Role of Bcs-type Pairing in Light Deformed Nuclei: a Relativistic Mean Field Approach

The odd-even staggering (OES) of nuclear masses has been recognized since the early days of nuclear physics. It manifests itself in the fact that the binding energy of a system with an odd particle number is lower than the arithmetic mean of the energies of the two neighboring even-particle-number systems. Häkkinen et al. 1, using the density-functional theory, argued that light alkali-metal clusters and light N = Z nuclei have a similar pattern of OES, irrespective of differences in the interactions between the fermions. Hence, they concluded that the OES in small nuclei appears to be a mere deformation effect rather than a consequence of pairing. On the other hand, Satula et al. 2, claimed that the OES in light atomic nuclei is strongly affected by both nucleonic pairing and the deformed mean field. According to them, the OES without taking pairing into account is simply due to Jahn-Teller effect 3 and it is substantially smaller than the experimental observation. It is worthwhile to note that, following Ref. 4, the pairing energy is about −0.8 MeV for a nuclear system of mass number A = 160. The rather small value of the correlation energy reflects the fact that only a few single particle levels lie within the interval of strong pair correlations. Thus the condition for the treatment in terms of a static pair field is only marginally satisfied. This makes clear that the concept of pairing may have some meaning for heavy mass nuclei. But the basis for pairing correlations in light nuclei is very questionable. The Bohr-Mottelson-Pines idea of applying BCS type pairing theory to nuclei