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# Accession Number:

## AD0648531

# Title:

## FIVE-DIMENSIONAL QUASISPIN. THE N, T-DEPENDENCE OF SHELL MODEL MATRIX ELEMENTS IN THE SENIORITY SCHEME.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## MICHIGAN UNIV ANN ARBOR DEPT OF PHYSICS

# Report Date:

## 1967-02-01

# Pagination or Media Count:

##
97.0

# Abstract:

## The five-dimensional quasispin formalism is used to factor out the n, T-dependent parts of shell model matrix elements in the seniority scheme and derive reduction formulae which make it possible to express matrix elements for states of definite isospin T in the configuration j exp. n in terms of the corresponding matrix elements for the configuration j exp. v. The n, T-dependent factors for one and two nucleon c.f.p.s, and for the matrix elements of one-body operators and the two-body interaction are expressed in terms of generalized R5 Wigner coefficients. The needed R5 Wigner coefficients are calculated in the form of general algebraic expressions for the seniorities v and reduced isospins t corresponding to the simpler R5 irreducible representations. In this first contribution the R5 representations omega sub 1 t j12-12v, t are restricted to omega sub 1 O, omega sub 1 12, tt, and the states of omega sub 1 l with n-v 4k-2T, k integer. Explicit expressions are given for the diagonal matrix elements of the general charge independent two-body interaction and the iso-vector and iso-tensor parts of the Coulomb interaction for seniorities v 0 and 1, and the v 2 states with n 4k2-2T. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#