5^{th} International Symposium on Nuclear Symmetry Energy NuSYM15, June 29 - July 2, 2015 Kraków, POLAND

### Constraints on the Momentum Dependence of the Symmetry Mean Field Potential

**Bill Lynch**

Michigan State University East Lansing, UNITED STATES

**Abstract**

Inside a finite nucleus or nuclear matter, a nucleon experiences a strong,
momentum-dependent interaction with its surrounding medium that leads to an apparent reduction of its inertial mass, described by the term effective mass" or k-mass². Such effective masses provide a convenient description of the momentum
dependencies of mean-field potentials that arise due to exchange and other non-localities, Lorentz properties of the nucleon-nucleon interaction, and higher-order terms. In neutron rich environments many theories predict that the difference between the momentum dependence of the potentials felt by protons and neutrons will cause the neutron and proton effective masses to differ. The sign of the difference between the neutron and proton effective masses is model dependent and the magnitude of this difference is density dependent. It strongly influences the symmetry energy and nuclear Equation of State (EoS), the magnitude of shell effects in nuclei far from stability, the thermal properties of neutron-rich nuclei, core-collapse supernovae, neutron stars, and neutron star cooling by neutrino emission. This motivates the need for experimental constraints on the mass splitting. In this talk, I will discuss how one can isolate this effective mass splitting from neutron/proton double ratios and distinguish
its effects from the effects from the density dependent but momentum independent nuclear symmetry mean field and other effects. I will also discuss briefly some of the challenges in modeling such data and how they may be overcome.