Density-Dependent Neutron-Neutron Interaction from Subleading Chiral Three-Neutron Forces

Abstract: Three-nucleon forces are an essential ingredient for an accurate description of nuclear few- and many-body systems. However, implementing them directly in many-body calculations is technically very challenging. Thus, there is a need for an efficient approximation method. By closing one nucleon line to a loop, it is possible to derive effective in-medium nucleon-nucleon interactions that represent the underlying three-nucleon forces, as constructed in Chiral Effective Field Theory. Since three-neutron forces are equally as important for the computation of the equation of state for pure neutron matter, this work applies the aforementioned approach to the subleading chiral three-neutron forces, in particular the short-range terms and relativistic corrections. It is shown in this work that, while many contributions to the in-medium neutron-neutron interaction are - apart from a constant factor - identical to the terms in isospin-symmetric matter, some differ drastically. Moreover, previously vanishing terms yield now non-zero contributions. As a result of this work, density-dependent in-medium neutron-neutron potentials are now available for the implementation in nuclear many-body calculations, either in closed analytical form, or requiring at most one numerical integration.