Atomic spectral lines are due to transitions of electrons between different atomic energy levels E, followed by emission of photons. Atomic levels are a manifestation of the electromagnetic interaction between electrons and nuclei. The energy levels of two atoms, the nuclei of which are different isotopes of the same element, are shifted one with respect to the other, despite the fact that the electric charges Z of the two isotopes are identical. This is so because isotopes differ by the number of neutrons, and therefore the masses and volumes of two isotopes are different; these differences give rise to the isotopic shift on atomic spectral lines.
In the case of two nuclear isomers, the number of protons and the number of neutrons are identical, but the quantum states and in particular the energy levels of the two nuclear isomers differ. This difference induces a difference in the electric charge distributions of two isomers and thus a difference δφ in the corresponding electrostatic nuclear potentials φ, which ultimately leads to a difference ΔE in the atomic energy levels. The isomeric shift on atomic spectral lines is then given by
where ψ is the wave function of the electron involved in the transition, e its electric charge, and the integration is performed over the electron coordinates.
The isotopic and the isomeric shift are similar in the sense that both are effects in which the finite size of the nucleus manifests itself and both are due to a difference in the electromagnetic interaction energy between the electrons and the nucleus of the atom. The isotopic shift had been known decades before the isomeric shift and provided useful but limited information about atomic nuclei. Unlike the isomeric shift, the isotopic shift was at first discovered in experiment and then interpreted theoretically (see also ). While in the case of the isotopic shift the determination of the interaction energy between electrons and nuclei is a relatively simple electromagnetic problem, for isomers the problem is more involved, since it is the strong interaction, which accounts for the isomeric excitation of the nucleus and thus for the difference of charge distributions of the two isomeric states. This circumstance explains in part why the nuclear isomeric shift was not discovered earlier: the appropriate nuclear theory and in particular the nuclear shell model were developed only in the late 1940s and early 1950s. As to the experimental observation of this shift, it also had to await the development of a new technique, that permitted spectroscopy with isomers, which are metastable nuclei. This too happened only in the 1950s.
While the isomeric shift is sensitive to the internal structure of the nucleus, the isotopic shift is (in a good approximation) not. Therefore, the nuclear physics information that can be obtained from the investigation of the isomeric shift, is superior to what can be obtained from isotopic-shift studies. The measurements through the isomeric shift of e.g. the difference of nuclear radii of the excited and ground state constitute one of the most sensitive tests of nuclear models. Moreover, combined with the Mössbauer effect, the isomeric shift constitutes at present a unique tool in many other fields besides physics.