Nuclear Lattice Effective Field Theory: An Introduction

Description

This primer begins with a brief introduction to the main ideas underlying Effective Field Theory (EFT) and describes how nuclear forces are obtained from first principles by introducing a Euclidean space-time lattice for chiral EFT. It subsequently develops the related technical aspects by addressing the two-nucleon problem on the lattice and clarifying how it fixes the numerical values of the low-energy constants of chiral EFT. In turn, the spherical wall method is introduced and used to show how improved lattice actions render higher-order corrections perturbative. The book also presents Monte Carlo algorithms used in actual calculations. In the last part of the book, the Euclidean time projection method is introduced and used to compute the ground-state properties of nuclei up to the mid-mass region. In this context, the construction of appropriate trial wave functions for the Euclidean time projection is discussed, as well as methods for determining the energies of the low-lying excitations and their spatial structure. In addition, the so-called adiabatic Hamiltonian, which allows nuclear reactions to be precisely calculated, is introduced using the example of alpha-alpha scattering. In closing, the book demonstrates how Nuclear Lattice EFT can be extended to studies of unphysical values of the fundamental parameters, using the triple-alpha process as a concrete example with implications for the anthropic view of the Universe. Nuclear Lattice Effective Field Theory offers a concise, self-contained, and introductory text suitable for self-study use by graduate students and newcomers to the field of modern computational techniques for atomic nuclei and nuclear reactions. Front Matter ....Pages i-xi Introduction to Effective Field Theory (Timo A. Lähde, Ulf-G. Meißner)....Pages 1-21 Nuclear Forces in Chiral EFT (Timo A. Lähde, Ulf-G. Meißner)....Pages 23-56 Lattice Formulations (Timo A. Lähde, Ulf-G. Meißner)....Pages 57-82 Lattice Chiral Effective Field Theory (Timo A. Lähde, Ulf-G. Meißner)....Pages 83-133 Two and Three Nucleons on the Lattice (Timo A. Lähde, Ulf-G. Meißner)....Pages 135-195 Lattice Monte Carlo (Timo A. Lähde, Ulf-G. Meißner)....Pages 197-251 Light and Medium-Mass Nuclei on the Lattice (Timo A. Lähde, Ulf-G. Meißner)....Pages 253-289 Further Developments (Timo A. Lähde, Ulf-G. Meißner)....Pages 291-311 Back Matter ....Pages 313-396