States in neighboring nuclear isobars that have the same total angular momentum, parity, and isotopic spin. They also have nearly identical nuclear structure wave functions except for the transformation of one or more neutrons into an equivalent number of protons, which occupy the same single-particle states as the neutrons. Analog states (or isobaric analog states, IAS) have been observed throughout the periodic table, indicating that isotopic spin is a good quantum number. See Angular momentum, I-spin, Nuclear structure, Parity (quantum mechanics)
Since the nucleon-nucleon interaction has been found to be approximately charge-independent, it is possible to consider protons and neutrons as representing different charge states of a single particle, that is, a nucleon. Thus, a level (commonly referred to as a parent state) in a nucleus with Z protons and N neutrons can be expected to have an analog in the neighboring isobar with Z protons and N neutrons (and the same total number of nucleons, A = ZN), where the protons and neutrons occupy the same orbits as those in the parent state. The energy difference between the parent and analog states predominantly arises from the increased contribution from the electrostatic Coulomb interaction to the total energy arising from the extra proton in the analog state. From this amount must be subtracted the neutron-proton mass difference of 0.782 MeV (energies are given on the atomic mass scale). The agreement between such calculated energies of analog states and their measured values is in general fairly precise but not exact. The reason is that small additional factors influence the level energies, such as electromagnetic effects, a small charge-dependent nuclear interaction, isospin mixing, and nuclear structure effects.
The study of analog states provides important information used to test nuclear theories. For example, the double charge-exchange reactions (&pgr;+, &pgr;-) [where &pgr;+ and &pgr;- represent a pion with positive and negative charge, respectively] have been used to identify double isobaric analog states, that is, analogs in isobars removed by 2 charge units. Such data have been useful for testing various formulas for predicting the relative masses of isobaric multiplets. Single and double charge-exchange reactions utilizing incident pions have also been used to investigate giant resonances built upon analog states. The single-particle structure of parent states can be studied by observing the particle decay of the analog state when the decay resides in the nuclear continuum. Measurements of the widths of analog states provide information pertaining to their fragmentation, for example, their mixing with states of the same spin and parity but with total isospin lower by one unit.