8 research outputs found
Classification of States in O(8) Proton-Neutron Pairing Model
Isoscalar (T=0) plus isovector (T=1) pairing hamiltonian in LS-coupling,
which is important for heavy N=Z nuclei, is solvable in terms of a O(8) algebra
for some special values of the mixing parameter that measures the competition
between T=0 and T=1 pairing. The O(8) algebra is generated, amongst others, by
the and pair creation and annihilation operators . Shell
model algebras, with only number conserving operators, that are complementary
to the , and sub-algebras are identified. The problem of
classification of states for a given number of nucleons (called `plethysm'
problem in group theory), for these group chains is solved explicitly for
states with O(8) seniority and 4. Using them, band structures in
isospin space are identified for states with and 3.Comment: 52 pages, 12 table
On the calculation of inner products of Schur functions
Two methods for calculating inner products of Schur functions in terms of outer products and plethysms are given and they are easy to implement on a machine. One of these is derived from a recent analysis of the SO(8) proton-neutron pairing model of atomic nuclei. The two methods allow for generation of inner products for the Schur functions of degree up to 20 and even beyond
Classification of basis states for (p-f)-nuclei (41 <= A <= 80) with minimal configuration energy
We give a complete classification of basis with unitari (U(A-1), U(3)) and permutational (S)A)) symmetries. Thse are suitable as functions for (p-f)- nuclei (41<= A <= 80) with minimal configuration energy. We also give a brief survey of way in which are obtained
The plethysm technique applied to the classification of nuclear states
A short summary of the theory of symmetric group and symmetric functions needed to follow the theory of Schur functions and plethysms is presented. One then defines plethysm, gives its properties and presents a procedure for its calculation. Finally, some aplications in atomic physics and nuclear structure are given
A dimension formula for reduced plethysms
The boson calculus formalism is used to construct realizations of basis states of irreducible representations of unitary groups taking as a paradigm the interacting boson models of atomic nuclei. These realizations, together with a theorem on plethysms for obtaining branching rules, allowed us to obtain a dimension formula for reduced plethysms. © 2005 IOP Publishing Ltd