Neutrino-Atom Elastic Scattering: Insights from Particle Physics

What happens generally when a neutrino/anti-neutrino collides with a light vs heavy atom?

My guess is, since neutrinos have very low cross section, their interaction is weak and therefore it will be an elastic scattering! For example:

$$ \overline{\nu} + He^3 \rightarrow \overline{\nu} + He^3 $$

and

$$ \nu + C^{12} \rightarrow \nu + C^{12} $$

But since I'm new to Particle physics and trying to learn by my own I'm not very sure!

Elastic scattering is always possible, inelastic reactions can be possible depending on the target nucleus and the neutrino energy. ##\nu + T \rightarrow {}^3He + e^-## is possible at any neutrino energy, for example, because tritium already has enough energy to decay even without neutrino.

A few points.

We usually write nuclei as ⁵⁰V..

Neutrinos and antineutrinos do different things. To a degree electron, muon and tau neutrinos do different things.

Interactions on matter can occur off a nuclear target or an electron target. The latter happens less often.

What you have drawn is called a "neutral current" event. They are less common than "charged current" events, when a neutrino comes in and a charged lepton goes out.