Neutron-Proton Mass Difference in Nuclear Matter and in Finite Nuclei and the Nolen-Schiffer Anomaly

¹ Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn, Germany
² Institut für Kernphysik and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich, Germany
³ Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
⁴ Institute of Nuclear Physics, Academy of Sciences of Uzbekistan, Tashkent - 132, Uzbekistan
⁵ Institute of Physics and Applied Physics, Yonsei University, Seoul, 120-749, Korea
⁶ Physics Department and Institute of Applied Physics, National University of Uzbekistan, Tashkent - 174, Uzbekistan

^a e-mail: a.wirzba@fz-juelich.de

Abstract

The neutron-proton mass difference in (isospin asymmetric) nuclear matter and finite nuclei is studied in the framework of a medium-modified Skyrme model. The proposed effective Lagrangian incorporates both the medium influence of the surrounding nuclear environment on the single nucleon properties and an explicit isospin-breaking effect in the mesonic sector. Energy-dependent charged and neutral pion optical potentials in the s- and p-wave channels are included as well. The present approach predicts that the neutron-proton mass difference is mainly dictated by its strong part and that it markedly decreases in neutron matter. Furthermore, the possible interplay between the effective nucleon mass in finite nuclei and the Nolen-Schiffer anomaly is discussed. In particular, we find that a correct description of the properties of mirror nuclei leads to a stringent restriction of possible modifications of the nucleon’s effective mass in nuclei.