Full Nuclide System Verification: The Systematic Law of Neutron Effective Mass in Nuclei

This paper performs a systematic calculation for all stable nuclides from hydrogen to bismuth-209 to examine the relationship between the effective mass of neutrons bound in nuclei and the rest mass of free neutrons. The calculation inputs are taken from the AME2020 Atomic Mass Evaluation, the ENDF/B-VIII.0 Nuclear Data Library, and the CODATA 2022 recommended values, with no fitting parameters. The results show that for all stable nuclides with atomic number Z ≥ 2, the deviation between the effective mass of neutrons bound in nuclei and the free neutron rest mass is strictly zero within experimental measurement error, covering a N/Z ratio range from 0.5 to 1.54, without any exception. For Z = 1, two special cases appear: the deuteron (²H) deviates by −0.511 MeV, precisely equal in absolute value to the electron rest energy; the triton (³H) deviates by approximately −0.217 MeV, a fixed negative offset. Z = 2 is the critical atomic number at which the effective mass of bound neutrons first closes upon the free neutron value. This paper reports the discovery of this systematic law. The preceding papers have independently derived the electron rest energy and proton mass [1,2]; the full nuclide verification presented here and those independent derivations are mutually consistent. All calculations use only algebra and publicly available data; any researcher can independently reproduce them.