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.

arXiv comment40 pages, 5 figures; Bachelor's thesis in physics, Technische Universität München, September 2020, supervised by Prof. Dr. Norbert Kaiser | The second version corrected the typing errors $(2p^2-q^2/4)\to (2p^2+q^2/4)$ in the ninth line of eq. (3.22), and $1/f_{\pi }^2\to 1/f_{\pi }^4$ in the coefficients of eq. (3.30) and eq. (3.32)

References in corpus (6)

• Peripheral Nucleon-Nucleon Phase Shifts and Chiral Symmetry
• Subleading contributions to the chiral three-nucleon force II: Short-range terms and relativistic corrections
• Density-dependent effective nucleon-nucleon interaction from chiral three-nucleon forces
• The equation of state of neutron matter, symmetry energy, and neutron star structure
• Density-dependent NN-interaction from subleading chiral 3N-forces: Long-range terms
• Density-dependent NN-interaction from subleading chiral 3N-forces: short-range terms and relativistic corrections

Cited by in corpus (2)

• Analysis of the neutron matter equation of state and the symmetry energy up to fourth order of chiral effective field theory
• The Equation of State of Neutron-Rich Matter at Fourth Order of Chiral Effective Field Theory and the Radius of a Medium-Mass Neutron Star