= Solution
{disambiguate=energy sketch}
The square-root branches avoid one another when $\Delta\ne0$; crossings with a parallel-spin branch are allowed because total <spin> projections differ. At zero field the positive-$\Delta$ sketch has one lower singlet and a triplet above it. The source supplies no numerical moment ratio, so the two panels show explicit illustrative signed choices, including the exactly compensated case.
\Image[/past-exam-of-the-advanced-quantum-physics-course-of-the-university-of-cambridge/2014/paper-1-aqp2014-spin-spectrum.png]
{title=Two-spin exchange and Zeeman energies depend on the signed moment ratio, with an exact parallel-spin degeneracy for opposite equal moments}
{source=paper-1-aqp2014-spin-spectrum.py}
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