OCTUPOLE VIBRATIONS OF SPHEROIDAL EVEN-EVEN NUCLEI

Journal Article · Sun Apr 01 00:00:00 EST 1962 · Dissertation Abstr.

OSTI ID:4820213

Lipas, P O

A theory is proposed for the low-lying odd parity states in deformed even-even nuclei in terms of collective octupole vibrations of the nuclear surface. As an introduction, the problem of quadrupole vibrations in spheroidal eveneven nuclei is reviewed in analytical detail within the context of the Bohr- Mottelson model. With the octupole degrees of freedom corresponding to the spherical harmonics Y/sub 30/ and Y/sub 3 plus or minus 2/, or with those corresponding to Y/sub 3 plus or minus 1/ and Y/sub 3 plus or minus 3/, the Hamiltonian obtained with the hydrodynamic moments of inertia is found to separate into a rotational and a vibrational part. Either pair of octupole degrees of freedom is combined with the usual quadrupole degrees of freedom, BETA and gamma , and small oscillations about a spheroidal equilibrium shape are considered. The arbitrarily restricted choice of the octupole degrees of freedom can be supported only by direct comparison with experiment. With the choice of Y//sub 30/ and Y/sub 3 plus or minus 2/ as the octupole degrees of freedom, the Schrodinger equation immediately yields the usual BETA vibrational state with a superimposed rotational band (K = 0, 1 = 0+, 2+, 41,...) and a b vibrational'' state with a superimposed rotational band (K = 0, I = 1-, a degenerate perturbation problera. The result gives rise to two vibrational states with K = 2, which are interpreted as the gamma vibration (even parity) and a g vibration ' (odd parity); the associated rotational bands both have I = 2, are also considered. The case of Y/sub 3 plus or minus 1/ and Y/sub 3 plus or minus 3/ as the octupole degrees of freedom is developed to the point where the remaining problem is purely mathematical. The resulting linear partial differential equation apparently requires a nuraerical solution. Perturbation corrections to the moment of inertia are calculated for the quadrupoleoctupole case with the Y/sub 30/ and Y/sub 3 plus or minus 2/ degrees of freedom. The reduced El, E2, and E3 gamma transition probabilities are calculated for all possible transitions between the bands (Ml transitions are forbidden). The model with Y/sub 30/ and Y/sub 3 plus or minus 2/ as the octupole degrees of freedom predicts the K = 0- and K = 2- bands observed in deformed eveneven nuclei. Theoretical and experimental values for J/J/sub gr/, where J is the moment of inertia in a vibrational band and J/sub gr/ is the ground state moment of inertia, are in fair agreement. Otherwise, few meaningful quantitative comparisons can be made due to the sparsity of experi mental data on the higher vibrational states and on gamma transitions between the bands.

• Research Organization: Rensselaer Polytechnic Inst., Troy, N.Y.
• NSA Number: NSA-16-024302
• OSTI ID: 4820213
• Journal Information: Dissertation Abstr., Vol. Vol: 22; Other Information: Orig. Receipt Date: 31-DEC-62
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

PHYSICS
COLLECTIVE MODEL
DEFORMATION
DIFFERENTIAL EQUATIONS
ELECTRIC MOMENTS
ENERGY LEVELS
EVEN EVEN NUCLEI
GAMMA RADIATION
INERTIAL FORCE
MOMENT OF INERTIA
NILSSON-MOTTELSON MODEL
NUCLEAR MODELS
NUCLEI
OCTUPOLES
OSCILLATIONS
PARITY
QUANTUM MECHANICS
ROTATION
SCHROEDINGER EQUATION
TRANSIENTS
VIBRATIONS