Model nuclear energy density functionals derived from ab initio calculations
This monograph focused on a method to link nuclear energy density functionals to the ab initio solution of the nuclear manybody problem. This method, proposed in Ref. [1], was here discussed in many aspects as well as applied to a stateofart ab initio approach.
We introduced the basis of the density functional theory, paying attention to the concept of generators of the functional. In parallel, we explored the SelfConsistent Green's Function approach as ab initio framework to calculate groundstate energies. We derived the model functional based on the LevyLieb constrained variation, which exploited the response of the nucleus to an external perturbation.
Using the Green's function technique and the NNLOsat chiral interaction in the ab initio Hamiltonian, seven semimagic nuclei were probed with perturbations induced by generators of two and threebody contact interaction (Skyrmelike). We employed the same generators to built model functionals, whereupon the coupling constants were fitted to reproduce the perturbed groundstate energies. Several parametrizations of the functionals were obtained for given choices of generators, selection of data points, and assumed uncertainties. We analysed the derived parametrizations according to their statistical performances, magnitude of the propagated errors, and corresponding nuclear matter description. Two parametrizations emerged as the most promising, but the model functionals built from them did not produce meaningful results. As it turned out, zerorange generators provided a poor description of the chiral interaction. Moreover, the performed error analysis suggested that the actual precision of the ab initio approach may not be sufficient to improve the quality of the novel energy density functionals.
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 JYU Dissertations [127]
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