Akito Arima

Interacting Boson Model of Collective States I. The Vibrational Limit

Abstract We propose a unified description of collective nuclear states in terms of a system of interacting bosons. We show that within this model both the vibrational and the rotational limit can be recovered. We study in detail the vibrational limit and bring attention to the possible existence of an unbroken SU(5)⊃0+(5) symmetry. We derive a large set of analytic relations for energies and electromagnetic transitions.

Interacting boson model of collective nuclear states II. The rotational limit

Abstract We discuss the rotational limit of the interacting boson model and bring attention to the possible existence of an unbroken SU(3) symmetry. We derive, within the framework of this symmetry, several analytic relations for energies and electromagnetic transition rates.

Interacting boson model of collective nuclear states IV. The O(6) limit

We discuss a third limit of the interacting boson model. We show that this limit is associated with the group O(6) of orthogonal transformations in six dimensions. We derive, within the framework of this symmetry, several closed expressions for energies and electromagnetic transition rates.

NUCLEAR SHELL-MODEL AND INTERACTING BOSONS

In this workshop we have seen that the interacting boson model provides us with a unified phenomenological description of vibrational, rotational and transitional nuclei.

Collective nuclear states as symmetric couplings of proton and neutron excitations

Collective nuclear states are described by symmetric couplings of proton and neutron pairs. These J=0 and J=2 pairs are represented by s- and d-bosons respectively. The multiplet structure of the combined system is given by representations of the SU (6) × SU (2) group, the Arima-Iachello interacting bosons corresponding to the fully symmetric ones. The validity of the boson picture is attributed to the attractive proton-neutron interaction which is also responsible for the transition from vibrational to rotational spectra.

SHELL MODEL DESCRIPTION OF INTERACTING BOSONS

The interacting boson model, describing collective states of even-even nuclei, is introduced as a drastic truncation of large scale shell model calculations. The shell model hamiltonian can be diagonalized by using a correspondence, or mapping, of the nucleon states in the truncated space into states obtained by coupling proton and neutron s- and d-bosons. The equivalent boson hamiltonian in a simple case is obtained and diagonalized. Eigenstates with definite proton-neutron symmetry (good F-spin) emerge for certain values of proton and neutron numbers. In general the situation is more complex but the results obtained follow closely the experimental data.

Interacting boson model of collective nuclear states III. The transition from SU(5) to SU(3)

Abstract We study the transition from the vibrational, SU(5), to the rotational, SU(3), limit of the interacting boson model. We show how this model can be used to calculate energies, electromagnetic transitions, multipole moments, nuclear radii, and two-nucleon transfer intensities in transitional nuclei.

Boson symmetries in vibrational nuclei

It is proposed that nuclei (away from closed shells and from regions of large deformation) be described as a boson gas. Exploiting the underlying O(5) symmetry analytic expressions for the eigenvalues of the boson Hamiltonian and for the transition matrix elements are obtained. The computed energy levels are in surprisingly good agreement with those recently observed in the (α, xnγ) and (heavy ions, xnγ)

THE INTERACTING BOSON MODEL

This chapter examines the algebraic and geometric properties of the interacting boson model-1, and reviews the interacting boson model-2. Explains that the model was originally introduced with only one kind of collective boson variable with angular momentum J=O and J=2 (the interacting boson model-1), and subsequently, a more elaborate version was introduced with two kinds of collective variables, proton bosons and neutron bosons (the interacting boson model-2). Discusses analytic solutions, transitional classes, extensions of the models, coherent states, transitional classes and shape-phase transitions, energy levels, electromagnetic transition rates, other properties, a microscopic description of interacting bosons, generalized seniority, the single j-shell, several j-shells, and the Ginocchio model. Excludes odd-even nuclei and the corresponding interacting boson-fermion models 1 and 2 from the review.

The structure of the sd-shell nuclei (I). C18, F18, O19, F19 and Ne20

Abstract A shell-model calculation for nuclei at the beginning of the 1s-0d shell has taken account of the configuration mixing of the 1s and 0d shells. The position of the 1s level relative to the 0d level and the strength of the spin-orbit interaction are taken from the observed 017 and F17 spectra. A residual interaction is introduced and is assumed to be central. The strength of this interaction is treated as a free parameter. The positions of the even-parity levels and their properties agree well with experiment. In particular, a rotational level structure in Ne20 is well explained. It is pointed out that the harmonic-oscillator w wave functions should be modified in the 1s wave function to reproduce the spectrum of O18. The configuration mixing is very large especially in nuclei of low isobaric spin. the central residual interaction favours the higher symmetric states in the ordinary space. Thus the concept of the symmetry has important physical meaning in these nuclei. The wave functions are found to be very similar to those given by the SU3 model, as was discovered by Elliot, but the mixing of different states is caused by the deviation of the residual interaction from the simple Q-Q force. The spin-orbit interaction also destroys the elegance of this SU3 model. Although this mixing is not so large, the M1 transition probabilities are strongly influenced.