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These interaction channels are mainly relevant at low energies due to their energy threshold, which is much lower than that of equivalent interactions on carbon-12.
However, carbon-13 makes up only about 1% of carbon nuclei in nature. Thus, even at low energies I’d estimate that the event rate of these interactions is about an order of magnitude smaller than that of neutrino-electron scattering. That would make this a very minor correction.
These interaction channels are mainly relevant at low energies due to their energy threshold, which is much lower than that of equivalent interactions on carbon-12.
However, carbon-13 makes up only about 1% of carbon nuclei in nature. Thus, even at low energies I’d estimate that the event rate of these interactions is about an order of magnitude smaller than that of neutrino-electron scattering. That would make this a very minor correction.
A theoretical calculation (including a nice numerical fit) of the cross-section is available.
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