Quantum Theory of Collective Motion: Quantized Self-Consistent Collective-Coordinate Method for the Large-Amplitude Nuclear Collective Motion

Marumori, Toshio; Sakata, Fumihiko; Une, Tsutomu; Hashimoto, Yukio; Maskawa, Toshihide

doi:10.1143/ptp.66.1651

Cited by 7 publications

(5 citation statements)

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“…This is still one of the most important problems in the nuclear many-body theory. One of the possible answers to this problem is given by the selfconsistentcollective-coordinate (SCC) method proposed by Marumori et al 25), 26) For the convenience of later discussions, let us recapitulate the basic idea of the original SCC method.…”

Section: Basic Idea Of the Scc Methodsmentioning

confidence: 99%

“…Marumori et al named this method "self-consistent collective-coordinate (SCC) method". 25), 26) From the above discussion we can understand that the TDHF method is considered to be a classical approximation to treat a quantum mechanical many-body system. Quantizing this classical system or replacing the collective parameters with boson operators, we can transfer it to a quantum mechanical many-boson system.…”

Section: Basic Idea Of the Scc Methodsmentioning

confidence: 99%

“…The quantized version of this method is, so to speak, "dynamical" boson mapping, in contrast to the ordinary boson mapping that may be called "static" boson mapping. While the original SCC method 25), 26) is a unitary theory, Shimizu and the present author 27), 28) proposed a D-type non-unitary extension whose small-amplitude limit tends to the ordinary D-type boson mapping. Its basic idea is explained in §8.…”

Section: §1 Introductionmentioning

confidence: 94%

“…One of the methods to take into account the contributions from both of the noncollective degrees of freedom and the ground-state correlation is the selfconsistentcollective-coordinate (SCC) method 25), 26) or its non-unitary extension. 27), 28) The quantized version of the SCC method is, so to speak, "dynamical" boson mapping, in contrast to the ordinary boson mapping that may be called "static" boson mapping.…”

Section: §8 Dynamical Boson Mapping -Non-unitary Selfconsistent-collmentioning

confidence: 99%

“…Since the RPA phonons are considered to be the "true" elementary mode of excitation in a nucleus, we strongly desire to have an extension of boson mapping based on the RPA phonons (not the TD phonons). The selfconsistent-collective-coordinate (SCC) method of Marumori et al 25), 26) makes this possible in the framework of the TDHF (time-dependent Hartree-Fock) theory. The quantized version of this method is, so to speak, "dynamical" boson mapping, in contrast to the ordinary boson mapping that may be called "static" boson mapping.…”

Section: §1 Introductionmentioning

confidence: 99%

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

Takada

2001

Prog. Theor. Phys. Suppl.

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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

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Section: Basic Idea Of the Scc Methodsmentioning

confidence: 99%

Section: Basic Idea Of the Scc Methodsmentioning

confidence: 99%