# Theoretical studies in nuclear structure. [Self-consistent cranking model for anharmonic collective vibrational states]

## Abstract

Two topics of current interest strongly anharmonic collective vibrations and collective rotation about a tilted axis - have been related through a theorem proposed by the principal in Theorem, states that if a system has an axis of rotational symmetry in a static mean-field approximation, then self-consistent cranking about this axis gives rise to symmetry-breaking bifurcations that occur for critical cranking frequencies [Omega][sub c] given by [Omega][sub c] = [omega][sub [mu]]/K[sub [mu]], where [omega][sub [mu]] is the small-oscillation (RPA) frequency of any normal mode carrying [h bar]K[sub [mu]] ([ne] 0) units of angular momentum along the symmetry axis. The bifurcations represent families of anharmonic oscillations built on the axially symmetric mean field. For certain values of K[sub [mu]], the solutions appear as rotations about an axis that is tilted with respect to the principal axis of the density distribution. The theorem has been tested on some simple models in preparation for more realistic calculations that are planned for the near future.

- Authors:

- Publication Date:

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

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

- OSTI Identifier:
- 6609040

- Report Number(s):
- DOE/ER/40640-2

ON: DE93012290

- 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; VIBRATIONAL STATES; CRANKING MODEL; MEAN-FIELD THEORY; PROGRESS REPORT; RANDOM PHASE APPROXIMATION; SELF-CONSISTENT FIELD; DOCUMENT TYPES; ENERGY LEVELS; EXCITED STATES; MATHEMATICAL MODELS; NUCLEAR MODELS; NUCLEI; 663110* - General & Average Properties of Nuclei & Nuclear Energy Levels- (1992-)

### Citation Formats

```
Marshalek, E R.
```*Theoretical studies in nuclear structure. [Self-consistent cranking model for anharmonic collective vibrational states]*. United States: N. p., 1992.
Web. doi:10.2172/6609040.

```
Marshalek, E R.
```*Theoretical studies in nuclear structure. [Self-consistent cranking model for anharmonic collective vibrational states]*. United States. https://doi.org/10.2172/6609040

```
Marshalek, E R. 1992.
"Theoretical studies in nuclear structure. [Self-consistent cranking model for anharmonic collective vibrational states]". United States. https://doi.org/10.2172/6609040. https://www.osti.gov/servlets/purl/6609040.
```

```
@article{osti_6609040,
```

title = {Theoretical studies in nuclear structure. [Self-consistent cranking model for anharmonic collective vibrational states]},

author = {Marshalek, E R},

abstractNote = {Two topics of current interest strongly anharmonic collective vibrations and collective rotation about a tilted axis - have been related through a theorem proposed by the principal in Theorem, states that if a system has an axis of rotational symmetry in a static mean-field approximation, then self-consistent cranking about this axis gives rise to symmetry-breaking bifurcations that occur for critical cranking frequencies [Omega][sub c] given by [Omega][sub c] = [omega][sub [mu]]/K[sub [mu]], where [omega][sub [mu]] is the small-oscillation (RPA) frequency of any normal mode carrying [h bar]K[sub [mu]] ([ne] 0) units of angular momentum along the symmetry axis. The bifurcations represent families of anharmonic oscillations built on the axially symmetric mean field. For certain values of K[sub [mu]], the solutions appear as rotations about an axis that is tilted with respect to the principal axis of the density distribution. The theorem has been tested on some simple models in preparation for more realistic calculations that are planned for the near future.},

doi = {10.2172/6609040},

url = {https://www.osti.gov/biblio/6609040},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1992},

month = {12}

}