Semi-Empirical Mass Formula

The semi-empirical mass formula, also called the Weizsäcker formula or the Bethe-Weizsäcker formula, is a formula in nuclear physics used to approximate the mass of an atomic nucleus from its number of protons and neutrons. First formulated by Carl Friedrich von Weizsäcker in 1935 and based on George Gamows liquid drop model of the nucleus, it combines theoretical reasoning with empirically fitted coefficients and, despite refinements to those coefficients over the decades, its basic structure has remained unchanged. The formula sums five terms representing different nuclear effects: a volume energy term for the packing of nucleons, a surface energy correction, a Coulomb term for the repulsion between protons, an asymmetry term reflecting the Pauli exclusion principle, and a pairing term accounting for the extra stability of paired nucleons. It gives strong predictions for the masses and binding energies of heavier nuclei, but performs poorly for very light nuclei such as helium-4 and cannot account for the extra stability found at certain magic numbers of protons or neutrons, which instead require the nuclear shell model to explain. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/