Measurement of the Neutron-Neutron Scattering Length

The ¹S₀ neutron-neutron scattering length aₙₙ characterizes the two-neutron interaction at low energies and therefore is a fundamental quantity in many broad research fields such as nuclear structure physics. There were numerous attempts to determine the scattering length in the past decades, some of them with contradicting results, also including more recent ones. The precise and accurate measurement of aₙₙ still remains challenging and to this day, in contrast to the proton-proton scattering length, no direct measurement via n-n scattering is feasible. In this work, a new approach to measure aₙₙ is presented that makes use of relativistic radioactive ion beams created at high energies, in order to investigate n-n scattering at low energies. The experiment will be conducted at the "Radioactive Ion Beam Factory" of the research institute RIKEN in Japan and aims at the investigation of the free two-neutron system using the knockout reactions ⁶He(p,pα)2n and t(p,2p)2n. Furthermore, single-neutron events resulting from the d(p,2p)n reaction will serve for calibration and validation purposes. In the case of the ⁶He(p,pα)2n reaction, the n-n scattering length is accessible by comparison of the experimentally determined two-neutron relative-energy spectrum to calculations using the effective field theory for halo nuclei, called "Halo EFT". For the t(p,2p)2n reaction, the corresponding calculations will instead be based on pionless EFT. For the purpose of this experiment, the new high-resolution neutron detector HIME is currently developed and constructed at the "Institut für Kernphysik" in Darmstadt, Germany. A prototype of that detector has already been built at RIKEN. In this work, it was taken in operation and tested with electronics from "Gesellschaft für Schwerionenforschung" in Darmstadt. All reactions will take place in inverse kinematics with a beam energy of about 200 MeV/nucleon, resulting in two-neutron systems that move with relativistic velocity in the laboratory system. Thereby, a nearly constant neutron-detection efficiency in the relative-energy region of interest can be achieved. The measurements will be kinematically complete, which allows for a strong background suppression. In order to reach sufficient resolution, the relative-energy spectrum will be reconstructed by direct invariant-mass measurement, requiring coincident two-neutron detection. The analysis methods for the reconstruction of the primary interaction points in the neutron detector, which have been developed in this work, are tested and discussed with simulated data. Due to the limited resolution, efficiency and acceptance of the experimental setup, the measured relative-energy distribution cannot be compared directly to theoretical calculations. Different approaches of solving this issue are presented and discussed with simulated data as well