The binding energies and stability of heavy and superheavy nuclei

Abstract

A realistic model-free description of the energies of heavy and superheavy nuclei is proposed. It is shown that: a) the charge Z* of the most stable isobar increases proportionally to the mass number A: Z* = aA + b, where a = 0.355, b = 9.3; b) the energy of β-decay of isobar Q_β(A, Z) increases as a linear function of the difference Z−Z*: Q_β = k(Z−Z*), where k = 1.13 MeV and D depends on the nuclear parity A; c) the energy of α-decay of isobars increases independently of parity in proportion to the difference Z−Z*: Q_α(A, Z) = Q_α^*(A) + λ(Z − Z*(A)), where λ = 2k(1–2a) = 0.65 MeV; d) the reduced energy of α-decay, Q_α^*(A) is minimal at A = A₀ = 232, where Q_α^*(A₀) = 4.9 MeV, and linearly increases at A ≠ A₀: Q_α^* = ε|A − A₀|, where ε = 0.212 MeV at A < A₀ and ε = 0.0838 MeV at A > A₀. Using the obtained formulas, the energies of α-decay are calculated for all heavy and superheavy nuclei with the rms deviation of 0.2 MeV. It is shown that the region near A = A₀ is the domain of most stable (heavy and superheavy) nuclei, and the region A > 280 is the domain of increased stability.