Systematics of Quadrupolar Correlation Energies

We calculate correlation energies associated with the quadrupole shape degrees of freedom with a view to improving the self-consistent mean-field theory of nuclear binding energies. Systematic results are presented for 605 even-even nuclei from mass number 16 to the heaviest whose mass has been measured, using the Skyrme SLy4 interaction and the generator coordinate method. Correlation energies range from 0.5 to 6.0 MeV, and their inclusion improves two qualitative deficiencies of the mean-field theory, namely, the exaggerated shell effect at neutron magic numbers and the failure of mean-field theory to describe mutually enhanced magicity. For the mass table as a whole, the quadrupolar correlations improve binding energies, separation energies, and separation energy differences by $20\%30\%$.

Figure 1

Top panel: Difference of experimental and mean-field energies for the SLy4 interaction [4], as a function of neutron number with lines connecting isotopic chains. Middle panel: Theoretical quadrupolar correlation energies of the even-even nuclei. Note the expanded energy scale. Bottom panel: Difference of experimental and theoretical energies including the correlation energy.

Figure 2

Two-proton gaps, Eq. (3), for Pb and Sn isotopic chains. Theoretical curves are the following: spherical mean field (short dashed lines); mean field allowing for static deformations (long dashed lines); present theory (solid lines). Experimental values [1] are shown as diamonds.