General projection from IBA-2 to IBA-1

We present general formulae for projecting operators of the proton-neutron interacting-boson approximation (IBA-2) into operators of the basic IBA (IBA-1), which ignores the proton-neutron difference. The formulae are valid for bosons of any spatial character (s, p, d, f, g, ...) and they are given for general one- and two-body tensor operators. The IBA-2 Hamiltonian with single-boson energies and quadrupole and dipole interactions for s, d and g bosons is considered as an example. The dependence of M1 and E2 matrix elements on the proton and neutron boson numbers is studied. (author)