The low-energy quadrupole mode of nuclei

Abstract

The phenomenological classification of collective quadrupole excitations by means of the Bohr-Hamiltonian (BH) is reviewed with focus on signatures for triaxility. The variants of the microscopic BH derived by means of the Adiabatic Time-Dependent Mean Field theory from the Pairing-plus-quadrupole-quadrupole interaction, the Shell Correction Method, the Skyrme Energy Density Functional, the Relativistic Mean Field Theory and the Gogny interaction are discussed and applications to concrete nuclides reviewed. The Generator Coordinate Method for the five-dimensional quadrupole deformation space and first applications to triaxial nuclei are presented. The phenomenological classification in the framework of the Interacting Boson Model is discussed with a critical view on the boson number counting rule. The recent success in calculating the model parameters by mapping the mean field deformation energy surface on the bosonic one is discussed and the applications listed. A critical assessment of the models is given with focus on the limitations due to the adiabatic approximation. The Tidal Wave approach and the Triaxial Projected Shell Model are presented as practical approaches to calculate spectral properties outside the adiabatic region. Keywords: Microscopic Bohr Hamiltonian; quadrupole excitations; triaxiality; IBM-1; triaxial projected shell model; tidal wave approach. PACS Number(s): 21.10.Re, 21.60.Ev, 21.60.Fw, 23.20.Lv, 24.10.Cn 1541001-1 Int. J. Mod. Phys. E 2015.24. Downloaded from www.worldscientific.com by UNIVERSITY OF QUEENSLAND on 09/30/15. For personal use only. Source: From Ref. 7. 1541001-2 Int. J. Mod. Phys. E 2015.24. Downloaded from www.worldscientific.com by UNIVERSITY OF QUEENSLAND on 09/30/15. For personal use only. The low-energy quadrupole mode of nucleiModel (TPSM), which take this coupling into account. Section 7 tries to assess the presently used models and points out some challenges, which seem important from the author's point of view. The BHThe Bohr coordinate system and Hamiltonian are reviewed in detail by Prochniak and Rohozinski. 9 The collective states are represented by wave functions of the components α µ (µ = −2, . . . , 2) of the scale-free quadrupole deformation tensor which are expressed by the five-dimensional (5D) spherical polar coordinates α µ = β cos γ D (2) 0,M (Ω) + 1541001-3 Int. J. Mod. Phys. E 2015.24. Downloaded from www.worldscientific.com by UNIVERSITY OF QUEENSLAND on 09/30/15. For personal use only. • Transitional nucleus (T in Fig. 17): The yrast energies are well approximated (J = I) by the expression J = Θ 0 + Θ 1 J, ω = J J , E(J) = J 0 1541001-30 Int. J. Mod. Phys. E 2015.24. Downloaded from www.worldscientific.com by UNIVERSITY OF QUEENSLAND on 09/30/15. For personal use only.

Longitudinal wobbling in 133La

“…As reviewed in Ref. [7], most of these nuclides seem to execute large-amplitude oscillations only around the axial shape. Partial evidence for stabilization of ground state triaxiality in these regions has been the observation of odd-I-low staggering of the quasi-γ band [8][9][10][11].…”

Beyond the Unified Model

“…Subsequent approaches based on the various selfconsistent mean field theories have been reviewed in Refs. [38,15,50,51]. The Inglis-Belyaev expressions (35,36) well reproduce the deformation dependence of the inertial parameters.…”

“…3 (d) and (e) illustrate the case when the intrinsic wave function carries its own angular momentumhΩ, which for nucleons in a non-rotating axial potential must have the direction of the symmetry axis. Since there is no collective rotation about the symmetry axis possible, the projection of the total angular momentum on the symmetry axis K must be equal to the intrinsic one, K = Ω. UsingĴ 1 =R 1 ,Ĵ 2 =R 2 , eigenvalues and eigenfunctions of the Unified Model Hamiltonian (15) are (20) where I ≥ K > 0. As seen in Fig.…”

Open questions on nuclear collective motion

“…From Ref. [2]. the rotational axis titled with repeat to the principal axes (Tilted Axes Crankinng).…”