# Theoretical studies in nuclear structure

## 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; USDOE, Washington, DC (United States)

- OSTI Identifier:
- 6048868

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

ON: DE92004025

- DOE Contract Number:
- FG02-91ER40640

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; DEFORMED NUCLEI; COLLECTIVE MODEL; NUCLEAR STRUCTURE; ANGULAR MOMENTUM; HAMILTONIANS; HARMONIC OSCILLATORS; MATRIX ELEMENTS; MOMENT OF INERTIA; PROGRESS REPORT; ROTATION; DOCUMENT TYPES; ELECTRONIC EQUIPMENT; EQUIPMENT; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MOTION; NUCLEAR MODELS; NUCLEI; OSCILLATORS; QUANTUM OPERATORS; 663120* - Nuclear Structure Models & Methods- (1992-)

### Citation Formats

```
Marshalek, E R.
```*Theoretical studies in nuclear structure*. United States: N. p., 1991.
Web. doi:10.2172/6048868.

```
Marshalek, E R.
```*Theoretical studies in nuclear structure*. United States. https://doi.org/10.2172/6048868

```
Marshalek, E R. 1991.
"Theoretical studies in nuclear structure". United States. https://doi.org/10.2172/6048868. https://www.osti.gov/servlets/purl/6048868.
```

```
@article{osti_6048868,
```

title = {Theoretical studies in nuclear structure},

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 = {10.2172/6048868},

url = {https://www.osti.gov/biblio/6048868},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1991},

month = {11}

}