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

We present the development of the extended Skyrme N2LO pseudo-potential 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 behaviour of the solutions at the origin. Finally, a fitting procedure for such a N2LO interaction is discussed and we provide a first parametrization. Typical ground-state observables are calculated and compared against experimental data.