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Phenomenological effective interactions like Skyrme forces are currently used in mean--field calculations in nuclear physics. Mean--field models have strong analogies with the first order of the perturbative many--body problem and the currently used effective interactions are adjusted at the mean--field level. In this work, we analyze the renormalizability of the nuclear many--body problem in the case where the effective Skyrme interaction is employed in its standard form and the perturbative problem is solved up to second order. We focus on symmetric nuclear matter and its equation of state, which can be calculated analytically at this order. It is shown that only by applying specific density dependence and constraints to the interaction parameters could renormalizability be guaranteed in principle. This indicates that the standard Skyrme interaction does not in general lead to a renormalizable theory. For achieving renormalizability, other terms should be added to the interaction and employed perturbatively only at first order.
This is a very short presentation regarding developments in the theory of nuclear many-body problems, as seen and experienced by the author during the past 60 years with particular emphasis on the contributions of Gerry Brown and his research-group.
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists ca
The application of renormalization group methods to microscopic nuclear many-body calculations is discussed. We present the solution of the renormalization group equations in the particle-hole channels for neutron matter and the application to S-wave
We begin with a brief overview of lattice calculations using chiral effective field theory and some recent applications. We then describe several methods for computing scattering on the lattice. After that we focus on the main goal, explaining the th
We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear many-body problem. These methods use continuous unitary transformations to evolve the nucl