Resolution of the hyperfine puzzle and its significance for two fermion Dirac atoms

The hyperfine interaction in the ground state of a hydrogen atom of assumed radius $R$ is proportional to $-1/R^3$, raising the question of why the hyperfine interaction does not lead to collapse of hydrogen, or positronium. We approach the problem in terms of a minimax variational calculation based on the exact Gordon solution of the Dirac equation for the hydrogen atom ground state. The full Dirac treatment leads to the result that in an assumed variational state of size $R$, when $R$ minimizes the total energy the magnetic moment of the electron assumes its usual value, $e\hbar/2mc$, but when $R