Nuclear Coupling Schemes with a Surface Delta Interaction

Recent work indicates that the major part of the residual interaction in nuclei, namely, both the quadrupole and pairing interactions, acts primarily when particles are near the nuclear surface. Since the oneparticle radial wave functions at the surface are essentially state-independent, a surface interaction implies that all radial integrals are approximately the same. Thus for a surface delta function all radial integrals are assumed to be identical. For mixed two-particle configurations, e.g. ${(s, d)}^2$, the surface delta-function interaction gives a first excited 2+ state at a lower energy than a conventional delta function acting throughout the nuclear volume. For the ${{(s, d)}^4}_{T=2\mathrm{}}$ configuration one obtains essentially a vibrational spectrum in both cases. However, for the ${{(s, d)}^4}_{T=0\mathrm{}}$ configuration involving both neutrons and protons, the conventional delta function and surface delta function give quite different spectra. The former leads to a spectrum similar to the two-particle case, whereas for a surface delta-function interaction, the lowest states are 0+, 2+, and 4+ with a near-rotational spacing. It appears then that it is possible to obtain a rotational spectrum even with a short-range interaction, provided we have mixed configurations and both neutrons and protons participating.