Conclusions

This work contains the analysis of an interplay between pairing and mean-field effects on binding energies of many-fermion systems. While most of our discussion is concerned with nuclear systems, the main conclusions also apply to other finite-size superconductors such as grains.

The analysis of binding energies of several exactly-solvable Hamiltonians (allowing variations in the magnitude of pairing correlations) demonstrates that the three-mass indicator, $\Delta^{(3)}(2n+1)$, is indeed an excellent measure of pairing correlations, and the symmetric filter $\delta{e}$adequately extracts the effective single-particle spacings from the measured binding energies of deformed nuclei. According to the analysis of nuclear masses, the mean-field contribution to the OES is significant in light nuclei, but it is reduced to $\sim$100-200keV in heavy deformed nuclei [32] due to the relatively close spacing of single-particle levels.

For deformed nuclei with weak and intermediate pairing correlations, there is a nice consistency between the approximate results obtained within the mean-field approach (BCS or HFB) and the exact results. However, for strongly paired nearly-spherical nuclei, there is no clear correlation between $\Delta^{(3)}(2n+1)$ and the pairing deformation $\Delta^0$. Also, the energy-spacing filters are superior over the mean-field single-particle energies in assessing the single-particle properties of the system.

Approximate expressions of binding-energy indicators have been derived in the limits of weak and strong pairing. These formulae nicely explain the gross particle number dependence seen in the exact results.

This research was supported in part by the U.S. Department of Energy under Contract Nos. DE-FG02-96ER40963 (University of Tennessee), DE-FG05-87ER40361 (Joint Institute for Heavy Ion Research), DE-AC05-96OR22464 with Lockheed Martin Energy Research Corp. (Oak Ridge National Laboratory), and by the Polish Committee for Scientific Research (KBN) under Contract No. 2 P03B 040 14.