# Deformation of nuclei as a function of angular momentum in the U(6)containsSU(3) model

## Abstract

In the framework of a hybrid rotational model, proposed recently by Moshinsky as a consequence of a comparison between the Gneuss and Greiner extension of the Bohr and Mottelson model and the interacting boson model, we study the shape of nuclei by calculating the average of the expectation value of the square of the deformation parameter ..beta.. with respect to the rotational states with the same angular momentum belonging to a given irreducible representation of SU(3). This work generalises to three dimensions the corresponding analysis carried out in two dimensions by Chacon, Moshinsky, and Vanagas. We use the canonical chain for U(3), i.e.,the chain U(6)containsU(3)containsU(2)containsU(1), to obtain an analytical formula for the quantity studied. We bring out the overall stretching effect of the angular momentum on the shape of nuclei. The influence of other parameters, such as the boson number and the irreducible representation of SU(3), is also studied.

- Authors:

- Publication Date:

- Research Org.:
- Institut de Physique Nucleaire (and I N2 P3), Universite Claude Bernard-1, 43, Bd. du 11 Novembre 1918, 69622 Villeurbanne Cedex, France

- OSTI Identifier:
- 5876168

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Ann. Phys. (N.Y.); (United States); Journal Volume: 136:2

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; DEFORMED NUCLEI; ROTATIONAL STATES; ANGULAR MOMENTUM; EXPECTATION VALUE; HAMILTONIANS; INTERACTING BOSON MODEL; IRREDUCIBLE REPRESENTATIONS; NILSSON-MOTTELSON MODEL; SU-3 GROUPS; U-6 GROUPS; ENERGY LEVELS; EXCITED STATES; LIE GROUPS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NUCLEAR MODELS; NUCLEI; QUANTUM OPERATORS; SHELL MODELS; SU GROUPS; SYMMETRY GROUPS; U GROUPS; 653007* - Nuclear Theory- Nuclear Models- (-1987); 653004 - Nuclear Theory- Nuclear Moments & Spin- (-1987)

### Citation Formats

```
Partensky, A.
```*Deformation of nuclei as a function of angular momentum in the U(6)containsSU(3) model*. United States: N. p., 1981.
Web. doi:10.1016/0003-4916(81)90102-0.

```
Partensky, A.
```*Deformation of nuclei as a function of angular momentum in the U(6)containsSU(3) model*. United States. doi:10.1016/0003-4916(81)90102-0.

```
Partensky, A. Thu .
"Deformation of nuclei as a function of angular momentum in the U(6)containsSU(3) model". United States. doi:10.1016/0003-4916(81)90102-0.
```

```
@article{osti_5876168,
```

title = {Deformation of nuclei as a function of angular momentum in the U(6)containsSU(3) model},

author = {Partensky, A.},

abstractNote = {In the framework of a hybrid rotational model, proposed recently by Moshinsky as a consequence of a comparison between the Gneuss and Greiner extension of the Bohr and Mottelson model and the interacting boson model, we study the shape of nuclei by calculating the average of the expectation value of the square of the deformation parameter ..beta.. with respect to the rotational states with the same angular momentum belonging to a given irreducible representation of SU(3). This work generalises to three dimensions the corresponding analysis carried out in two dimensions by Chacon, Moshinsky, and Vanagas. We use the canonical chain for U(3), i.e.,the chain U(6)containsU(3)containsU(2)containsU(1), to obtain an analytical formula for the quantity studied. We bring out the overall stretching effect of the angular momentum on the shape of nuclei. The influence of other parameters, such as the boson number and the irreducible representation of SU(3), is also studied.},

doi = {10.1016/0003-4916(81)90102-0},

journal = {Ann. Phys. (N.Y.); (United States)},

number = ,

volume = 136:2,

place = {United States},

year = {Thu Oct 15 00:00:00 EDT 1981},

month = {Thu Oct 15 00:00:00 EDT 1981}

}