Calculation of strongly-coupled rotational bands in terms of the tilted axis cranking model

Abstract

Recently observed strongly-coupled rotational bands associated with the ν [505] IntroductionBohr-Mottelson's strong-coupling model [1] is the first pioneering work which is capable to describe interplay between the collective and the single-particle rotational motions in well-deformed nuclei. It successfully reproduce both the energy spectra and the electromagnetic transition properties of rotational bands in odd nuclei. It is, however, of phenomenological nature since essential quantities like the moment of inertia and the quadrupole moment are model-parameters and are adjusted in comparison with experimental data. One has to combine it with a more microscopic model such as the Nilsson single-particle model. Another drawback of the model is that it is based on the adiabatic assumption of the collective rotation and the application to the high angular momentum regime is not straightforward. The particle-rotor model [1, 2] is a possible means to extend the idea by lifting the adiabatic assumption and including the effect of Coriolis coupling by exact diagonalization, although it is still semi-phenomenological in the sense that the macroscopic "rotor" part is explicitly introduced. Nowadays, fully microscopic approaches are available, for example, the variation after full angular momentum projection base on the generalized mean-field [3] and the projected shell model [4]. However, they are very complicated and lose simplicity of the model. On the other hand, by taking into account the effect of rotation unperturbatively, the mean-field theory has been extended in the rotating frame: The cranking model or the Cranked Shell Model (CSM) [5], which is simple and yet microscopic, has been successfully applied to understand various high-spin phenomena [6] such as backbending of moment of inertia. Recently, this cranking model has been further extended in such a way to include the tilting degrees of freedom of rotation-axis relative to the deformed shape; the Tilted Axis Cranking (TAC) model [7,8,9] (the conventional cranking is called the Principal Axis Cranking (PAC) model, instead), which gives nice interpretations of new types of nuclear rotational motions, e.g. the shears bands [10] and the chiral bands [9,11]. Although these cranking models treat the rotational motion in a semiclassical manner, its simplicity allows us to have a clear physical picture of various collective rotational motions, which are actually a result of the complex nuclear many-body problem.The purpose of the present paper is two folds: The first is to give a clear relationship between the strong-coupling model and the TAC model. The second is to apply the TAC model to the 1

Systematic study of multi-quasiparticleK-isomeric bands in tungsten isotopes by the extended projected shell model

“…K isomers have been studied in various methods, e.g., the cranked mean-field model or the tilted axis cranking model [15][16][17][18], the Wood Saxon quasiparticle random-phase approximation model and random-phase approximation method based on the sloping surface [19], and the configuration-constrained nuclear potential energy calculations [20]. However, if one wants to describe K isomers and their associated rotational bands on an equal footing, then one has to go beyond the mean field and perform shell-model-like calculations.…”

Precession mode on high-K configurations: non-collective axially-symmetric limit of wobbling motion

“…Making full use of the axial symmetry, the RPA formalism has been developed [21,22,23,24], which is capable of describing the rotational band based on the high-K state as a multi-phonon band, i.e., the precession band. Recently, the same kind of rotational bands built on high-K isomers have also been studied by means of the tilted axis cranking model [25,26,27,28].…”