On the hyperfine splitting of the hydrogen atom in a spherical box

Abstract

The hyperfine splitting of the hydrogenlike atom confined to a sphere of radius r0 is examined as a function of r0. The wavefunction is made to vanish at r=r0 and is normalized to unity over the finite sphere. The effect of decreasing r0 (i.e., compressing the sphere isotropically) on the hyperfine splitting A of the ground state is nonlinear, with A increasing approximately as r−10. Comparison with atomic hydrogen trapped in α-quartz is made.