Solution of Hartree-Fock-Bogoliubov equations and fitting procedure using the N2LO Skyrme pseudopotential in spherical symmetry

We present the development of the extended Skyrme N2LO pseudopotential in the case of spherical even-even nuclei calculations. The energy density functional is first presented. Then we derive the mean-field equations and discuss the numerical method used to solve the resulting fourth-order differential equation together with the behavior of the solutions at the origin. Finally, a fitting procedure for such an N2LO interaction is discussed and we provide a first parametrization. Typical ground-state observables are calculated and compared against experimental data.

Figure 1

Isoscalar densities in ${}^{208}\mathrm{Pb}$ calculated using single-particle wave functions obtained by a SLy5 mean-field solution. See text for details.

Figure 2

Radial dependence of the coefficients defined in Eq. (32) for ${}^{208}\mathrm{Pb}$ obtained using the SN2LO1 and SLy5 interactions. See text for details.

Figure 3

Same as Fig. 2, but for centrifugal fields given in Eq. (32).

Figure 4

Same as Fig. 2 but for the spin-orbit fields given in Eq. (32).

Figure 5

Precision obtained with whisky against lenteur as a function of the cutoff energy in the Wood-Saxon basis for ${}^{40}\mathrm{Ca}$ (+) and ${}^{208}\mathrm{Pb}$ ($\times$). See text for details.

Figure 6

Isoscalar particle density and pairing density for ${}^{120}\mathrm{Sn}$ obtained with a self-consistent mean-field calculation with the SLy5 interaction.

Figure 7

Landau parameters in SNM for the SN2LO1 pseudopotential as a function of the density of the system. See text for details.

Figure 8

Critical densities in SNM as a function of transferred momentum $q$. The horizontal dashed lines represent the saturation density ${\rho }_0$ and the critical density ${\rho }_{\mathrm{crit}}$.

Figure 9

Equation of state for SNM and PNM obtained with the N2LO Skyrme interaction. The squares represent the values obtained from BHF calculations.

Figure 10

Correlation between the effective mass and the nuclear incompressibility in infinite nuclear matter for different values of the power of the density-dependent term. The curves correspond to different values of the power of the density dependence; dotted curves correspond to standard N1LO Skyrme EDF while dashed ones correspond to N2LO Skyrme EDF.

Figure 11

Difference of binding energies obtained with SN2LO1 and SLy5 and experimental values extracted from Ref. [72].

Figure 12

Proton radii difference of two interactions (SN2LO1/SLy5) calculated with whisky with experimental radii obtained in Ref. [73].

Figure 13

Systematic comparison of binding energies for isotopic (isotonic) chains calculated with our extended Skyrme interaction SN2LO1 and experimental ones. On the same figure we also compare with the SLy5 parametrization. See text for details.

Figure 14

Systematic comparison of proton radii. Experimental data are taken from Ref. [73].

Figure 15

Neutron single-particle energies around the Fermi energy in the ${}^{40}\mathrm{Ca}$ for SLy5 and SN2LO1 parametrizations. The experimental values are taken from Ref. [90]. See text for details.

Figure 16

Same as Fig. 15, but for ${}^{208}\mathrm{Pb}$.