Summary

We have developed a computer code that is able to solve the self-consistent equations resulting from the use of the generalized N$^3$LO energy density functional introduced in Ref. [4]. For different terms of the functional, the resulting mean-field expressions were systematically formulated by using the spherical-tensor representation, which was also introduced in Ref. [4]. In Section 3 we presented the general equations, needed for any choice of basis, and in Section 4 we developed expressions needed to implement the formalism in the spherical harmonic oscillator basis.

The present version of the program is based on the spherical harmonic oscillator basis and can be used to calculate, for example, ground state properties of spherical nuclei using standard Skyrme forces. For this purpose, it has some advantage compared to other codes, because of its fast execution time and stability.

The motivation to construct the code, and its main new feature, is the possibility to test the influence of higher order derivative terms included in the mean field. The values of the higher order coupling constants can be calculated from the density-matrix expansions starting from other interactions or by direct fits to experimental data, and both approaches are presently being explored. The formalism was derived in a general way, so as to include non-spherical multipoles, and thus it can also be used for linear-response calculations [16], which go beyond the mean field. Extensions to include pairing, better treatment of the continuum, and statically deformed densities are also being developed.