A two-fluid model of nuclear rotations and surface vibrations

Abstract

A simple phenomenological two-fluid model of nuclear collective motion previously used by the authors to discuss rotations is extended to include surface vibrations.The model is applied to a study of the rare-earth nuclei 154Gd, 164Er and 168Yb in an investigation of the rotation-vibration coupling in the presence of Coriolis antipairing effects and of the effects of Coriolis antipairing in the / I bands.

Derivation of microscopic uni-axial unified adiabatic Bohr–Mottelson rotational model

“…The observed moment of inertia is a factor of about two smaller than that for a rigid flow. These results suggested to Cusson and others [23][24][25][26] to use a velocity field that is a sum of irrotational-flow and rigid-body velocity fields and to show that any value of the moment of inertia between those for irrotational and rigid-body flows can be obtained by adjusting the ratio of these two velocity fields. Other authors [27][28][29] used a classical two-fluid model consisting of an inner non-rotating (superfluid) core fluid and a rotating outer (normal) fluid to obtain agreement with the experimental data for the moment of inertia.…”

“…As noted in Section 2.1, it is desirable (as a step in solving the rotation-intrinsic Schrödinger equation (24) or (26) or (28)) to choose the Euler angle θ such that the Coriolis-coupling term F Φ in Eq. (24) or (26) or (28) vanishes, and hence to account completely for the effect of the Coriolis interaction on the rotational (i.e., on the kinematic moment of inertia ) and intrinsic motions.…”

“…(24) or (26) or (28) vanishes, and hence to account completely for the effect of the Coriolis interaction on the rotational (i.e., on the kinematic moment of inertia ) and intrinsic motions. Therefore, we want to choose θ such that the quantity in Eq.…”

“…(19). However, these rigid-plus-irrotational flow solutions may be of interest in connection with the phenomenological hydrodynamic collective models of the rotational motion and currents in nuclei that use a velocity field that is a sum of rigid and irrotational flows [16,[23][24][25][26][27][83][84][85][86][87][88][89][90][91][92], and where there exists implicitly a strong intrinsic-rotation Coriolis coupling. 3 We note that the rigid-flow motion in Eqs.…”

“…But these velocity fields depend on the intrinsic wavefunction and the corresponding intrinsic wavefunction is not rotationally invariant and hence is not consistent with the rotational model. This study is of interest in connection with previous phenomenological hydrodynamic analyses of the rotational motion and currents in nuclei that use a velocity field that is a sum of rigid and irrotational flows [16,[23][24][25][26][27][83][84][85][86][87][88][89][90][91][92].…”