Theory of collective vibrations of even-even spheroidal nuclei

Thesis/Dissertation · Thu Mar 01 00:00:00 EST 1962

DOI:https://doi.org/10.2172/4787134· OSTI ID:4787134

Marshalek, Eugene R. ^[1]

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1. Univ. of California, Berkeley, CA (United States)

A version of the Inglis "cranking model'' is presented which describes nuclear shape oscillations without the adiabatic approximation. The collective frequencies of a system of particles moving in a time-dependent shell model potential are obtained as solutions of a dispersion equation usually associated with the random phase approximation (RPA). The method used is equivalent to an extension of the cranking model first devised by Araujo. It is shown that the form of the dispersion equation follows from a suitable definition of vibrational spectrum'' in a system with coupled collective and intrinsic degrees of freedom. It is also shown that the generalized cranking model is equivalent to the time-dependent self-consistent field method applied to an appropriate long-range two-body force. Extensive numerical applications are made to quadrupole vibrations of even-even deformed nuclei, using Nilsson's single particle eigenvalues and asymptotic wave functions, and taking residual pairing interactions into account by means of the Bogolyubov canonical transformation method. Vibrational frequencies, mass parameters, force constants, reduced electric quadrupole transition probabilities, and vibration-rotation interaction coefficients of the "BETA" and "gamma" quadrupole modes are theoretically estimated for rare earth and actinide isotopes, and compared with experimental values.

• Research Organization: Univ. of California, Berkeley, CA (United States)
• Sponsoring Organization: US Atomic Energy Commission (AEC)
• DOE Contract Number: W-7405-ENG-48
• NSA Number: NSA-16-029787
• OSTI ID: 4787134
• Report Number(s): UCRL-10046
• Resource Relation: Other Information: Orig. Receipt Date: 31-DEC-62
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ACTINIDES
BOGOLIUBOV METHOD
CRANKING MODEL
DEFORMATION
DEFORMED NUCLEI
DIFFERENTIAL EQUATIONS
DISPERSION THEORY
EIGENVALUES
ENERGY LEVELS
EVEN EVEN NUCLEI
FREQUENCY
INTERACTIONS
MOTION
NILSSON MODEL
NUCLEAR MODELS
NUCLEI
NUCLEONS
NUMERICALS
OSCILLATIONS
PARTICLES
PROBABILITY
QUADRUPOLES
QUANTUM MECHANICS
RARE EARTHS
SHELL MODELS
SPHERES
STATISTICS
TRANSITIONS