Spontaneous fission instability of the neutron-deficient No and Rf isotopes: The new isotope No249

In the heaviest elements, the instability of atomic nuclei against spontaneous fission leads to ever shorter nuclear half-lives. Upon falling below a timescale of ${10}^{\ensuremath{-}14}$ s, the border of existence of isotopes is crossed because this is the timescale on which the formation of atomic shells occurs. Analysis of the experimental data on the spontaneous fission half-lives of Rf isotopes in relation with their expected single-particle orbitals hint at a potentially abrupt decrease in half-lives of unknown neutron-deficient Rf isotopes with neutron numbers $l149$, which suggests that the isotopic border is already almost reached. However, this conjecture, which cannot be explained within the current knowledge, was directly related to uncertainty in the experimental data on $^{253}\mathrm{Rf}$. We revisited the decay of $^{253}\mathrm{Rf}$ and identified two fission activities, which are attributed to decays of the two different states with half-lives of $12.{8}_{\ensuremath{-}3.4}^{+7.0}$ ms and ${44}_{\ensuremath{-}10}^{+17}\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$. In addition, hitherto unknown $\ensuremath{\alpha}$ decay in $^{253}\mathrm{Rf}$, which is followed by $\ensuremath{\alpha}$ decay of the new isotope $^{249}\mathrm{No}$ with a half-life of ${15}_{\ensuremath{-}7}^{+74}$ ms, was observed. Based on our new data, no abrupt decreases in half-lives of the neutron-deficient No and Rf isotopes are expected, which is in line with theoretical predictions. Fission half-lives of the two different states in $^{253}\mathrm{Rf}$ are benchmark cases for the theoretical description of the single-particle orbital influence on the fission process.