# NUCLEAR ROTATIONAL SPECTRA, THE ELLIOTT MODEL, AND THE P$sub 2$ FORCE

## Abstract

The essentisl features of the Elliott Model with the momentum-dependent quadrupole-quadrupole operator which leads to L(L + 1) rotational spectra are reviewed. The operator is reduced to a momentum-independent residual interaction differing from the P/sub 2/ interaction. The model Hamiltonian is separated into a rotational Hamiltonian, a deformed intrinsic" Hamiltonian, and a perturbation term. The eigenfunctions and eigenvalues of the intrinsic" Hamiltonian are found and used in Inglis' cranking model formula to calculate the moment of inertia. The model is modified by taking a mixture of the long-range P/sub 2/" interaction with the short-range delta -function force. For an intermediate mixture, the spectrum obtained resembles the spectrum predicted by the collective vibrational model. Finally, the implications of a P/sub 2/ residual interaction for direct-interaction inelastic scattering processes are considered. The question is discussed whether the P/sub 2/ residual interaction may be observed in rotational nuclei, and, it so, whether the strength of the P/sub 2/ interaction scattering experiments is consistent with that determined from the observed rotational spectra. Within the rough approximations made, the few experimental results available are not inconsistent with the calculation. (auth)

- Authors:

- Publication Date:

- Research Org.:
- Stanford Univ., Calif.

- OSTI Identifier:
- 4823493

- NSA Number:
- NSA-16-023118

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

- Additional Journal Information:
- Journal Volume: Vol: 126; Other Information: Orig. Receipt Date: 31-DEC-62

- Country of Publication:
- Country unknown/Code not available

- Language:
- English

- Subject:
- PHYSICS; DIFFERENTIAL EQUATIONS; DIRECT REACTIONS; EIGENFUNCTIONS; EIGENVALUES; HAMILTONIAN; INERTIAL FORCE; INTERACTIONS; MATHEMATICS; MOMENT OF INERTIA; MOMENTUM; NUCLEAR MODELS; NUCLEAR REACTIONS; NUCLEI; NUMERICALS; ROTATION; SCATTERING; SPECTRA

### Citation Formats

```
Willey, R S.
```*NUCLEAR ROTATIONAL SPECTRA, THE ELLIOTT MODEL, AND THE P$sub 2$ FORCE*. Country unknown/Code not available: N. p., 1962.
Web. doi:10.1103/PhysRev.126.1127.

```
Willey, R S.
```*NUCLEAR ROTATIONAL SPECTRA, THE ELLIOTT MODEL, AND THE P$sub 2$ FORCE*. Country unknown/Code not available. https://doi.org/10.1103/PhysRev.126.1127

```
Willey, R S. 1962.
"NUCLEAR ROTATIONAL SPECTRA, THE ELLIOTT MODEL, AND THE P$sub 2$ FORCE". Country unknown/Code not available. https://doi.org/10.1103/PhysRev.126.1127.
```

```
@article{osti_4823493,
```

title = {NUCLEAR ROTATIONAL SPECTRA, THE ELLIOTT MODEL, AND THE P$sub 2$ FORCE},

author = {Willey, R S},

abstractNote = {The essentisl features of the Elliott Model with the momentum-dependent quadrupole-quadrupole operator which leads to L(L + 1) rotational spectra are reviewed. The operator is reduced to a momentum-independent residual interaction differing from the P/sub 2/ interaction. The model Hamiltonian is separated into a rotational Hamiltonian, a deformed intrinsic" Hamiltonian, and a perturbation term. The eigenfunctions and eigenvalues of the intrinsic" Hamiltonian are found and used in Inglis' cranking model formula to calculate the moment of inertia. The model is modified by taking a mixture of the long-range P/sub 2/" interaction with the short-range delta -function force. For an intermediate mixture, the spectrum obtained resembles the spectrum predicted by the collective vibrational model. Finally, the implications of a P/sub 2/ residual interaction for direct-interaction inelastic scattering processes are considered. The question is discussed whether the P/sub 2/ residual interaction may be observed in rotational nuclei, and, it so, whether the strength of the P/sub 2/ interaction scattering experiments is consistent with that determined from the observed rotational spectra. Within the rough approximations made, the few experimental results available are not inconsistent with the calculation. (auth)},

doi = {10.1103/PhysRev.126.1127},

url = {https://www.osti.gov/biblio/4823493},
journal = {Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D},

number = ,

volume = Vol: 126,

place = {Country unknown/Code not available},

year = {1962},

month = {5}

}