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Standard Model (SM) of particle physics has achieved enormous success in describing the interactions among the known fundamental constituents of nature, yet it fails to describe phenomena for which there is very strong experimental…
An effective field theory (EFT) for a nuclear reaction at low energies is studied. The astrophysical $S$-factor of radiative $\alpha$ capture on $^{12}$C at the Gamow-peak energy, $T_G=0.3$ MeV, is a fundamental quantity in…
The virtues of an effective field theory (EFT) approach to many-body problems are illustrated by deriving the expansion for the energy of an homogeneous, interacting Fermi gas at low density and zero temperature. A renormalization scheme…
Nuclear density functional theory (DFT) is the only microscopic, global approach to the structure of atomic nuclei. It is used in numerous applications, from determining the limits of stability to gaining a deep understanding of the…
Effective field theory (EFT) is generalized to investigate the rotational motion of triaxially deformed even-even nuclei. A Hamiltonian, called the triaxial rotor model (TRM), is obtained up to next-to-leading order (NLO) within the EFT…
Fundamental issues involving nuclei in the celebrated solar neutrino problem are discussed in terms of an effective field theory adapted to nuclear few-body systems, with a focus on the proton fusion process and the hep process. Our…
During the past two decades, chiral effective field theory has become a popular tool to derive nuclear forces from first principles. Two-nucleon interactions have been worked out up to sixth order of chiral perturbation theory and…
The development of systematic effective field theories (EFTs) for nuclear forces and advances in solving the nuclear many-body problem have greatly improved our understanding of dense nuclear matter and the structure of finite nuclei. For…
The present contribution does not aim at replacing the huge and often excellent literature on DFT for atomic nuclei, but tries to provide an updated introduction to this topic. The goal would be, ideally, to help a fresh M.Sc. or Ph.D.…
We discuss the role effective field theory plays in making predictions in nuclear physics in an approach that combines both the high sophistication of the standard nuclear many-body approach and the power of systematic higher chiral-order…
Chiral effective field theory ($\chi$EFT) is a powerful tool for studying electroweak processes in nuclei. I discuss $\chi$EFT calculations of three key nuclear electroweak processes: primordial deuterium production, proton-proton fusion,…
We study a relation between nuclear forces based on phenomenological approach (V_ph) and nuclear effective field theory (V_EFT) from a viewpoint of renormalization group. We find the relation between these two types of nuclear force using…
Density functional theory (DFT) became a universal approach to compute ground-state and excited configurations of many-electron systems held together by an external one-body potential in condensed-matter, atomic, and molecular physics. At…
High-precision calculations of electroweak processes in light nuclei are of great importance for multiple reasons. Gerry Brown together with Dan-Olof Riska published in 1972 a famous calculation on radiative capture of a thermal neutron on…
The effective field theory (EFT) for triaxially deformed even-even nuclei is generalized to include the vibrational degrees of freedom. The pertinent Hamiltonian is constructed up to next-to-leading order. The leading order part describes…
Ever since quantum field theory was first applied to the derivation of nuclear forces in the mid-20th century, the renormalization of pion exchange with realistic couplings has presented a challenge. The implementation of effective field…
We develop an effective field theory (EFT) for deformed odd-mass nuclei. These are described as an axially symmetric core to which a nucleon is coupled. In the coordinate system fixed to the core the nucleon is subject to an axially…
These lectures are a pedagogical -- not comprehensive -- introduction to the applications of effective field theory in the context of nuclear and atomic physics. A common feature of these applications is the interplay between…
To obtain an understanding of the structure and reactions of nuclear systems from first principles has been a long-standing goal of nuclear physics. In this respect, few- and many-body systems provide a unique laboratory for studying…
This review gives an overview of effective field theory (EFT) as applied at finite density, with a focus on nuclear many-body systems. Uniform systems with short-range interactions illustrate the ingredients and virtues of many-body EFT and…