Abstract
In finite model space suitable for many-body calculations via the no-core shell model (NCSM), I illustrate the direct application of the effective field theory (EFT) principles to solving the many-body Schrodinger equation. Two different avenues for fixing the low-energy constants naturally arising in an EFT approach are discussed. I review results for both nuclear and trapped atomic systems, using effective theories formally similar, albeit describing different underlying physics.
Highlights
Significant progress has been reported in the last decade toward achieving the holy grail of nuclear theory: a first principle description of the properties of atomic nuclei
We review the efforts to combine the power of effective field theory (EFT) with the no-core shell model (NCSM), with the goal of extending the benefits of QCD compatible solutions to a larger class of nuclei, and of eliminating the model dependence and mitigating some shortcomings of the conventional NCSM
The remaining constants, C00(ω, Nmax) and D0(ω, Nmax) are adjusted in each model space, so that the tritium and the 4He binding energies are reproduced. This is somehow different from the usual approach in EFT, where the two-body forces are fixed by the two-body scattering data
Summary
Significant progress has been reported in the last decade toward achieving the holy grail of nuclear theory: a first principle description of the properties of atomic nuclei. This success is due to both a better understanding of the internucleon interactions, as well as the advent of increased computing power, supported by the development of sophisticated numerical algorithms. Phenomenological and one-boson exchange models have provided guidance and have proved successful in applications to light nuclei; but a deeper understanding of the interactions between nucleons has been achieved using effective field theories (EFTs) [1–3], which provide interactions consistent with the symmetries of the underlying theory of the strong interactions, QCD.
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