Semi-empirical mass formula

Nuclear physics
Nucleus Nucleons p n Nuclear matter Nuclear force Nuclear structure Nuclear reaction
Models of the nucleus Liquid drop Nuclear shell model Interacting boson model Ab initio
Nuclides' classification Isotopes – equal Z Isobars – equal A Isotones – equal N Isodiaphers – equal N − Z Isomers – equal all the above Mirror nuclei – Z ↔ N Stable Magic Even/odd Halo Borromean
Nuclear stability Binding energy p–n ratio Drip line Island of stability Valley of stability Stable nuclide
Radioactive decay Alpha α Beta β 2β 0v β+ K/L capture Isomeric Gamma γ Internal conversion Spontaneous fission Cluster decay Neutron emission Proton emission Decay energy Decay chain Decay product Radiogenic nuclide
Nuclear fission Spontaneous Products pair breaking Photofission
Capturing processes electron 2× neutron s r proton p rp
High-energy processes Spallation by cosmic ray Photodisintegration
Nucleosynthesis and nuclear astrophysics Nuclear fusion Processes: Stellar Big Bang Supernova Nuclides: Primordial Cosmogenic Artificial
High-energy nuclear physics Quark–gluon plasma RHIC LHC
Scientists Alvarez Becquerel Bethe A. Bohr N. Bohr Chadwick Cockcroft Ir. Curie Fr. Curie Pi. Curie Skłodowska-Curie Davisson Fermi Hahn Jensen Lawrence Mayer Meitner Oliphant Oppenheimer Proca Purcell Rabi Rutherford Soddy Strassmann Świątecki Szilárd Teller Thomson Walton Wigner
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In nuclear physics, the semi-empirical mass formula (SEMF) (sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approximate the mass of an atomic nucleus from its number of protons and neutrons. As the name suggests, it is based partly on theory and partly on empirical measurements. The formula represents the liquid-drop model proposed by George Gamow,^[1] which can account for most of the terms in the formula and gives rough estimates for the values of the coefficients. It was first formulated in 1935 by German physicist Carl Friedrich von Weizsäcker,^[2] and although refinements have been made to the coefficients over the years, the structure of the formula remains the same today.

The formula gives a good approximation for atomic masses and thereby other effects. However, it fails to explain the existence of lines of greater binding energy at certain numbers of protons and neutrons. These numbers, known as magic numbers, are the foundation of the nuclear shell model.