Collective rotations and moments of inertia in the classical mechanics of a deformed oscillator shell model
An alternative to the concepts of the rigid rotor or of the liquid drop as points of departure for the description of collective nuclear motions is presented. The Lagrangian and Hamiltonian of a classical system of A bodies of equal mass are expressed in terms of nonredundant dynamical coordinates defined microscopically so as to correspond to the rotational and vibrational degrees of freedom used customarily in models of collective nuclear motions. Three dynamical coordinates describe the orientation of the principal axes of the tensor of inertia, and three coordinates describe the principal moments of inertia. The potential energy is assumed to depend only on the principal moments of inertia, so that the Lagnangian and Hamiltonian have simple separable forms. The orientation of the principal axes and the intrinsic structure are specified as functionals, rather than point functions, of angular coordinates. The relationships between the equilibrium values of the moments of inertia, the total angular momentum, and other constants of the motion are unambiguous and complete, and these form the basis for a classical theory of the mass parameter of collective rotations for axially symmetric systems. A type of collective motion which is neither a rotation of principal axes nor a shape oscillation appears naturally in this approach. The motion may be intuitively pictured as a coherent flow, and a constant of the motion roughly describable as the vorticity of the flow plays a key role in the description of moments of inertia. The calculation of the energy of axially symmetric systems, if the condition of shape equilibrium is postulated, is found to be formally analogous to the procedures of the variable-moment-of-inertia model. (4 figures) (auth)
- Research Organization:
- Hahn Meitner Institut fuer Kernforschung, Berlin
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-29-025651
- OSTI ID:
- 4334703
- Journal Information:
- Nucl. Phys., A, v. A221, no. 3, pp. 608-628, Other Information: Orig. Receipt Date: 30-JUN-74
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
Similar Records
Simplified description of. gamma. vibrations in permanently deformed nuclei
THE ROTATIONAL PROPERTIES OF NUCLEI