Symmetry, constrained bosons and collectivity
Abstract
Collective states in a given nucleus can be associated with a subset of states of the oscillator shell model (OSM). This subset is characterized by a definite irreducible representation (irrep) of the orthogonal subgroup O(n) of the U(3n) symmetry group of the OSM, where n is the number of nucleons. We show that these collective states can be described with the help of s and d bosons also constrained by the same irrep of O(n) and indicate a procedure by which these bosons can be determined as functions of the coordinates a and momenta of the many nucleon problem. An analogy with the Zeeman effect for a one particle problem in an oscillator potential, illustrates the elementary nature of the concepts involved.
 Publication:

Nuclear Physics A
 Pub Date:
 June 1984
 DOI:
 10.1016/03759474(84)903385
 Bibcode:
 1984NuPhA.421...81M