17 research outputs found
Lattice methods and the nuclear few- and many-body problem
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.Comment: 20 pages, 3 figures, Submitted to Lect. Notes Phys., "An advanced
course in computational nuclear physics: Bridging the scales from quarks to
neutron stars", M. Hjorth-Jensen, M. P. Lombardo, U. van Kolck, Editor
Ab initio alpha-alpha scattering
Processes involving alpha particles and alpha-like nuclei comprise a major
part of stellar nucleosynthesis and hypothesized mechanisms for thermonuclear
supernovae. In an effort towards understanding alpha processes from first
principles, we describe in this letter the first ab initio calculation of
alpha-alpha scattering. We use lattice effective field theory to describe the
low-energy interactions of nucleons and apply a technique called the adiabatic
projection method to reduce the eight-body system to an effective two-cluster
system. We find good agreement between lattice results and experimental phase
shifts for S-wave and D-wave scattering. The computational scaling with
particle number suggests that alpha processes involving heavier nuclei are also
within reach in the near future.Comment: 6 pages, 6 figure
Ab Initio Nuclear Thermodynamics
We propose a new Monte Carlo method called the pinhole trace algorithm for ab initio calculations of the thermodynamics of nuclear systems. For typical simulations of interest, the computational speedup relative to conventional grand-canonical ensemble calculations can be as large as a factor of one thousand. Using a leading-order effective interaction that reproduces the properties of many atomic nuclei and neutron matter to a few percent accuracy, we determine the location of the critical point and the liquid-vapor coexistence line for symmetric nuclear matter with equal numbers of protons and neutrons. We also present the first ab initio study of the density and temperature dependence of nuclear clustering
Causality bounds for neutron-proton scattering
We consider the constraints of causality and unitarity for the low-energy
interactions of protons and neutrons. We derive a general theorem that
non-vanishing partial-wave mixing cannot be reproduced with zero-range
interactions without violating causality or unitarity. We define and calculate
interaction length scales which we call the causal range and the Cauchy-Schwarz
range for all spin channels up to J = 3. For some channels we find that these
length scales are as large as 5 fm. We investigate the origin of these large
lengths and discuss their significance for the choice of momentum cutoff scales
in effective field theory and universality in many-body Fermi systems.Comment: 36 pages, 10 figures, 7 tables, version to appear in Eur. Phys. J.