LSU Historical Dissertations and Theses

1996

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics and Astronomy

Jerry P. Draayer

Abstract

The origin and validity of pseudospin symmetry, which is characteristic for heavy atomic nuclei (\$A \ge 100\$), are discussed. The transformation to the pseudospin representation for physically significant operators is performed by means of specially designed analytical techniques. The many-particle helicity operator is found to accomplish the transformation to the pseudospin basis in the scope of realistic nuclear models. Estimates based on both nonrelativistic mean-field and relativistic Dirac-Brueckner results show that in the helicity-transformed space nucleons move in a finite-depth, strongly nonlocal, potential with an effectively reduced spin-orbit strength. Since the chirality operation is the limiting case of the helicity operation for massless hadrons, the difference between the standard and helicity-transformed representation disappears in the high-energy chiral limit. A procedure for applications of the pseudospin transformation within the frame-work of the spherical oscillator shell model is developed. It is valid for operators expressed in terms of single-particle variables and is based on permutation rules for special rotational invariants. The procedure is applied to a number of physical operators including several rotational scalars, the spin and orbital momenta, and the quadrupole moment. An algorithm for generating an approximation to the pseudospin transformation, which gives a simple and accurate expression for dominant parts of required transforms, is also given. The algebras associated with pseudospin transformations are considered. The analytical results thus obtained constitute the necessary input data for the nuclear structure calculations within the pseudo SU(3) algebraic collective model and its symplectic extension. An operator, responsible for the transformation to the pseudospin representation within the oscillator shell model at an arbitrary triaxial deformation, is constructed as a special projection of the momentum helicity operator. Since the exact transformation of relevant operators cannot be performed in a closed analytical form, a procedure of approximate transformation is formulated as a generalization of the similar procedure for the spherical shell model. In the spherical and asymptotic prolate limits the transforms thus derived reduce to the familiar exact results. The approximate transform of a modified Nilsson Hamiltonian is found to be almost indistinguishable from the "pseudo" Hamiltonian with the strongly reduced spin-orbit strength.

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