Nuclear intrinsic vorticity and its coupling to global rotations

Mikhailov, I.N.; Quentin, P.; Samsoen, D.

doi:10.1016/s0375-9474(97)00401-6

Cited by 22 publications

(28 citation statements)

References 34 publications

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“…[5] for some relevant references), a simple ansatz for such a coupling is provided by the S-ellipsoid fluid dynamics as studied classically in great details by Chandrasekhar in the context of celestial self-gravitating objects [6]. It makes use of a velocity field which is linear in the coordinates and produces a coupling of a global rotation with an intrinsic mode corresponding to a motion tangential to the body surface which is supposed to be ellipsoidal.…”

Section: Introduction and Methodsmentioning

confidence: 99%

Equivalence of pairing correlations and intrinsic vortical currents in rotating nuclei

et al. 2003

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The present paper aims at proving that the collective effects of pairing correlations in rotating nuclei can be embodied by a simple S-type couplingà la Chandrasekhar between rotational and intrinsic vortical collective modes. The demonstration is performed on the basis of a comparison between the solutions of microscopic calculations within the HFB and the HF Routhian formalisms. The HF Routhian solutions are constrained to have the same Kelvin circulation expectation value as the HFB ones. It is shown in several mass regions, pairing regimes, and for various spin values that this procedure yields moments of inertia, angular velocities, and current distributions which are very similar within both formalisms. We finally present perspectives for further studies.

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Section: Introduction and Methodsmentioning

confidence: 99%

Equivalence of pairing correlations and intrinsic vortical currents in rotating nuclei

et al. 2003

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“…Refs. [8,34,35] ) will lead to a classical mode of global rotation which may be adequately described by the Routhian approximation, yielding thus an almost pure vacuum state. The latter is proposed to offer an explanation for the observed maximum of the occupancies of 1p-1h states, going from zero to zero while increasing at small ω values.…”

Section: Presentation and Discussion Of Our Resultsmentioning

confidence: 99%

A particle-number conserving description of rotational correlated states

et al. 2010

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“…24 where a Lagrangian constraining field proportional to the operatorL AB in (32) was added phenomenologically to the CM Hamiltonian H in (31) to account for the interaction between the rotation and intrinsic motions except that in ref. 24, λ was a c-number. The above-mentioned similarity is apparent from the relation between the operators L AB ,L AB , andt AB .…”

Section: Variational Methods For Solving Smrm Equationmentioning

confidence: 99%

“…where we have used (17), (23), (24), (63), and (64). Then, we obtain the following definition of the moment inertia that is consistent with the energy increment and the expectation value of the angular momentum:…”

Section: Solution Of Smrm Equationmentioning

confidence: 99%

A semiclassical, microscopic model for nuclear collective rotation

Gulshani

2006

Can. J. Phys.

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In this article, a semiclassical, microscopic model (dubbed SMRM) is derived to describe collective rotation in deformed nuclei. The SMRM is derived by transforming the time-dependent, multiparticle Schrödinger equation to a rotating frame whose axes are chosen to coincide with the principal axes of the expectation value of an arbitrary, secondrank, symmetric, tensor (nuclear shape) operatorˆ . This transformation circumvents the difficulty associated with the introduction of redundant particle coordinates in the Villars' transformation. The SMRM Schrödinger equation, which resembles the cranking model (CM) equation, is a time-dependent, time-reversal-invariant, nonlinear integro-differential equation. In this equation, the angular velocity is determined by the wave function and deformationrotation shear operators, and this introduces the nonlinearity in the equation. A variational method is proposed and justified to obtain: a stationary solution of the SMRM Schrödinger equation in the Rayleigh-Ritz Hartree-Fock particle-hole formalism, the rotational energy increment, and the associated moment of inertia. When exchange interaction terms are neglected or a separable interaction is used, the SMRM moment of inertia is shown to reduce to that given by the CM provided that a certain relationship exists between the moment of inertia and the expectation value ofˆ . However, the SMRM and CM wave functions are not the same (SMRM preserves and CM violates time-reversal invariance) implying that the calculated values of other parameters, including the moment of inertia at higher values of the angular momentum, may not be the same in the two models. In any case, the SMRM derives the CM moment of inertia from a microscopic, time-reversal invariant, nonlinear theory. PACS Nos.: 21.60.Ev, 21.60.Fw, 21.60.Jz Résumé : Nous développons ici un modèle microscopique semi-classique (SMRM) pour décrire les rotations collectives dans les noyaux déformés. Ce modèle est obtenu en transformant l'équation de Schrödinger à N corps dépendante du temps dans un référentiel tournant dont les axes sont les valeurs propres d'un opérateur tensoriel symétrique du deuxième ordreˆ créé pour décrire la forme du noyau. Cette façon de faire évite la difficulté associée à l'introduction de coordonnées redondantes de particules dans la transformation de Villars. L'équation SMRM de Schrödinger, qui ressemble au modèle du cranking (CM), est une équation intégro-différentielle dépendante du temps et invariante sous renversement du temps. Dans cette équation la vitesse angulaire est déterminée par la fonction d'onde et les opérateurs de déformation-stress sous rotation, ce qui introduit une non-linéarité. Nous proposons et et justifions une méthode variationnelle pour obtenir les éléments suivants : une solution stationnaire de l'équation SMRM de Schrödinger dans le formalisme particule-trou

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Nuclear intrinsic vorticity and its coupling to global rotations

Cited by 22 publications

References 34 publications

Equivalence of pairing correlations and intrinsic vortical currents in rotating nuclei

Equivalence of pairing correlations and intrinsic vortical currents in rotating nuclei

A particle-number conserving description of rotational correlated states

A semiclassical, microscopic model for nuclear collective rotation

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