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Title: NUCLEAR MOMENTS OF INERTIA AND EFFECTIVE NUCLEON MASS

Abstract

The nuclear moment of inertia may be calculated as the sum of individual- nucleon contributions by treating the dynamics of one sample nucleon in the ellipsoidal harmonic-oscillator potential representing its interaction with the others, on the plausible assumption that the moment of inertia due to all the other nucleons is simply associated with the orientation of the axes of the distortion ellipsoid. The ellipsoid is allowed to rotate freely (in two dimensions) with conservation of angular momentum, but the treatment is rather similar to that given earlier on the basis of a constant angular velocity of the ellipsoid ( cranked model''), and the result is the same. The moment of inertia has the rigid value when the magnitude of the distortion of an open-shell nucleus is obtained in the most simple manner, by minimizing the sum of the oscillator energies with constant nuclear volume. The analogous problem of linear translation may be similarly treated. The moments of inertia of highly distorted nuclei are observed to be about half of the rigid value. One might hope to understand this discrepancy in terms of the nucleonic effective mass'' M/sub e/ approximately 1/2M which appears in some problems involving nucleons passing through nuclearmore » matter, and is required in the shell model to reconcile excitation with binding energies. The shell-model-type assumption considered most plausible is that the effective mass arises from simple dependence of the potential not on the canonical momentum but on the nucleon velocity relative to the axes of the rotating ellipsoid, and this is the assumption whose analogue gives a sensible result in the linear problem. The velocity dependence is taken to be a quadratic one, giving a simple expression for M/sub e/. It is shown that, with these assumptions, M/sub e/ is not effective for the moment-of-inertia problem and one still obtains the rigid value. (auth)« less

Authors:
Publication Date:
Research Org.:
CERN, Geneva
OSTI Identifier:
4302192
NSA Number:
NSA-13-000883
Resource Type:
Journal Article
Journal Name:
Nuclear Phys.
Additional Journal Information:
Journal Volume: Vol: 8; Other Information: Orig. Receipt Date: 31-DEC-59
Country of Publication:
Country unknown/Code not available
Language:
English
Subject:
PHYSICS AND MATHEMATICS; ANGULAR MOMENTUM; DEFORMATION; ENERGY; INTERACTIONS; MASS; MOMENTUM; NUCLEAR MODELS; NUCLEONS; OSCILLATIONS; QUANTUM MECHANICS; ROTATION; SHELL MODELS; VELOCITY; VOLUME

Citation Formats

Inglis, D R. NUCLEAR MOMENTS OF INERTIA AND EFFECTIVE NUCLEON MASS. Country unknown/Code not available: N. p., 1958. Web. doi:10.1016/0029-5582(58)90141-X.
Inglis, D R. NUCLEAR MOMENTS OF INERTIA AND EFFECTIVE NUCLEON MASS. Country unknown/Code not available. https://doi.org/10.1016/0029-5582(58)90141-X
Inglis, D R. 1958. "NUCLEAR MOMENTS OF INERTIA AND EFFECTIVE NUCLEON MASS". Country unknown/Code not available. https://doi.org/10.1016/0029-5582(58)90141-X.
@article{osti_4302192,
title = {NUCLEAR MOMENTS OF INERTIA AND EFFECTIVE NUCLEON MASS},
author = {Inglis, D R},
abstractNote = {The nuclear moment of inertia may be calculated as the sum of individual- nucleon contributions by treating the dynamics of one sample nucleon in the ellipsoidal harmonic-oscillator potential representing its interaction with the others, on the plausible assumption that the moment of inertia due to all the other nucleons is simply associated with the orientation of the axes of the distortion ellipsoid. The ellipsoid is allowed to rotate freely (in two dimensions) with conservation of angular momentum, but the treatment is rather similar to that given earlier on the basis of a constant angular velocity of the ellipsoid ( cranked model''), and the result is the same. The moment of inertia has the rigid value when the magnitude of the distortion of an open-shell nucleus is obtained in the most simple manner, by minimizing the sum of the oscillator energies with constant nuclear volume. The analogous problem of linear translation may be similarly treated. The moments of inertia of highly distorted nuclei are observed to be about half of the rigid value. One might hope to understand this discrepancy in terms of the nucleonic effective mass'' M/sub e/ approximately 1/2M which appears in some problems involving nucleons passing through nuclear matter, and is required in the shell model to reconcile excitation with binding energies. The shell-model-type assumption considered most plausible is that the effective mass arises from simple dependence of the potential not on the canonical momentum but on the nucleon velocity relative to the axes of the rotating ellipsoid, and this is the assumption whose analogue gives a sensible result in the linear problem. The velocity dependence is taken to be a quadratic one, giving a simple expression for M/sub e/. It is shown that, with these assumptions, M/sub e/ is not effective for the moment-of-inertia problem and one still obtains the rigid value. (auth)},
doi = {10.1016/0029-5582(58)90141-X},
url = {https://www.osti.gov/biblio/4302192}, journal = {Nuclear Phys.},
number = ,
volume = Vol: 8,
place = {Country unknown/Code not available},
year = {1958},
month = {9}
}