of artificially constructed "sub-matrices" $h$ of $H$, we propose a new and simple formula which predicts the lowest eigenvalue with remarkable precisions.Comment: six pages, four figures, Physical Review C, in pres

show abstract

Robustness of “noncollective” rotational behavior for nuclei in the presence of random interactions

Shen

Jiang

2021

Phys. Rev. C

View full text Add to dashboard Cite

A New Formulation of a Many-Level Shell Model: A Method of Constructing Orthonormal Basis States Analytically

Cited by 5 publications

References 2 publications

Non-Unitary Boson Mapping and Its Application to Nuclear Collective Motions

Non-Unitary Boson Mapping and Its Application to Nuclear Collective Motions

Lowest eigenvalue of the nuclear shell model Hamiltonian

Robustness of “noncollective” rotational behavior for nuclei in the presence of random interactions

Contact Info

Product

Resources

About