Fermion realization of the nuclear Sp(6,R) model

Abstract

A fermion realization of the nuclear Sp(6,R) model, which complements the traditional bosonic representation, is developed. A recursive process is presented in which symplectic matrix elements of arbitrary one-body fermion operators between states of excitation Nប and NЈប in the same or in different symplectic bands are related back to valence shell matrix elements, which can be evaluated by standard shell model techniques. Matrix elements so determined may be used to calculate observables such as electron scattering form factors which carry detailed structural information on nuclear wave functions.

Schematic model for QCD. I. Low energy meson states

“…(17) with the use of the notation of Ref. [23] for the SU(3) Clebsch-Gordan coefficients and their symmetry properties.…”

“…where we made use of the properties of the SU(2) [31] and SU(3) [23] ClebschGordan coefficients. The subindex 1 in the SU(3) Clebsch-Gordan coefficient indicates a multiplicity of one [23].…”

“…The phase convention of Ref. [23] was used. The symbol ⊗ denotes the combined product in SU f (3) and SU S (2).…”

Partial Dynamical Symmetry in a Fermion System

“…shells [6], andĈ (11) 1m =L m , the orbital angular momentum operator). A fermion realization of these generators is given in [7].…”

“…(11) 1m =L m , the orbital angular momentum operator). A fermion realization of these generators is given in [7].A basis for the symplectic model is generated by applying symmetrically coupled products of the 2hω raising operator (20) with itself to the usual 0hω many-particle shell-model states. Each 0hω starting configuration is characterized by the distribution of oscillator quanta into the three cartesian directions, {σ 1 , σ 2 , σ 3 } (σ 1 ≥ σ 2 ≥ σ 3 ), or, equivalently, by its U(1)×SU(3) quantum numbers N σ (λ σ , µ σ ).…”