Abstract A unification of the single-particle and collective models is presented, which starts from the A-nucleon Schrödinger equation. It has the advantage of defining the various degrees of freedom in terms of the space vectors of the nucleons. The spin-orbit coupling is redefined. The model gives the relevant results of the conventional unified model, but also gives some additional information. It is shown for example why the g R factors for the collective part of the magnetic moment may deviate considerably from what was assumed so far.