Effect of pairing correlations on incompressibility and symmetry energy in nuclear matter and finite nuclei

The role of superfluidity in incompressibility and in symmetry energy is studied in nuclear matter and finite nuclei. Several pairing interactions are used: surface, mixed, and isovector dependent. Pairing has a small effect on the nuclear matter incompressibility at saturation density, but the effects are significant at lower densities. The pairing effect on the centroid energy of the isoscalar giant monopole resonance (GMR) is also evaluated for Pb and Sn isotopes by using a microscopic constrained-HFB approach and is found to change at most by 10% the nucleus incompressibility $K_A$. It is shown by using the local density approximation that most of the pairing effect on the GMR centroid comes from the low-density nuclear surface.

Figure 1

Pairing gap ${\Delta }_{\tau }$, pairing energy per particle ${\epsilon }_{\mathrm{pair}}/\rho$, percentage of pairing energy with respect to the total energy $\epsilon$, and equation of state around the saturation point in symmetric matter obtained with various pairing interactions employed in connection with the SLy5 Skyrme interaction. The solid, dotted, and dashed lines correspond to the IS pairing interactions with $\eta =0.35$, 0.65, and 1.0, respectively, in Eq. (3). The dash-dotted and dash-dotted-dotted lines show the results of $\mathrm{IS}+\mathrm{IV}$ interactions in Ref. [15] (MSH) and Ref. [16] (YS), respectively. See the text for details.

Figure 2

(top) Pressure, incompressibility, and symmetry energy without pairing, and (bottom) the contributions of various pairing interactions to these quantities. The HF energy ${\epsilon }_{\mathrm{Skyrme}}$ is calculated using the SLy5 interaction. For details, see the caption to Fig. 1 and the text.

Figure 3

(bottom) Radial dependence of $\epsilon (r)$, $K_{\mathrm{Nucl}}(r)$, and $S_A(r)$ for the various pairing interactions considered using the SLy5 force in ${}^{120}\mathrm{Sn}$ within the LDA. (top) The contribution of the Skyrme term plus the kinetic term. See the caption to Fig. 1 and the text for details.

Figure 4

$K_{\infty }$ vs $K_A$ for ${}^{208}\mathrm{Pb}$ obtained by the CHF method for several Skyrme interactions.

Figure 5

$K_{\infty }$ vs $K_A$ for ${}^{114}\mathrm{Sn}$ obtained by the CHF and the CHFB method with surface-type and mixed-type pairing interactions for several Skyrme interactions.

Figure 6

Same as Fig. 5, but for ${}^{120}\mathrm{Sn}$.