# Theoretical studies in nuclear structure. Progress report, June 1, 1991--November 30, 1991

## Abstract

In this period, the work has centered on two topics. The first is the study of a novel type of collective rotation in which an atomic nucleus with an inversion-symmetric shape rotates uniformly about an axis that is not a principal axis of the quadrupole tensor of the density distribution. This mode is referred to as tilted rotation. By using the cranking model together with higher-order corrections, it was shown that tilted rotation is indeed possible, not only within a microscopic framework, but also within the framework of collective models such as the IBM. The maximum tilt angle of {pi}/4 is realized for a certain class of states in the U(5) limit. The second topic, which actually was suggested during the course of the first investigation, is concerned with a new way of representing collective harmonic-oscillator algebras using boson-mapping techniques. In this approach, the many-phonon eigenvectors of a 2{lambda}+1-dimensional oscillator having good angular momentum are represented by simple products of boson operators acting on a vacuum. This representation may simplify the calculation of reduced matrix elements of arbitrary operators in collective models, but more work needs to be done.

- Authors:

- Publication Date:

- Research Org.:
- Notre Dame Univ., IN (United States)

- Sponsoring Org.:
- USDOE, Washington, DC (United States)

- OSTI Identifier:
- 10107501

- Report Number(s):
- DOE/ER/40640-1

ON: DE92004025

- DOE Contract Number:
- FG02-91ER40640

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: Nov 1991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; NUCLEAR STRUCTURE; DEFORMED NUCLEI; COLLECTIVE MODEL; PROGRESS REPORT; ANGULAR MOMENTUM; HARMONIC OSCILLATORS; MATRIX ELEMENTS; HAMILTONIANS; ROTATION; MOMENT OF INERTIA; 663120; NUCLEAR STRUCTURE MODELS AND METHODS

### Citation Formats

```
Marshalek, E R.
```*Theoretical studies in nuclear structure. Progress report, June 1, 1991--November 30, 1991*. United States: N. p., 1991.
Web. doi:10.2172/10107501.

```
Marshalek, E R.
```*Theoretical studies in nuclear structure. Progress report, June 1, 1991--November 30, 1991*. United States. https://doi.org/10.2172/10107501

```
Marshalek, E R. 1991.
"Theoretical studies in nuclear structure. Progress report, June 1, 1991--November 30, 1991". United States. https://doi.org/10.2172/10107501. https://www.osti.gov/servlets/purl/10107501.
```

```
@article{osti_10107501,
```

title = {Theoretical studies in nuclear structure. Progress report, June 1, 1991--November 30, 1991},

author = {Marshalek, E R},

abstractNote = {In this period, the work has centered on two topics. The first is the study of a novel type of collective rotation in which an atomic nucleus with an inversion-symmetric shape rotates uniformly about an axis that is not a principal axis of the quadrupole tensor of the density distribution. This mode is referred to as tilted rotation. By using the cranking model together with higher-order corrections, it was shown that tilted rotation is indeed possible, not only within a microscopic framework, but also within the framework of collective models such as the IBM. The maximum tilt angle of {pi}/4 is realized for a certain class of states in the U(5) limit. The second topic, which actually was suggested during the course of the first investigation, is concerned with a new way of representing collective harmonic-oscillator algebras using boson-mapping techniques. In this approach, the many-phonon eigenvectors of a 2{lambda}+1-dimensional oscillator having good angular momentum are represented by simple products of boson operators acting on a vacuum. This representation may simplify the calculation of reduced matrix elements of arbitrary operators in collective models, but more work needs to be done.},

doi = {10.2172/10107501},

url = {https://www.osti.gov/biblio/10107501},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1991},

month = {11}

}