The spin of the ground state of an atom (Q1914386)

This paper is concerned with the total spin of the ground state of an atom when each election is given a value \(\pm{1\over 2}\) for the spin. It is proved for a neutral atom with nuclear charge \(z\) that \[ \text{total spin }\leq cz^\gamma,\quad\gamma< 1, \] where \(c\) is a constant that does not depend upon \(z\). It is also conjectured that for an atom, the order of magnitude of the spin can be as large as \(z^{1/3}\).