Kvantmekanisk sammanflätning i nukleon-nukleonspridning - ABRAHAMSSON, LUCAS; CAVALLIN, ALMA; HANEBRING, LISE; HANSEN, HAMPUS; KARLSSON ÖHMAN, ERIK; LEO (My University, 2023)
The following report studies the quantum entanglement phenomenon analytically and numerically. Spe cifically, the degree to which the scattering operators S and M entangle a neutron and a proton with respect to spin during a scattering process is investigated. The M matrix is computed analytically, using a low-energy approximation considering only s-waves, as well as numerically. This study differentiates itself from prior research by investigating entanglement based on the M ope rator instead of the S operator. The numerical calculation of M is possible without making the s-wave approximation, thus resulting in a more realistic model where it is possible to analyze higher energies and the scattering angle dependence. Numerical calculations are performed using provided code, and the convergence of the calculations with respect to partial waves and sampling points is analyzed. Entanglement measures are calculated nume rically using various methods, including Monte Carlo integration, which is implemented in Python. Two entanglement measures are presented and compared, and the entanglement power is then used to inve stigate entanglement in nucleon-nucleon scattering. The study establishes that there is no combination of kinetic energy and scattering angle that yields a fully entangled final state in spin space for all pos sible initial states. Similarly, there is no combination of kinetic energy and scattering angle that yields a non-entangled final state for all possible initial states. The entanglement power of the analytic S and M operators is investigated. It is found that the entang lement power for M converges to a non-zero value in the low-energy limit, which is also observed in the numerical results. The entanglement power of the analytically derived M matrix is compared with the numerically calculated one and shows good agreement for energies up to a few MeV. The analytical expression of M establishes that no entanglement occurs in the interaction at very low energies if the nucleons initially have parallel spins. This is also verified in the numerical results for specific initial states.
Keywords: entanglement, scattering, nucleon, strong force, Nijmegen potential, partial waves, two-nucleon system, entanglement power