Title page for ETD etd-04112008-095727

Type of Document Dissertation
Author Drumev, Kalin
Author's Email Address kdrume1@lsu.edu
URN etd-04112008-095727
Title Towards an Extended Microscopic Theory for the Upper-fp-shell Nuclei
Degree Doctor of Philosophy (Ph.D.)
Department Physics & Astronomy
Advisory Committee
Advisor Name Title
Jerry P. Draayer Committee Chair
A. Ravi P. Rau Committee Member
Jeffrey Blackmon Committee Member
John Wefel Committee Member
Kermit Murray Dean's Representative
  • shell model
  • models based on group theory
  • collective levels
  • upper-fp-shell nuclei
Date of Defense 2008-04-10
Availability unrestricted
An extended SU(3) shell model that for the first time

explicitly includes particles from the unique-parity

levels in nuclei is introduced. Its relevance is established through

calculations performed with realistic interactions for a group of

upper fp-shell isotopes where valence nucleons beyond the N=28=Z core

occupy levels of the normal-parity upper $fp$-shell

($f_{5/2},p_{3/2},p_{1/2}$) and the unique-parity $g_{9/2}$

intruder configuration. Specifically, the outcome suggests that

the pseudo-SU(3) symmetry is quite good throughout the region and

that only part of the configurations are relevant for the structure

of the low-lying states. The levels of the upper $fp$-shell are

handled within the framework of an m-scheme basis as well as

its pseudo-SU(3) counterpart, and respectively, the $g_{9/2}$

as a single level and as a member for the complete $gds$ shell.

More detailed analyses of the extended SU(3) model are done for

two nuclei of special interest in astrophysics, namely the waiting-point

nuclei $^{64}$Ge and $^{68}$Se. The strengths and limitations

of the theory are demonstrated by its ability to describe various

nuclear characteristics. Specifically, energy spectra, B(E2)

transition strengths and wave-function content are compared with

the realistic results. In addition, the dominance of configurations with

different distribution of particles and the role that several

newly-introduced terms play in the Hamiltonian are investigated.

The extended SU(3) approach allows one to better probe the effects

of deformation and account for these key properties of the system

within a highly-truncated model space.

The model also promises to be useful for nuclei from the

rare-earth and actinide regions. Specifically, by ensuring

a robust number of collective degrees of freedom and

Hamiltonians with a larger number of degrees of freedom,

it should allow one to give a satisfactory explanation of

the experimentally-observed existence of an abundance of

low-lying $0^{+}$ states and very strongly enhanced B(E2)

strengths found in these nuclei. This version of the theory

will extend previous results from the pseudo-SU(3) model

where the role of nucleons in the intruder levels was

relegated to a very simple renormalization of the dynamics

defined by nucleons in the normal-parity spaces only.

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