# A REMARK ON THE MOMENTS OF INERTIA OF ROTATING NUCLEI

## Abstract

The quantum mechanical description of a two dimensional rotating system of particles is studed to elucidate the meaning of the effective moments of inertia of nuclei. The method of canonical transformations is employed. The rotational kinetic energy of a canonical form'' is obtained by introducing an internal angular momentum L/sub in/. The Coriolis force arising from the coupling of L/sub in/ with the rotational angular velocity is found to be responsible for the deviation of the moment of inertia from its hydrodynamical value. The explicit form of L/sub in/ is given as a function of the positions and momenta of individual particles. This form of L/sub in/ should be used for deriving the eIfective moment of inertia. Comparison with the cranking model of Inglis is discussed. (auth) Results of measurement of the energy dependence of the cross sections are presented for the following reactions: (n, gamma ) in Fe, Pb, and Cl; (n,p) in He/sup 3/, N/sup 14/, and Cl; and (n, alpha ) in Li/sup 6/ and B/sup 10/. Neutron energies up to 30 kev were employed. It is shown that the cross section for the B/sup 10/(n, alpha ) reaction lies below the 1/v law, the deviation beingmore »

- Authors:

- Publication Date:

- Research Org.:
- Kyoto Univ.

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 4341761

- NSA Number:
- NSA-12-008703

- Resource Type:
- Journal Article

- Journal Name:
- Progr. Theoret. Phys. (Kyoto)

- Additional Journal Information:
- Journal Volume: Vol: 18; Other Information: Orig. Receipt Date: 31-DEC-58

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

- Language:
- English

- Subject:
- PHYSICS; CORIOLIS FORCE; FLUID FLOW; MATHEMATICS; MECHANICS; MOMENTUM; NUCLEAR MODELS; NUCLEI; NUCLEONS; QUANTUM MECHANICS; ROTATION; VELOCITY

### Citation Formats

```
Hayakawa, S, and Marumori, T.
```*A REMARK ON THE MOMENTS OF INERTIA OF ROTATING NUCLEI*. Country unknown/Code not available: N. p., 1957.
Web. doi:10.1143/PTP.18.396.

```
Hayakawa, S, & Marumori, T.
```*A REMARK ON THE MOMENTS OF INERTIA OF ROTATING NUCLEI*. Country unknown/Code not available. https://doi.org/10.1143/PTP.18.396

```
Hayakawa, S, and Marumori, T. 1957.
"A REMARK ON THE MOMENTS OF INERTIA OF ROTATING NUCLEI". Country unknown/Code not available. https://doi.org/10.1143/PTP.18.396.
```

```
@article{osti_4341761,
```

title = {A REMARK ON THE MOMENTS OF INERTIA OF ROTATING NUCLEI},

author = {Hayakawa, S and Marumori, T},

abstractNote = {The quantum mechanical description of a two dimensional rotating system of particles is studed to elucidate the meaning of the effective moments of inertia of nuclei. The method of canonical transformations is employed. The rotational kinetic energy of a canonical form'' is obtained by introducing an internal angular momentum L/sub in/. The Coriolis force arising from the coupling of L/sub in/ with the rotational angular velocity is found to be responsible for the deviation of the moment of inertia from its hydrodynamical value. The explicit form of L/sub in/ is given as a function of the positions and momenta of individual particles. This form of L/sub in/ should be used for deriving the eIfective moment of inertia. Comparison with the cranking model of Inglis is discussed. (auth) Results of measurement of the energy dependence of the cross sections are presented for the following reactions: (n, gamma ) in Fe, Pb, and Cl; (n,p) in He/sup 3/, N/sup 14/, and Cl; and (n, alpha ) in Li/sup 6/ and B/sup 10/. Neutron energies up to 30 kev were employed. It is shown that the cross section for the B/sup 10/(n, alpha ) reaction lies below the 1/v law, the deviation being smaller than 5 to 10%. The deviation of the Li/sup 6/(n, alpha ) cross section from the 1/v law is even less. lt is concluded that the Bti nucleus has an excited level vdth an angular momentum J = 5/2/sup +/ or 7/2/sup +/ , a neutron resonance energy E/sub r/ ~250 kev, and widths GAMMA /sub alpha / ~ 400 and GAMMA /sub n/ ~ 200 kev. An appreciable deviation of the He/sup 3/(n,p) cross section from the 1/v law has been detected which may indicate the existence in the He/sup 4/ nucleus of an excited level vdth one of the two sets of parameters: 1) J u 1/sup +/, --E/sub r/ ~ 200 kev, proton width for an excitation energy equal to the neutron binding energy GAMMA p/sup o/ ~ 200 kev and 2) J = 0/ sup +/, --E/sub r/ ~ 500 kev, GAMMA /sub p/o ~ 1200 kev. (auth)},

doi = {10.1143/PTP.18.396},

url = {https://www.osti.gov/biblio/4341761},
journal = {Progr. Theoret. Phys. (Kyoto)},

number = ,

volume = Vol: 18,

place = {Country unknown/Code not available},

year = {1957},

month = {10}

}