Algebraic Shells and the Interacting Boson Model of the Nucleus

Abstract

It is well known that, for the simplest possible case of a shell (spin s=1/2, orbital angular momentum I=0), the four shell states transform according to the smallest spin representation (1/2,1/2) of the algebra so(5). In this article it is shown that, within the (space of the) Clifford algebra associated with the fernnion operators, an algebraic shell can be found which is a generalization of the standard shell. The algebraic shell states go over into the standard shell states on the quotient space of the Clifford algebra with respect to a left ideal generated by the identity operator 1 (which corresponds to the standard vacuum state).