Exact canonically conjugate momenta to quadrupole-type collective coordinates and derivation of nuclear quadrupole-type collective Hamiltonian

Nishiyama, Seiya; Providência, João da

doi:10.1016/j.nuclphysa.2014.01.001

Cited by 4 publications

(4 citation statements)

References 36 publications

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“…It was also proposed by us and one of the present author's (S.N.) in the first quantized manner for a description of a quadrupole type nuclear collective motion [10]. As is clear from the structure of (3.1), the variables Π 0,0 k are no longer one-body operators but essentially many-body operators.…”

Section: Exact Canonically Conjugate Momentamentioning

confidence: 74%

“…How to go beyond the usual mean field theories towards a construction of a theory for large-amplitude collective motions in nuclei [5,6]? Applying Tomonaga's idea for collective motion theory [7,8] to nuclei with the aid of the Sunakawa's discrete integral equation method [9], we developed a collective description of surface oscillations of nuclei [10,11]. It gives a possible microscopic foundation of nuclear collective motions related to the Bohr-Mottelson model [12].…”

Section: Introductionmentioning

confidence: 99%

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Exact canonically conjugate momenta approach to a one-dimensional neutron–proton system, I

Nishiyama

Providência

2015

Int. J. Mod. Phys. E

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Introducing collective variables, a collective description of nuclear surface oscillations has been developed with the first quantized language, contrary to the second quantized one in Sunakawa's approach for a Bose system. It overcomes difficulties remaining in the traditional theories of nuclear collective motions: Collective momenta are not exact canonically conjugate to collective coordinates and are not independent. On the contrary to such a description, Tomonaga first gave the basic idea to approach elementary excitations in a one-dimensional Fermi system. The Sunakawa's approach for a Fermi system is also expected to work well for such a problem. In this paper, on the isospin space, we define a density operator and further following Tomonaga, introduce a collective momentum. We propose an exact canonically momenta approach to a one-dimensional neutron-proton (N-P) system under the use of the Grassmann variables.

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Section: Exact Canonically Conjugate Momentamentioning

confidence: 74%

Section: Introductionmentioning

confidence: 99%

Exact canonically conjugate momenta approach to a one-dimensional neutron–proton system, I

Nishiyama

Providência

2015

Int. J. Mod. Phys. E

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“…Applying Tomonaga's basic idea in his collective motion theory [4] to nuclei, with the aid of Sunakawa's integral equation method [5], one of the present authors (S.N.) developed the description of nuclear surface oscillations [6] and of two-dimensional nuclei [7]. These descriptions are considered to provide a possible microscopic foundation of nuclear collective motion derived from the Bohr-Mottelson model (BMM) [8,9,10].…”

Section: Introductionmentioning

confidence: 99%

A possible quantum fluid-dynamical approach to vortex motion in nuclei

Nishiyama

Providência

2017

Int. J. Mod. Phys. E

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The essential point of Bohr-Mottelson theory is to assume a irrotational flow. As was already suggested by Marumori and Watanabe, the internal rotational motion, i.e., the vortex motion, however, may exist also in nuclei. So, we have a necessity of taking the vortex motion into consideration. In a classical fluid dynamics, there are various ways to treat the internal rotational velocity. The Clebsch representation, v(x) = -\nabla \phi(x) + \lambda(x) \nabla \psi(x) (\phi ; velocity potential, \lambda and \psi: Clebsch parameters) is very powerful and has an advantage deriving equations of fluid motion from a Lagransian. Making the best use of the advantage, Kronig-Thellung, Ziman and Ito obtained a Hamiltonian including the internal rotational motion, the vortex motion, through the term \lambda(x) \nabla \psi(x). Going to quantum fluid dynamics, Ziman and Thellung finally derived a roton spectrum of liquid Helium II postulated by Landau. Is it possible to apply such the manner to a description of the collective vortex motion in nuclei? The description of such a collective motion has never been treated in the Bohr-Mottelson model (BMM) for a long time. In this paper, we will investigate a possibility of describing the vortex motion in nuclei basing on the theories of Ziman and Ito together with Marumori's work.Comment: 23 pages, no figures, Publication versio

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“…Very recently we have given exact canonically conjugate momenta to quadrupole-type collective coordinates and have derived a nuclear quadrupole-type collective Hamiltonian [10] (referred to as I). The exact canonically conjugate momenta Π 2µ to the quadrupole-type collective coordinates φ 2µ is derived by modifying the approximate momenta π 2µ adopted by Miyazima-Tamura [8] with the use of the discrete version of the Sunakawa's integral equation [3].…”

Section: Introductionmentioning

confidence: 99%

Description of collective motion in two-dimensional nuclei; Tomonaga's method revisited

Nishiyama¹,

Providência²

2015

Nuclear Physics A

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Four decades ago, Tomonaga proposed the elementary theory of quantum mechanical collective motion of two-dimensional nuclei of N nucleons. The theory is based essentially on neglecting 1 √ N against unity. Very recently we have given exact canonically conjugate momenta to quadrupole-type collective coordinates under some subsidiary conditions and have derived nuclear quadrupole-type collective Hamiltonian. Even in the case of simple two-dimensional nuclei, we require a subsidiary condition to obtain exact canonical variables. Particularly the structure of the collective subspace satisfying the subsidiary condition is studied in detail. This subsidiary condition is important to investigate the structure of the collective subspace.

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Exact canonically conjugate momenta to quadrupole-type collective coordinates and derivation of nuclear quadrupole-type collective Hamiltonian

Cited by 4 publications

References 36 publications

Exact canonically conjugate momenta approach to a one-dimensional neutron–proton system, I

Exact canonically conjugate momenta approach to a one-dimensional neutron–proton system, I

A possible quantum fluid-dynamical approach to vortex motion in nuclei

Description of collective motion in two-dimensional nuclei; Tomonaga's method revisited

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