This is one of a few difficulties I have with the paper. They do not talk about what specific neutrino-nucleus interactions would be stimulated, nor do they ballpark numbers for rates based on the known solar neutrino flux.
Also, their proposed method of testing their hypothesis may hit a snag: while the sun produces a very pure flux of neutrinos, reactors produce a nearly-pure flux of antineutrinos. There are differences in how the two interact, so more investigation should be done to determine if such a proposed experiment could return a signal.
If it means anything, I do happen to be a graduate student working in the field of neutrino physics.