Deformation properties of the projected spherical single particle basis

Deformed single particle energies obtained by averaging a particle-core Hamiltonian with a projected spherical basis depend on a deformation parameter and an arbitrary constant defining the canonical transformation relating the collective quadrupole coordinates and momenta with the boson operators. When the mentioned basis describes the single particle motion of either protons or neutrons the parameters involved are isospin dependent. An algorithm for fixing these parameters is formulated and then applied for 194 isotopes covering a good part of the nuclide chart. Relation with the Nilsson deformed basis is pointed out in terms of deformation dependence of the corresponding single particle energies as well as of the nucleon densities and their symmetries. The proposed projected spherical basis provides an efficient tool for the description of spherical and deformed nuclei in a unified fashion.