Neutron drip line

As a last example we consider the two-neutron drip line for $Z=48$. The case of $Z=50$ is not interesting for our example because there the neutron pairing correlations vanish at the two-neutron drip line (at least for the pairing force considered here), so the residual coupling between the bound and scattering states disappears. The two-neutron drip line is defined by the vanishing Fermi energy, $\lambda_N=0$. In such a system, the HFB approximation leads to a fully continuous quasiparticle spectrum and the minimum quasiparticle energy is determined by the pairing correlations only [26]. In this extreme situation it is important to check if the box boundary conditions have any significant effect on the results. To this end, we have performed calculations with the box size $R_{\mathrm{box}}$ varying between 10 and 35fm and with the regularized pairing field corresponding to $E_{\mathrm{max}}=60$ MeV.

Figure 9: Differences between the total energy, number of neutrons, neutron rms radius, and neutron pairing gap, and their corresponding average asymptotic values (see text), calculated for the $Z=48$ two-neutron drip line nucleus.

$\begin{matrix} \includegraphics*[scale=0.5,bb=96 53 485 340]{figcvdrip.ps} & \includegraphics*[scale=0.5,bb=96 53 485 340]{figcvdripr.ps} \\ \end{matrix}$

We used the same method as in Sec. 8.1 to estimate the average asymptotic values (for $R_{\mathrm{box}}$$\geq$25fm) of the total energy $E^{(a)}$=$-$1095.400501MeV, neutron number $\langle n\rangle^{(a)}$=117.053163, pairing gap $\langle \Delta_N\rangle^{(a)}$1.150396MeV, and neutron rms radius $\langle r_N\rangle^{(a)}$=5.557959fm. Differences of these observables relative to the above average values are reported in Fig. 9. It is seen that the energy is stable up to several keV once the radius of the box is bigger than 25fm, and no further significant change is obtained by enlarging it. The mean neutron number is very stable too, despite the large spatial extension of the neutron density in such a drip line nucleus. As discussed in Ref. [26], the appearance of a giant neutron halo is prevented by the pairing correlations (the pairing anti-halo effect) and the neutron rms radius is perfectly stable with increasing box size. The same is also true for the neutron pairing gap.