﻿ Interacting boson model

# Interacting boson model

In the Interacting Boson Approximation (IBA ) is approximate methods to describe the structure of atomic nuclei. Often this procedure is also called Interacting Boson Model ( IBM) called. The model is particularly suitable for the description of nuclei from cerium to lead straight Nukleonzahl. At the IBA all nucleons are coupled in pairs outside a nuclear shell to bosons - in this case, particles with angular momentum 0 (s- boson ) or 2 ( d- boson ). Established in 1974, originally developed by Akito Arima and Francesco Iachello model coupled to a boson two neutrons and two protons to a boson. A similar method was developed almost simultaneously by Janssen, Jolos and Dönau. This so-called IBA -1 model is therefore only for the description of nuclei with even neutron and proton are ( gg - cores). The scope of the cores from cerium to lead is given mainly by the fact that a very large mass range between the shell with neutron number 82 and the corresponding proton shell at the lead with Z = 82 exists, where you can pull very many of these bosons into consideration needs. The Bosonenanzahl is counted in the model in the past from the next shell from completion. The coupling of the bosons with each other is done by a simple two - body force.

## Algebraic structure

Often the three subalgebras U ( 5), SO (6) and SU (3) are shown graphically by the so-called Casten triangle. The vertices correspond to these three chains of embedded algebras. Frequently such an image contains other items that are designated by X (5 ) and E ( 5). It is, however, not to algebras of IBM.

When applied to atomic nuclei corresponds to the U ( 5) limit a vibrator, the SO (6 ) limit a soft - core and the SU (3) limit a rotor.

## Extensions of the model

An extension introduces bosons with higher angular momentum, so-called g - bosons. Another possibility is to regard more complicated interactions than 2 - body forces. But could will shown that both extensions are equivalent partially mathematically. An important extension was the distinction between proton and neutron bosons. This extension is also called the IBA -2 model. Last has yet to be informed of the possibility to couple individual nucleons with bosons, eg with an odd number of neutrons the leftover neutron is then coupled to the bosons. This extension is called IBMF, the coupling with two unpaired nucleons IBMFF. The consideration of fermions leads to other very interesting aspects, such as Boson - fermion symmetry, called supersymmetry, which plays an important role in particle physics.

## Writings

• Arima, Iachello Collective nuclear states as representations of a SU ( 6) Group, Physical Review Letters, Bd.35, 1975, S.1070
• Arima, Iachello The interacting boson model, Cambridge University Press 1987
• Arima, Iachello Interacting boson model of collective states, Part 1 (the vibrational limit) Annals of physics Vol 99, 1976, p 253-317, Part 2 ( the rotationally limit) ibid. Vol 111, 1978, pp. 201-38, Part 3 with Scholten (the transition from the SU ( 5) to SU (3) ), ibid. Vol 115, 1978, pp. 325-66, Part 4 (the O ( 6 ) limit ) ibid. Vol 123, 1979, S.468 -92
• Arima, Iachello Interacting Boson Model The, Annual Review of Nuclear and Particle Science Vol 31, 1981, p.75
• Nuclear physics
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