Even and odd atomic nuclei

In nuclear physics, properties of a nucleus depend on evenness or oddness of its atomic number Z, neutron number N and, consequently, of their sum, the mass number A. Most notably, oddness of both Z and N tends to lower the nuclear binding energy, making odd nuclei, generally, less stable. This effect is not only experimentally observed, but is included to the semi-empirical mass formula and explained by some other nuclear models, such as nuclear shell model. This remarkable difference of nuclear binding energy between neighbouring nuclei, especially of odd-A isobars, has important consequences for beta decay.

Also, the nuclear spin is integer for all even-A nuclei and non-integer (half-integer) for all odd-A nuclei.

The neutron–proton ratio is not the only factor affecting nuclear stability. Adding neutrons to isotopes can vary their nuclear spins and nuclear shapes, causing differences in neutron capture cross-sections and gamma spectroscopy and nuclear magnetic resonance properties. If too many or too few neutrons are present with regard to the nuclear binding energy optimum, the nucleus becomes unstable and subject to certain types of nuclear decay. Unstable nuclides with a nonoptimal number of neutrons or protons decay by beta decay (including positron decay), electron capture or other exotic means, such as spontaneous fission and cluster decay.

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