Neutron-drip-line calculations

 

Having at our disposal a viable method for performing deformed HFB calculations up to the drip lines, we have performed a systematic study of the equilibrium properties of the neutron-rich nuclei in all even-Z isotopic chains with proton numbers from Z=2-18. In this way, we have explored the neighborhood of the neutron-drip line for all neutron numbers from N=6-40.

We first performed spherical HFB+SLy4 calculations in coordinate space, using the methods and the code developed in Ref. [6]. We used volume delta pairing, with a coupling constant V₀=-218.5MeVfm³, adjusted as in Ref.  [43]. This value is very close to the one used in our deformed THO code (see Sec. 4.1), suggesting that the effective pairing phase spaces used in the two approaches are very similar to one another.

From the spherical calculations, we obtained that the heaviest even isotopes, for which the Fermi energies are negative are: ⁸He, ¹²B, ²²C, ²⁸O, ³⁰Ne, ⁴⁴Mg, ⁴⁶Si, ⁵⁰S, ⁵⁸Ar. We used these spherical results as a starting point for our deformed calculations.

Next, within the deformed THO formalism, we found that the heaviest isotopes with negative Fermi energies are: ⁸He, ¹²B, ²²C, ²⁸O, ³⁶Ne, ⁴⁴Mg, ⁴⁶Si, ⁵²S, ⁵⁸Ar. The results obtained for these nuclei are summarized in Fig. 7. By comparing the deformed results to the spherical results, we see that the position of the last bound nucleus is influenced by deformation only in ³⁶Ne and ⁵²S. Volume pairing correlations are very weak in these nuclei; indeed, in all but the one case of ³⁶Ne, neutron pairing vanishes in the last bound nucleus of an isotopic chain. This suggests the necessity of using a surface pairing force here. Such a conclusion is supported by the fact that HB calculations [57], carried out with a Gogny pairing force, give sizable neutron pairing correlations in this region (Note that surface pairing and Gogny pairing produce quite similar distributions [7] over the single-particle states.)

Since neutron pairing vanishes in ¹²B, our result is identical to that of Ref. [30], namely that the SLy4 force does not produce ¹⁴B as bound, in disagreement with experiment [60]. Similarly, neither pairing nor deformation effects are present in the calculated ²⁸O nucleus, and hence this nucleus remains bound (see discussion in Sec. 4.2). On the other hand, the SLy4 force correctly describes ⁸He [60] and ²²C as the last bound nuclei of their respective isotope chains [61].

A remarkable result obtained in our calculations is that the last bound nuclei for all chains of isotopes heavier than oxygen have oblate ground-state shapes. In all of them, the mechanism for this effect is identical to that discussed for the Mg isotopes (see Sec. 4.3), namely that the neutron Fermi energy $\lambda_{n}$, as a function of the neutron number N, becomes positive for smaller values of N in the prolate ground states than it does in the oblate secondary minima. Therefore, in the heaviest bound isotopes, the prolate states are unbound, whereas the oblate states continue to be bound and become the ground-state configurations.