The experimental and theoretical evidence for intrinsic reflection-asymmetric shapes in nuclei is reviewed. The theoretical methods discussed cover a wide spectrum, from mean-field theory and its extensions to algebraic and cluster approaches. The experimental data for nuclear ground states and at low and high spin, cited as evidence for reflection asymmetry, are collected and categorized. The extensive data on electric dipole transition moments and their theoretical interpretation are surveyed, along with available data on electric octupole moments. The evidence for reflection-asymmetric molecular states in light nuclei is summarized. The application of reflection-asymmetric theories to descriptions of the fission barrier, bimodal fission, superdeformation, and hyperdeformations is reviewed, and some other perspectives in the wider context of nuclear physics are also given. [S0034-6861(96)00102-X]

Intrinsic reflection asymmetry in atomic nuclei

Origin of the multipole pairing interactions

Microscopic analysis of nuclear collective motions in terms of the boson expansion theory: (II). Numerical calculations

TheK
π=0+, 2+ and 4+ states are considered in doubly even deformed nuclei. It is shown that in the quasiparticle-phonon nuclear model (QPNM) and in the interacting boson model (IBM) a vibrational state has one dominating component. The states withK

 π
 =0
 3
 +
 , 0
 4
 +
 0
 5
 +
 2
 2
 +
 , 2
 3
 +
 , 4
 1
 +
 and 4
 2
 +
 have a dominating one-phonon component within the QPNM and a two- or three-boson component within the IBM. According to the QPNM the contribution of two-phonon components to the wave functions of these states is less than 10%, i.e. there is a qualitative discrepancy in describing the structure of these states within the QPNM and the IBM. The experimental data indicate the existence in these states of one-phonon or two-quasiparticle components. They are rather well described within the QPNM. These states cannot be described within the IBM. This is due to the fact that the IBM takes into account only a small part of the space of two-quasiparticle states, just the one entering intoΒ- andγ-vibrational states.

Confrontation between the quasiparticle-phonon nuclear model and the interacting boson model for deformed nuclei

Microscopic analysis of nuclear collective motions in terms of the boson expansion theory: (I). Formulation

Using the space translation invariance of the nuclear Hamiltonian the residual interaction for the rotating nucleus is constructed The nuclear Hamiltonian thus obtained is used to describe negative-parity states near the yrast line within the random-phase approximation (RPA) The connection between the Goldstone modes of motion (spurious states) and the symmetries of equations of motion for the negative-parity states near the yrast line is found

http://iopscience.iop.org/article/10.1088/0305-4616/10/7/008/pdf

The RPA and restoration of translational symmetry of the Hamiltonian of a rotating nucleus

The general form of nuclear Hamiltonian equation of motion is derived within the Random Phase Approximation (RPA). The connection between the Goldstone modes of motion (spurious states) and the equations of motion is shown. The general method of extraction of spurious states from the solution of the RPA equations of motion is proposed.

Extraction of the spurious states from the solution of the motion equation within the random phase approximation

Our results confirm the fact that the CHFB + RPA model, originally introduced for high-spin states, can be successfully used in a low-spin region for the description of states near the yrast line. To get a better agreement with experimental data, one has to go beyond the scope of the RPA and to involve into the Hamiltonian also the terms of higher order in the boson expansion which lead to the mixing of states with different signature. This mixing is expected to play a role especially in the low-spin region. The inclusion of the residual interactions completely restoring the rotational symmetry of the total Hamiltonian (see [34]) into our model can also improve the results.

Application of the RPA method based on the cranked Hartree-Fock-Bogoubov model in168Er and158Dy

The alignment of the intrinsic angular momentum of a rotating nucleus into the rotational axis is studied in terms of a simple quasi-adiabatic approach. In the framework of this approach using the “quasi-particle + phonon” model with Harris non-adiabatic corrections it is possible to describe the rotational bands up to relatively high spins. In the case of235U it is demonstrated that this simple approach enables the qualitative description of the process of alignment of the intrinsic angular momentum with respect to the rotational axis.

S. Cwiok

Papers

The RPA and restoration of translational symmetry of the Hamiltonian of a rotating nucleus

Extraction of the spurious states from the solution of the motion equation within the random phase approximation

Application of the RPA method based on the cranked Hartree-Fock-Bogoubov model in168Er and158Dy

Non-adiabatic effects and coriolis interactions in odd deformed nuclei