 Axial spin-three-halves resonance coincidence

For $H=D{S}_z^2+g{\mu }_{B}B{S}_z$ with $D>0$ and a transverse oscillating field, the allowed gaps are $g{\mu }_{B}B$, $|g{\mu }_{B}B-2D|$ and $g{\mu }_{B}B+2D$. Below $h\nu =2D$, the positive-field solutions are $h\nu$, $2D-h\nu$ and $2D+h\nu$ in units of $g{\mu }_{B}B$. At $h\nu =D$ two transitions coincide, leaving two distinct resonance fields. At $h\nu =2D$ a zero-field resonance must be counted separately.