  In the well-known Nilsson diagrams, depicting the dependence of the nuclear
single-particle energy levels on quadrupole deformation, a spin paradox appears
{as the deformation sets in, leading from spherical shapes to prolate deformed
shapes with cylindrical symmetry}. Bunches of levels corresponding to a
spherical shell model orbital, sharing the same orbital angular momentum and
the same total angular momentum, appear to correspond to Nilsson energy levels,
labeled by asymptotic quantum numbers in cylindrical coordinates, some of which
have spin up, while some others have spin down. Furthermore, for some orbitals
the correspondence between spherical shell model quantum numbers and Nilsson
asymptotic quantum numbers is not the same for protons and for neutrons.
Introducing a new rule of correspondence between the two sets of quantum
numbers, we show that the spin paradox is resolved and full agreement between
the proton and neutron Nilsson diagrams is established. The form of the Nilsson
diagrams as a function of the quadrupole deformation remains unchanged, the
only difference between the new diagrams and the traditional ones being the
mutual exchange of the Nilsson labels for certain pairs of single-particle
energy levels.
