Editing Semi-empirical mass formula (section)

{{Short description|Formula to approximate nuclear mass based on nucleon counts}}
{{Nuclear physics}}
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 [[proton]]s and [[neutron]]s. As the name suggests, it is based partly on [[scientific theory|theory]] and partly on [[empirical evidence|empirical measurements]]. The formula represents the '''liquid-drop model''' proposed by [[George Gamow]],<ref>{{cite journal |last=Gamow |first=George |year=1930 |title=Mass Defect Curve and Nuclear Constitution |journal=[[Proceedings of the Royal Society A]] |jstor=95297 |bibcode=1930RSPSA.126..632G |doi=10.1098/rspa.1930.0032 |doi-access=free |volume=126 |issue=803 |pages=632–644}}</ref> 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]],<ref>{{cite journal |last=von Weizsäcker |first=C. F. |year=1935 |title=Zur Theorie der Kernmassen |journal=[[Zeitschrift für Physik]] |language=de |bibcode=1935ZPhy...96..431W |doi=10.1007/BF01337700 |volume=96 |issue=7–8 |pages=431–458|s2cid=118231854 }}</ref> 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 number (physics)|magic numbers]], are the foundation of the [[nuclear shell model]].