Effective field theory approach to nuclear matter

Nuclear matter refers to an infinite system of nucleons interacting via only the strong force, with the electromagnetic force being turned off. One's main objective in describing nuclear matter is to determine the nuclear matter density and binding energy per particle. It has been studied for nearly seven decades, with early work on nuclear matter based on the liquid drop model for nucleons and the modern conventional approach based on a nuclear potential with a repulsive core.;An accurate description of nuclear matter starting from free-space nuclear forces has not been achieved. The complexity of the system makes approximations inevitable, so the challenge is to find a consistent truncation scheme with controlled errors. Effective field theories could be well suited for the task. We have taken some important first steps towards understanding how to apply effective field theory to the nuclear matter medium. In a perturbative model calculation, we have shown how the effective field theory expansion parameter and breakdown scale in nuclear matter are determined and how they are related to the corresponding free space quantities.;Conventional nuclear matter calculations have shown that different nucleon-nucleon potentials that give the same phase shifts can give significantly different binding energy curves in nuclear matter. The interpretation has been that the differences are due to off-shell effects and that one needs to find the potential that has the "correct" off-shell behavior. From the effective field theory perspective, different regularization schemes or field redefinitions should give the same result order-by-order in the effective field theory expansion.;By considering certain field redefinitions we have demonstrated how the apparent dependence of the nuclear matter observables on the off-shell properties of the two-nucleon potential is removed in the context of the effective field theory approach. We have shown how field redefinitions shift contributions between purely off-shell two-body interactions and many-body forces, leaving both the scattering and finite density observables unchanged. If only the transformed two-body potentials are kept, the nuclear matter saturation point will depend on the off-shell part. We have also shown the correspondence between field redefinitions and unitary transformations, which have traditionally been used to generate phase-equivalent nucleon-nucleon potentials.