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Algebraic Collective Model Description of $^{166}$Er

G. Thiamová

Published Jan 1, 2015• 1 citation
Publisher

Abstract

A simple, four-parameter algebraic collective model (ACM) Hamiltonian is used to describe 166Er. In this nucleus anharmonic double-γ vibrations are observed and the third excited 0+ state has been identified as a candidate for a bandhead of a β band. In contrast to γ-vibrational bands, systematically observed in deformed nuclei, β-vibrational bands are rarely well realized in nuclei and their observation and interpretation is still far from satisfactory. The purpose of the present paper is to show how the ACM model is capable to address complex properties of deformed nuclei in this region and what are its successes and weak points.

DOI
10.35840/2631-5017/2501

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Algebraic Collective Model Description of 166^{166}166Er
A simple, four-parameter algebraic collective model (ACM) Hamiltonian is used to describe 166Er. In this nucleus anharmonic double-γ vibrations are observed and the third excited 0+ state has been identified as a candidate for a bandhead of a β band. In contrast to γ-vibrational bands, systematically observed in deformed nuclei, β-vibrational bands are rarely well realized in nuclei and their observation and interpretation is still far from satisfactory. The purpose of the present paper is to show how the ACM model is capable to address complex properties of deformed nuclei in this region and what are its successes and weak points.
I will review developments and applications of an algebraic version of Bohr’scollective model (BM), known as the algebraic collective model (ACM) withinwhich fully converged calculations can be performed for a range of Hamiltonians.Examining the algebraic structure underlying the BM has clarified itsrelationship with the interacting boson model (IBM), with which it has relatedsolvable limits. I will review results of comparison of the two models for thecase of both axially-symmetric and triaxial rotor. Predictions for single andmulti-phonon excitations of deformed nuclei will be discussed and comparedwith data.
Abstract. The mean-field approximation predicts pairing and shape phase transitions in nuclei as a function of temperature or excitation energy. However, in the finite nucleus the singularities of these phase transitions are smoothed out by quantal and thermal fluctuations. An interesting question is whether signatures of these transitions survive despite the large fluctuations. The shell model Monte Carlo (SMMC) approach enables us to calculate the statistical properties of nuclei beyond the mean-field approximation in model spaces that are many orders of magnitude larger than spaces that can be treated by conventional diagonalization methods. We have extended the SMMC method to heavy nuclei and used it to study the transition from vibrational (spherical) to rotational (deformed) nuclei in families of rare-earth isotopes. We have calculated collective enhancement factors of level densities as a function of excitation energy and found that the decay of the vibrational and rotational enhancements is well correlated with the pairing and shape phase transitions, respectively.
The mean-field approximation predicts pairing and shape phase transitions in nuclei as a function of temperature or excitation energy. However, in the finite nucleus the singularities of these phase transitions are smoothed out by quantal and thermal fluctuations. An interesting question is whether signatures of these transitions survive despite the large fluctuations. The shell model Monte Carlo (SMMC) approach enables us to calculate the statistical properties of nuclei beyond the mean-field approximation in model spaces that are many orders of magnitude larger than spaces that can be treated by conventional diagonalization methods. We have extended the SMMC method to heavy nuclei and used it to study the transition from vibrational (spherical) to rotational (deformed) nuclei in families of rare-earth isotopes. We have calculated collective enhancement factors of level densities as a function of excitation energy and found that the decay of the vibrational and rotational enhancements is well correlated with the pairing and shape phase transitions, respectively.
A model Hamiltonian describing a two-level system with a crossing plus a pairing force is investigated using technique of large-amplitude collective motion. The collective path, which is determined by the decoupling conditions, is found to be almost identical to the one in the Born-Oppenheimer approximation for the case of a strong pairing force. For the weak pairing case, the obtained path describes a diabatic dynamics of the system. PACS number(s): 21.60.-n, 36.40.Sx Nuclei and metallic clusters are finite fermionic many-body systems which support many kinds of collective motion. While properties of high-frequency vibrations (giant resonances) may be well reproduced by the random-phase approximation (RPA), some low-frequency vibrations exhibit an anharmonic nature that the RPA cannot describe. Shape coexistence and fission phenomena in nuclei and clusters also have such a large amplitude nature. In order to investigate these kinds of large amplitude collective motion, one would like to reduce the number of degrees of freedom to a few judiciously chosen collective coordinates. In order to determine the collective coordinates self-consistently, we use the theory of adiabatic