Extension of the Bethe-Weizsäcker mass formula to light nuclei and some new shell closures

Abstract

This new mass formula explains the shape of the binding energy versus neutron number curve of all the elements from Li to Bi. A simple comparison of the one-neutron separation energy versus neutron number curve with the experimental data clearly delineates positions of all the known old and new magic numbers, reveals extra stability at neutron number $N=16$ $(Z=7,8),$ $N=14$ $(Z=7--10),$ $Z=14$ $(N=13\ensuremath{-}19),$ $N=6$ $(Z=3--8),$ and loss of magicity for nuclei with $N=8$ $(Z=4)$ and $N=20$ $(Z=12--17).$ It supports existence of ${}^{32}\mathrm{Ne},$ ${}^{35}\mathrm{Na},$ ${}^{38}\mathrm{Mg},$ and ${}^{41}\mathrm{Al}$ nuclei as the last bound isotopes of Ne, Na, Mg, Al, and suggests ${}^{26}\mathrm{O}$ as a bound nucleus.