title: Density-matrix expansions and novel nuclear energy density functionals based on chiral effective field theory
Creators: name: Zurek, Lars
Publisher: name: UNSPECIFIED
Year: 2023

description: Nuclear structure is complex. A successful and widely used approach to describe atomic nuclei is nuclear density functional theory. It stands out from a range of existing methods by being applicable to all nuclei thanks to its mild computational scaling, at the same time generally reproducing properties of known nuclei accurately, and being rooted in fundamental theorems. However, for various applications higher accuracy than achieved at present and reliable uncertainty estimates are needed. In addition, extrapolations into territory without experimental data are potentially uncontrolled. How to improve the predictive power of energy density functionals is not clear though due to their largely empirical nature. This is different for ab initio many-body approaches that employ nuclear interaction models based on chiral effective field theory, which provides by construction a recipe for improvement. While ab initio methods, which are more microscopic than density functional theory, are now able to target heavy and open-shell nuclei thanks to tremendous progress in the last decades, the treatment of both at the same time still poses a significant computational challenge. Moreover, the agreement of predictions with experimental results is at present not as good as for energy density functionals. Therefore, a unification of ab initio approaches and nuclear energy density functionals would be welcome. The idea studied in this thesis is to extend conventional Skyrme functionals, which consist of short-range terms, with terms that describe long-range pion exchange from chiral effective field theory at the Hartree-Fock level. Hartree terms are incorporated essentially exactly and Fock terms are included by converting them to quasi-local form by employing a density-matrix expansion. The first part of this work consists in a detailed examination of density-matrix expansions for the use in nuclear structure calculations. We investigate various choices and expansion schemes for scalar contributions. Fock energies from pion exchanges are generally well approximated by all variants considered. The use of the density-matrix expansion for chiral pion contributions is therefore supported by this investigation. Nevertheless we find different possibilities to improve over established implementations. This includes using variants that do not truncate at two derivatives in every functional term and using adjusted expansion coordinate schemes for three-nucleon interactions. For scalar-isovector energies we observe the separate treatment of neutrons and protons to be important. The results are found to apply under broad conditions, although self-consistency is not yet tested. The second part of this work is a study focusing on the actual construction of hybrid energy density functionals consisting of chiral and phenomenological Skyrme terms. We discuss the form of the included contributions and the parameter optimization protocol and construct the GUDE family of functionals. When including pion contributions beyond next-to-leading order in the chiral expansion, we find significant improvements over a reference Skyrme functional constructed following the same protocol. In particular, nuclear masses are better reproduced. We analyze the importance of different pion contributions and identify which terms drive the observed improvements, allowing us to set up a functional with the minimal number of chiral terms necessary. Since pions are incorporated without adding further optimization parameters to the functionals, the improvements can be attributed to the functional form of these terms. Our work therefore suggests that the considered chiral contributions constitute useful ingredients for ab initio energy density functionals.