Representations of U(3) in U(N)

J. P. Draayer, Louisiana State University
Y. Leschber, Louisiana State University
S. C. Park, Louisiana State University
R. Lopez, Louisiana State University


An interactive FORTRAN code for determining the representations of U(3) that occur in a representation of U(N) is introduced. The U(N)→U(3) chain is the basic group structure of the isotropic oscillator in three dimensions. In particular, N = (n+1)(n+2)/2 is the degeneracy of the shell with n quanta per level. Since the oscillator potential is a good starting approximation for the self-consistent field that binds nucleons in the nucleus, motivation for the work comes from nuclear physics, and in particular, from studies of quadrupole collective phenomena in deformed nuclear systems. A PASCAL version of the program, which is simpler because the basic algorithm is a recursive one, is also available. © 1989.