Massformel

Massformel, or the mass formula, is a semi-empirical relation in nuclear physics that expresses the binding energy and thus the mass of an atomic nucleus as a function of its proton number Z and mass number A. The idea is to decompose the binding energy into several contributing terms that reflect different physical effects observed in nuclei: a volume term that grows with A, a surface term that reduces binding near the surface, a Coulomb term that accounts for proton–proton repulsion, an asymmetry term that penalizes neutron–proton imbalance, and a pairing term that reflects nucleon pairing.

The most widely cited form is the Bethe–Weizsäcker semi-empirical mass formula (SEMF):

B(A,Z) = a_v A − a_s A^(2/3) − a_c Z(Z−1) A^(−1/3) − a_sym (A−2Z)^2 / A + δ(A,Z),

where B is the binding energy. The last term δ(A,Z) is a pairing term that is positive for even-even nuclei, negative for odd-odd nuclei, and vanishes for odd A in its simplest version. The total mass of a nucleus is related to the binding energy by M(A,Z) = Z m_p + N m_n − B/c^2, with N = A − Z.

Mass formulas are used to estimate unknown nuclear masses, locate drip lines, and inform models of nucleosynthesis. They are inherently approximate, depending on fitted parameters and neglecting detailed shell effects. Modern mass models incorporate shell corrections and microscopic input (for example FRDM, HFB, and Duflo–Zuker approaches) to improve accuracy.