Probing long-lived radioactive isotopes on the double-logarithmic Segrè chart.

Isotopes have been widely applied in a variety of scientific subjects; many aspects of isotopes, however, remain not well understood. In this study, I investigate the relation between the number of neutrons () and the number of protons () in stable isotopes of non-radioactive elements and long-lived isotopes of radioactive elements at the double-linear scale (conventional Segrè chart) and the double-logarithmic scale. Statistical analyses show that is a power-law function of for these isotopes: = 0.73 × . This power-law relation provides better predictions for the numbers of neutrons in stable isotopes of non-radioactive elements and long-lived isotopes of radioactive elements than the linear relation on the conventional Segrè chart. The power-law pattern reveled here offers empirical guidance for probing long-lived isotopes of unknown radioactive elements.