I’ve also been looking into this, except as a prospective transfer. It seems the department is relatively small, and probably as selective as any other major at UCB, if not more. I believe you would have to be in the College of Chemistry, but I could be wrong.
Nuclear Engineering isn’t really a sub branch of ChemE. It has more in common with Material Engineering and Sciences…but really, it requires the same core classes as most engineering majors (up to thermodynamics and materials), but has a large series of NE only classes. It usually doesn’t require much more chemistry than a mechanical or electrical engineer…
UC-Berkeley’s “Joint-major” is unique in it’s focus, which is around fuel processing and not nuclear reactor operations.
^You can make that argument. Mechanical is as close a match as any. Nukes focus much more on (nuclear) physics and thermodynamics, more than chemistry.