Factorization of the j = 7/2 shell of neutrons and protons : Transformation coefficients to states of good particle number

Abstract

Complete tabulations are given, for the j = 7/2 nuclear shell, of the transformation coefficients to states of good particle number needed in a new method of nuclear spectroscopy based on a quasiparticle factorization of the j-shell. The method leads to a classification scheme in which total angular momentum and isospin are good quantum numbers and in which the calculation of matrix elements can be carried out simply by standard techniques of Racah algebra, without the use of coefficients of fractional parentage and with the use of only a very small number of reduced matrix elements. These reduced matrix elements also are tabulated. A few sample calculations show how matrix elements of one- and two-body operators, single nucleon and pair creation operators, ..., can be calculated with this technique and the present tabulations.