• The neutron separation energy becomes negative at \( {}^{25}\mbox{O} \), making this nucleus unstable with respect to the emission of one neutron. A nucleus like \( {}^{24}\mbox{O} \) is thus the last stable oxygen isotopes which has been observed. Oxygen-26 has been "found":"journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.142503" to be unbound with respect to \( {}^{24}\mbox{O} \).
• We note also that there are large shell-gaps for some nuclei, meaning that more energy is needed to remove one nucleon. These gaps are used to define so-called magic numbers. For the oxygen isotopes we see a clear gap for \( {}^{16}\mbox{O} \). We will interpret this gap as one of several experimental properties that define so-called magic numbers. In our discussion below we will make a first interpretation using single-particle states from the harmonic oscillator and the Woods-Saxon potential.

In the exercises below you will be asked to perform a similar analysis for other chains of isotopes and interpret the results.