Charge Distribution of Excited Isomeric Nuclei and Atomic Spectra (The Nuclear Isomeric Shift)

Attention is called to a characteristic of excited nuclei almost unstudied until present, neither theoretically nor experimentally—namely the charge distribution. The comparison of the charge distributions of two isomeric nuclei is automatically realized in atomic spectra, giving rise to the nuclear isomeric shift on spectral lines.

Some general theoretical aspects of this effect are discussed here. Only odd nuclei with optical protons are studied. It is assumed (A) that the transitions are single-particle ones, and (B) that the Rosenthal-Breit perturbation theory is valid.

Under these assumptions it is shown that but for the sign, the effect is a pure single-particle effect, given by the optical protons. The sign of the shift is generally intimately related to the whole nuclear configuration. In the case of two characteristic transitions it is shown that the order of magnitude of the effect does not depend on the shape of nuclear potential. By specializing to two particular forms of nuclear potential (harmonic oscillator and infinite square well), it is shown that there exists a very simple relation between the shift and the characteristics of the two nuclear states involved. Numerical applications are given for ${\mathrm{In}}^{115}$iii and ${\mathrm{Au}}^{197}$i. The theoretical value of the effect is clearly within the reach of atomic spectroscopy (≥${10}^{-2\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$).