Elimination of Body-Frame Singularities in the Separation of Three Collective Angles in Quantum $N$-Body Problems

The appearance of body-frame singularities in gauge potentials when three collective angles are separated by means of Wigner $D$-functions is a fundamental difficulty in the quantum $N$-body problem. We show that the use of the overcomplete basis of minimal multipolar harmonics allows these singularities to be avoided at the expense of increasing the dimension of the resulting system of coupled equations describing the internal motion of the system.