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This article presents several challenges to nuclear many-body theory and our understanding of the stability of nuclear matte r. In order to achieve this, we present five different cases, starting with an idealized toy model. These cases expose problems that need to be understood in order to match recent advances in nuclear theory with current experimental programs in low-energy nuclear physics. In particular, we focus on our current understanding, or lack thereof, of many-body forces, and how they evolve as functions of the number of particles . We provide examples of discrepancies between theory and experiment and outline some selected perspectives for future research directions.
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We present microscopic valence-shell calculations of pairing gaps in the calcium isotopes, focusing on the role of three-nucleon (3N) forces and many-body processes. In most cases, we find a reduction in pairing strength when the leading chiral 3N forces are included, compared to results with low-momentum two-nucleon (NN) interactions only. This is in agreement with a recent energy density functional study. At the NN level, calculations that include particle-particle and hole-hole ladder contributions lead to smaller pairing gaps compared with experiment. When particle-hole contributions as well as the normal-ordered one- and two-body parts of 3N forces are consistently included to third order, we find reasonable agreement with experimental three-point mass differences. This highlights the important role of 3N forces and many-body processes for pairing in nuclei. Finally, we relate pairing gaps to the evolution of nuclear structure in neutron-rich calcium isotopes and study the predictions for the 2+ excitation energies, in particular for 54Ca.
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 nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the many-body Schrodinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory, Configuration-Interaction Monte Carlo, and the Self-Consistent Greens Function approach. The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.
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. Much of his work was based on Brueckners formulation of the nuclear many-body problem. It is reviewed briefly together with the Moszkowski-Scott separation method that was an important part of his early work. The core-polarisation and his work related to effective interactions in general are also addressed.
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 theory and algorithms relevant to lattice simulations of nuclear few- and many-body systems. We discuss the exact equivalence of four different lattice formalisms, the Grassmann path integral, transfer matrix operator, Grassmann path integral with auxiliary fields, and transfer matrix operator with auxiliary fields. Along with our analysis we include several coding examples and a number of exercises for the calculations of few- and many-body systems at leading order in chiral effective field theory.
The goal of nuclear structure theory is to build a comprehensive microscopic framework in which properties of nuclei and extended nuclear matter, and nuclear reactions and decays can all be consistently described. Due to novel theoretical concepts, breakthroughs in the experimentation with rare isotopes, increased exchange of ideas across different research areas, and the progress in computer technologies and numerical algorithms, nuclear theorists have been quite successful in solving various bits and pieces of the nuclear many-body puzzle and the prospects are exciting. This article contains a brief, personal perspective on the status of the field.
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