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We derive a zero-range pseudopotential that includes all possible terms up tosixth order in derivatives. Within the Hartree-Fock approximation, it gives theaverage energy that corresponds to a quasi-local nuclear Energy DensityFunctional (EDF) built of derivatives of the one-body density matrix up tosixth order. The direct reference of the EDF to the pseudopotential acts as aconstraint that divides the number of independent coupling constants of the EDFby two. This allows, e.g., for expressing the isovector part of the functionalin terms of the isoscalar part, or vice versa. We also derive the analogous setof constraints for the coupling constants of the EDF that is restricted byspherical, space-inversion, and time-reversal symmetries.

Effective pseudopotential for energy density functionals with higher order derivatives