Numerical Framework

As the pairing renormalization and regularization procedures remove the divergent part of the abnormal density in a different way, one can expect some numerical differences between both methods. In order to compare their results, we have performed numerical calculations using two numerical codes solving the HFB equations:

• HFBRAD [27] - solves the HFB equations in the spherically symmetric coordinate basis. The maximum angular momenta used in calculations were $j_{\mbox{\rm\scriptsize {max}}}=39/2$ for neutrons and $j_{\mbox{\rm\scriptsize {max}}}=25/2$ for protons.
• HFBTHO [26] - diagonalizes the HFB problem in the axially symmetric transformed harmonic oscillator (HO) basis. Unless stated otherwise, we use $N_{osc}=$ 20 HO shells in the basis.

In our calculations, we use the SLy4 [28] and SkP [12] parameterizations of the Skyrme functional in the p-h channel and the contact density-dependent force in the p-p channel, which leads to the pairing energy density of the form:

$$\mathcal{H}_{pair}({\bf r}) = \frac{1}{2}g(\mathbf{r})\tilde{\rho}(\mathbf{r})^{2}=$$

$$= \frac{1}{2}V_0 \left[1-V_1\left(\frac{\rho(\mathbf{r})}{\rho_0}\right)~ \right]\tilde{\rho}(\mathbf{r})^{2} ,$$ (14)

where $\rho_0=0.16$fm$^{-3}$. For $V_1=0$ the resulting pairing interaction is called volume pairing, while $V_1=1/2$ corresponds to the so-called mixed pairing prescription (Ref. [29] and references quoted therein).