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

Nishiyama, Seiya; Providência, João da

doi:10.1016/j.nuclphysa.2014.12.005

Cited by 2 publications

(2 citation statements)

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“…Our exact canonically conjugate momenta to collective coordinates are found from a viewpoint different from the canonical transformation theory and the group theory [13,14,15]. Recently we got exact canonical variables, revisiting the Tomonaga's work and described a collective motion also in two-dimensional nuclei [16].…”

Section: Introductionmentioning

confidence: 90%

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: Introductionmentioning

confidence: 90%

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

Cited by 2 publications

References 16 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

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