Effective Theories in Few-Body Physics
Effective theories are a controlled approach to making approximations in physics. We describe here work on two applications of effective theory techniques in few-body physics, specifically to nuclear and atomic systems.
First, we analytically reduce the chiral three-nucleon interaction at NNLO to a density-dependent effective two-body potential by summing the third particle over the states of a spin-symmetric Fermi gas. Results are given for the potential in momentum space and in coordinate space, where the potential is seen to be nonlocal. An expansion of the potential in the difference of the nonlocal coordinates is made in order to arrive at a fully local effective two-body potential.
We then explore the two-body spectra of spin-1/2 fermions in isotropic harmonic traps with external spin-orbit potentials and short range two-body interactions. Using a truncated basis of total angular momentum eigenstates, which is known to be equivalent to an effective theory when the atomic gas is harmonically confined, nonperturbative results are presented for experimentally realistic forms of the spin-orbit coupling: a pure Rashba coupling, Rashba and Dresselhaus couplings in equal parts, and a Weyl-type coupling. The technique is easily adapted to bosonic systems and other forms of spin-orbit coupling.