Nuclear pairing from chiral pion-nucleon dynamics: Applications to finite nuclei

The ${}^1{S}_0$ pairing gap in isospin-symmetric nuclear matter and finite nuclei is investigated using the chiral nucleon-nucleon potential at the next-to-next-to-next-to-leading order (N${}^3$LO) order in the two-body sector and the next-to-next-to-leading order (N${}^2$LO) order in the three-body sector. To include realistic nuclear forces in the relativistic Hartree-Bogoliubov (RHB) framework, we employ a separable form of the pairing interaction that is adjusted to the nuclear matter pairing gap computed with a bare nuclear force. The separable pairing force is applied to the analysis of pairing properties for several isotopic and isotonic chains of spherical nuclei.

Figure 1

Pairing gaps in symmetric nuclear matter in the ${}^1{S}_0$ channel as functions of the Fermi momentum. The dashed curve is obtained by including only the two-body ($V_{2B}$) chiral interaction, whereas the solid curve also includes the contribution of three-body ($V_{3B}$) forces. The gaps are compared to those obtained in Ref. [34] using the $V_{\mathrm{lowk}}$ potential.

Figure 2

Theoretical average neutron pairing gaps (7) of the even-even isotopes of nickel $Z=28$, tin $Z=50$, and lead $Z=82$, compared to the empirical values calculated from experimental masses using Eq. (8) (upper panel). Absolute deviations of the calculated binding energies from the experimental values [35] (lower panel).

Figure 3

Same as described in the caption to Fig. 3 but for the chains of isotones $N=28$, $N=50$, and $N=82$.

Figure 4

$M^{*}/M$ as function of the baryon density $\rho$ employed in the FKVW functional (solid) [6], and the effective mass derived by Holt et al. [30] from microscopic chiral two- and three-nucleon interactions using a density-matrix expansion.

Figure 5

Right panel: High-density behavior of the ${}^1{S}_0$ pairing gap in symmetric nuclear matter obtained from $V_{2B}$ and $V_{3B}$ forces (black circles), in comparison with gaps calculated using a single-Gaussian (green [light gray] diamonds) ansatz and a linear combination of three Gaussians (orange [drak gray] diamonds) for the separable pairing interaction introduced in Sec. 3. For smaller values of the Fermi momentum the differences are negligible. Left panel: Average neutron pairing gaps Eq. (7) for the even-even isotopes of nickel, tin, and lead, calculated with a single-Gaussian ansatz (green [light gray] diamonds) and a three-Gaussians ansatz (orange [dark gray] diamonds) for the separable pairing force, in comparison with empirical values (red squares).