Starting from the $A$-nucleon Schrödinger equation, collective and single particle degrees are separated by a transformation. Pure collective and pure single particle states appear as special states of one complete orthogonal system of functions. The formulae of the conventional unified model are obtained, augmented by restrictions caused by constraints on the new single particle coordinates. Sum rules for the magnetic dipole and the electric quadrupole moments of mirror nuclei, which are consequences of these constraints, are presented.

• Received 29 May 1984

DOI:https://doi.org/10.1103/PhysRevC.30.2067