  We calculate correlation energies associated with the quadrupolar shape
degrees of freedom with a view to improving the self-consistent mean-field
theory of nuclear binding energies. The Generator Coordinate Method is employed
using mean-field wave functions and the Skyrme SLy4 interaction. Systematic
results are presented for 605 even-even nuclei of known binding energies, going
from mass A=16 up to the heaviest known. The correlation energies range from
0.5 to 6.0 MeV in magnitude and are rather smooth except for large variations
at magic numbers and in light nuclei. Inclusion of these correlation energies
in the calculated binding energy is found to improve two deficiencies of the
Skyrme mean field theory. The pure mean field theory has an exaggerated shell
effect at neutron magic numbers and addition of the correlation energies reduce
it. The correlations also explain the phenomenon of mutually enhanced magicity,
an interaction between neutron and proton shell effects that is not explicable
in mean field theory.
