# A microscopic derivation of nuclear collective rotation-vibration model and its application to nuclei

## Abstract

We derive a microscopic version of the successful phenomenological hydrodynamic model of Bohr-Davydov-Faessler-Greiner for collective rotation-vibration motion of an axially symmetric deformed nucleus. The derivation is not limited to small oscillation amplitude. The nuclear Schrodinger equation is canonically transformed to collective co-ordinates, which is then linearized using a constrained variational method. The associated constraints are imposed on the wavefunction rather than on the particle co-ordinates. The approach yields three self-consistent, time-reversal invariant, cranking-type Schrodinger equations for the rotation-vibration and intrinsic motions, and a self-consistency equation. For harmonic oscillator mean-field potentials, these equations are solved in closed forms for excitation energy, cut-off angular momentum, and other nuclear properties for the ground-state rotational band in some deformed nuclei. The results are compared with measured data.

- Authors:

- NUTECH Services, 3313 Fenwick Crescent, Mississauga, Ontario, L5L 5N1 (Canada)

- Publication Date:

- OSTI Identifier:
- 22608492

- Resource Type:
- Journal Article

- Journal Name:
- AIP Conference Proceedings

- Additional Journal Information:
- Journal Volume: 1753; Journal Issue: 1; Conference: Latin American symposium on nuclear physics and applications, Medellin (Colombia), 30 Nov - 4 Dec 2015; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; AXIAL SYMMETRY; DEFORMED NUCLEI; EXCITATION; GROUND STATES; HARMONIC OSCILLATORS; HYDRODYNAMIC MODEL; MEAN-FIELD THEORY; NUCLEAR PROPERTIES; OSCILLATIONS; ROTATION; ROTATIONAL STATES; ROTATION-VIBRATION MODEL; SCHROEDINGER EQUATION; VARIATIONAL METHODS; WAVE FUNCTIONS

### Citation Formats

```
Gulshani, P., E-mail: matlap@bell.net.
```*A microscopic derivation of nuclear collective rotation-vibration model and its application to nuclei*. United States: N. p., 2016.
Web. doi:10.1063/1.4955344.

```
Gulshani, P., E-mail: matlap@bell.net.
```*A microscopic derivation of nuclear collective rotation-vibration model and its application to nuclei*. United States. doi:10.1063/1.4955344.

```
Gulshani, P., E-mail: matlap@bell.net. Thu .
"A microscopic derivation of nuclear collective rotation-vibration model and its application to nuclei". United States. doi:10.1063/1.4955344.
```

```
@article{osti_22608492,
```

title = {A microscopic derivation of nuclear collective rotation-vibration model and its application to nuclei},

author = {Gulshani, P., E-mail: matlap@bell.net},

abstractNote = {We derive a microscopic version of the successful phenomenological hydrodynamic model of Bohr-Davydov-Faessler-Greiner for collective rotation-vibration motion of an axially symmetric deformed nucleus. The derivation is not limited to small oscillation amplitude. The nuclear Schrodinger equation is canonically transformed to collective co-ordinates, which is then linearized using a constrained variational method. The associated constraints are imposed on the wavefunction rather than on the particle co-ordinates. The approach yields three self-consistent, time-reversal invariant, cranking-type Schrodinger equations for the rotation-vibration and intrinsic motions, and a self-consistency equation. For harmonic oscillator mean-field potentials, these equations are solved in closed forms for excitation energy, cut-off angular momentum, and other nuclear properties for the ground-state rotational band in some deformed nuclei. The results are compared with measured data.},

doi = {10.1063/1.4955344},

journal = {AIP Conference Proceedings},

issn = {0094-243X},

number = 1,

volume = 1753,

place = {United States},

year = {2016},

month = {7}

}