The interacting Boson model with the exceptional groups G2 and E6

Abstract

The extension of the interacting Boson model of (IBM) nuclei to sdgi bosons leads naturally to the group structure U28→SU3→SO3. There exist alternative group structures involving the exceptional Lie groups G2 and E6, namely, U28→SU7→SO7→G2→SO3 and U28→SU27×U1→E6→G2→SO3. This represents a different use of G2 to that used in the atomic and nuclear spectroscopy of the f shell. In this paper, details of the explicit construction of the group generators, the calculation of the relevant isoscalar factors, and branching rules will be shown and specific application to the nuclear levels of the A=200 isotope of Hg will be made. The analysis of the foregoing example encourages the more general application of these group structures.