ABSTRACT
It was mentioned above that certain Hamiltonians which do not commute with components of F-spin may still have eigenstates which have definite F-spins. The eigenvalues of such eigenstates, however, depend on MF . Simple examples of such Hamiltonians are offered by adding terms, proportional to F 0 and (F 0)2, to a Hamiltonian which is a scalar in F-spin. We saw more interesting examples in Section 39 in which the lowest eigenstates have definite values of F-spin, F = N/2. In general, eigenstates of IBA-2 Hamiltonians are not characterized by definite values of F-spin. Still, in some cases, the lowest eigenstates may have large amplitudes of F = N/2 states. In such cases it may be a good approximation to replace the IBA-2 Hamiltonian by another one whose eigenstates have definite F-spins. The latter is equivalent, for F = N/2 states, to an IBA-1 Hamiltonian whose coefficients depend explicitly on MF (Scholten 1980, Harter et al. 1985).
