Concurrence in Neutron–Proton Scattering for Polarization-Induced Mixed States

We investigate spin entanglement generated in neutron–proton scattering by evaluating the concurrence from the scattered two-nucleon density matrix. While previous studies mainly discussed pure initial spin states, the present work extends the analysis to polarization-induced mixed states, including partially polarized and unpolarized cases, within a unified framework. Initial polarization directions along the x, y, and [Formula: see text] axes are considered. Here, the [Formula: see text] axis is along the incident momentum, the y axis is normal to the scattering plane, and the x axis completes a right-handed system. We then examine the dependence of the concurrence on the incident energy, scattering angle, polarization degree, and polarization direction. The results show that the angular dependence of the concurrence becomes more pronounced as the incident energy increases. Although the concurrence tends to decrease overall as the polarization degree is reduced, this behavior is not uniform over all scattering angles, and in some regions unpolarized mixed states yield larger concurrence than fully polarized pure states. The concurrence is also found to be sensitive to the initial polarization direction. These features indicate that the entanglement generated in neutron–proton scattering reflects the interference structure of the scattering amplitudes. The present framework provides a basis for discussing spin entanglement under more realistic experimental conditions beyond pure-state idealizations.