  While ab initio many-body techniques have been able to successfully describe
the properties of light and intermediate mass nuclei based on chiral effective
field theory interactions, neutron-rich nuclei still remain out of reach for
these methods. Conversely, energy density functional approaches can be used to
calculate properties of heavy nuclei but rely mostly on phenomenological
interactions. A usable form of the nuclear energy density functional that is
rooted in the modern theory of nuclear forces was presented recently. The first
component of this new set of functionals corresponds to the direct part
(Hartree term) of the expectation value of local chiral potentials on a Slater
determinant. The exchange term, which is a functional of the non-local density,
is transformed into a local functional by applying the density matrix
expansion. In order to reduce the computational cost due to the direct
implementation of non-separable, local interactions in the Hartree term, we use
an approximation to represent the regularized Yukawa functions in terms of a
sum of (separable) Gaussian functions. These proceedings analyze the accuracy
of such an approximation in terms of the number of Gaussian functions and look
for an optimal value that gives an acceptable level of accuracy while
maintaining the computational memory requirements in a many-body calculation as
low as possible.
