PAIRING IN NEUTRON-RICH NUCLEI

A proper theoretical description of weakly bound heavy systems requires taking into account the particle-particle (p-p, pairing) correlations on the same footing as the particle-hole (p-h) correlations, which - on the mean-field level - is done in the framework of the theories based on the Hartree-Fock-Bogoliubov (HFB) method. In this method, it is essential to solve the equations for the self-consistent densities and mean fields in order to allow the pairing correlations to build up with a full coupling to particle continuum [3,4].

Since in finite nuclei no derivation of the pairing force from first principles is available yet, there are many variations in the choice of pairing forces used in calculations. Unfortunately, for drip-line nuclei, in which the pairing effects are crucially important due to the coupling to the continuum, the effective pairing interaction is not known. Recently, we discussed this problem in a series of papers [6,7,8] within the coordinate-space spherical HFB. In the actual HFB calculations based on the Skyrme forces in the p-h channel (as, e.g., the SLy4 parametrization [9] used in our work), contact pairing interaction is usually used. Two different forms have been used up to now - the volume type, $V^{\delta }_{\rm {vol}}({\bf r},{\bf r}^{\prime })=V_{0}\; \delta ({\bf r}- {\bf r}^{\prime })$, or the surface type, $V^{\delta }_{\rm {surf}}({\bf r},{\bf r}^{\prime })=V_{0}\; [1-(\rho ({\bf r})/\rho_{0})^\alpha]\; \delta ({\bf r}- {\bf r}^{\prime })$, where $\rho_{0}$=0.16fm^-3 is the saturation density, V₀ defines the strength of the interaction, and $\alpha$ governs the intensity of interaction at low densities [6]. (The origin of the terms ``volume" and ``surface" has been discussed in Refs. [4,10].) In reality, however, the pairing interaction is most likely of an intermediate character between the volume and surface forms. In particular, the force which is a fifty-fifty mixture of both types,

$$V^{\delta }_{\rm {mix}}({\bf r},{\bf r}^{\prime })= \frac{1}{... ...( V^{\delta }_{\rm {vol}} + V^{\delta }_{\rm {surf}} \right) ,$$ (2)

performs quite well [8,11] in reproducing the general mass-dependence of the odd-even mass staggering parameter $\Delta^{(3)}$ centered at odd particle numbers [12,13].

Figure 2 illustrates the impact of different pairing interactions on neutron pairing gaps in very neutron-rich isotones around N=82. The experimental data that exist for Z$\geq$50 do not indicate any definite change in neutron pairing with varying proton numbers. However, the surface pairing interactions (bottom panels) give a slow dependence for Z$\geq$50 that is dramatically accelerated after crossing the shell gap at Z=50. On the other hand, the volume and intermediate-type pairing forces predict a slow dependence all the way through to very near the neutron drip line. (It is worth noting that both experimentally and theoretically neutron pairing decreases in Sn and Te isotopes as one goes across the N=50 magic gap. We shall come back to this observation in Sec. 5.) It is clear that measurements of only several nuclear masses on neutron-rich nuclei with Z<50 will allow us to strongly discriminate between the pairing interactions that have different density dependencies.

  

Figure 2: Comparison between the experimental neutron pairing gaps $\Delta_N$ (upper left panel) and the corresponding results of the spherical HFB method for the Skyrme SLy4 force [9] and five different versions of the zero-range pairing interaction (see text).