F. Iachello

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.

THE INTERACTING BOSON-FERMION MODEL

Part I. The Interacting Boson-Fermion Model - 1: 1. Operators 2. Algebras 3. Bose-Fermi symmetries 4. Superalgebras 5. Numerical studies 6. Geometry Part II. The Interacting Boson-Fermion Model - 2: 7. Operators 8. Algebras 9. Superalgebras 10. Numerical studies Part III. The Interacting Boson-Fermion Model-K: 11. The interacting boson-fermion models 3 and 4 Part IV. High-Lying Collective Modes.

Algebraic methods for molecular rotation-vibration spectra

Abstract Algebraic techniques similar to those recently introduced in nuclear physics may be useful in the treatment of molecular Spectra. A spectrum generating algebra appropriate to diatomic molecules is constructed. This algebra, U(4), is the simplest generalization to 3-D of the algebra of the 1-D Morse oscillator and a simplification of the U(6)algebra of nuclear rotation-vibration spectra.

Group theory approach to scattering

Abstract We show that both bound and scattering states of a certain class of potentials are related to the unitary representations of certain groups. In this class, several potentials of practical interest, such as the Morse and Poschl-Teller potentials, are included. The fact that not only bound states but also scattering states are connected with group representations suggests that an algebraic treatment of scattering problems similar to that of bound state problems may be possible.