A Universal Descent Potential for Spontaneous Nuclear Transformations

The direction of spontaneous nuclear transformations is confronted with two accounting frameworks, corresponding to two hypotheses about the constitution of the nucleus. The standard accounting (the nucleus as protons and neutrons, surrounded by orbital electrons) defines B(Z,A) = Z·m(¹H) + (A−Z)·mn − m(Z,A). The hypothesis under test (the nucleus as protons bound by internal electrons, neutrality being completed by the external shell, the electron being the same particle inside and outside) calls for the “separated constituents” frame of reference: A bare protons and A electrons, whose metrological realization is A·m(¹H); one defines BH(Z,A) = A·m(¹H) − m(Z,A), the total configuration energy of the proton-electron edifice. An automated, exhaustive audit of the AME2020 and NUBASE2020 tables (3,558 nuclides; 5,985 positively observed spontaneous transitions, including ground states, isomers and β-delayed modes) establishes: (i) BH increases strictly in 5,985 cases out of 5,985, without exception and without parameters: the identity ΔBH = Q is verified numerically to within 10⁻⁴ keV; (ii) B decreases in 114 observed transitions, all belonging to the β− family in the broad sense (β−, 2β−, β-delayed, isomeric β−), and the empirical list of violations coincides exactly, in both directions, with the analytical rule Q < k·(mn − mh) = k·782.347 keV, where k is the number of n→p conversions. The separated-constituents frame thus behaves as a universal descent potential for all recorded nuclear transformations, while the standard frame requires the mass difference mn − mh as a corrective directional parameter. The same identity extends the result, as a theorem, to any nuclear reaction conserving A: fusion, captures and decays fall, in this frame, under a single process (mass loss through partial mutual annihilation of paired particles) whose progression is continuous and of constant direction: radioactivity is an integral part of nucleosynthesis.