will thus have greater strong interaction between them and stronger binding energy. This makes it energetically favourable (i.e. having lower energy) for protons to form pairs of opposite spin. The same is true for neutrons. Calculating the coefficients The coefficients are calculated by fitting to experimentally measured masses of nuclei. Their values can vary depending on how they are fitted to the data and which unit is used to express the mass. Several examples are as shown below. The formula does not consider the internal shell structure of the nucleus. The semi-empirical mass formula therefore provides a good fit to heavier nuclei, and a poor fit to very light nuclei, especially 4He. For light nuclei, it is usually better to use a model that takes this shell structure into account. Examples of consequences of the formula By maximizing with respect to Z, one would find the best neutron–proton ratio N/Z for a given atomic weight A. We get This is roughly 1 for light nuclei, but for heavy nuclei the ratio grows in good agreement with experiment. By substituting the above value of Z back into , one obtains the binding energy as a function of the atomic weight, . Maximizing with respect to A gives the nucleus which is most strongly bound, i.e. most stable. The value we get is A = 63 (copper), close to the measured values of A = 62 (nickel) and A = 58 (iron). The liquid-drop model also allows the computation of fission barriers for nuclei, which determine the stability of a nucleus against spontaneous fission. It was originally speculated that elements beyond atomic number 104 could not exist, as they would undergo fission with very short half-lives, though this formula did not consider stabilizing effects of closed nuclear shells. A modified formula considering shell effects reproduces known data and the predicted island of stability (in which fission barriers and half-lives are expected to increase, reaching a maximum at the shell closures), though also suggests a possible limit to existence of superheavy nuclei beyond Z = 120 and N = 184. References Sources External links Nuclear liquid drop model in the hyperphysics online reference at Georgia State University. Liquid drop model with parameter fit from First Observations of Excited States in the Neutron Deficient Nuclei 160,161W and 159Ta, Alex Keenan, PhD thesis, University of Liverpool, 1999 (HTML version). Nuclear physics Nuclear chemistry Radiochemistry Mass