# Nuclear Physics Question

How could I calculate the chance of a proton actually joining the nucleus and 2 protons and 3 and so on? Assuming a large number of protons are fired at a substance?

• You could calculate the scattering amplitude for $| p \rangle + | nucleus \rangle \rightarrow |new nucleus \rangle$ with some simple nuclear model. – Kolandiolaka Jun 25 at 6:39

What you're looking for is the absorption cross section $$\sigma$$ of the target. This quantity has units of area, and is typically measured in barns (1 barn = 1 b = 10-28 m2.) There are many such cross-sections one can define, for any particle interaction you might care to name. If you have a beam of protons with a flux of $$f$$ (i.e., $$f$$ protons per area per time), and you send this beam at a target for a time $$\Delta t$$, then the expected number of absorptions is $$\langle N \rangle = f \sigma \Delta t.$$