# Elementary question on pion-proton scattering cross-section

Is $E_k$ the energy of the outgoing or incoming pion?

The first peak is supposed to be a delta baryon.

What does the graph tell us, experimentally? A pion of kinetic energy x comes in, then we look at the graph and find the cross-section, so then we have the probability of what happening? Or is $E_k$ the net loss in kinetic energy of the pion, and this graph tells us the distribution of its energy loss?

How is this graph constructed, what is measured?

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I am not sure but I think $E_k$ cannot be the incoming pion kinetic energy. From the graph, this energy is about $250\ MeV$. If the target protons are at rest, this is not enough energy to produce Δ resonances which have rest masses larger than $1\ GeV$ –  Dario Alexander May 1 '13 at 10:31
What reference did the graph come from? –  Qmechanic May 1 '13 at 10:42
Subatomic physics, Henley 3rd edition –  I am very happy May 1 '13 at 10:50
@DarioAlexander The proton is excited to a delta (as opposed to a whole new particle being created), so it is the difference of rest masses which matters. That's only around 290 MeV. –  dmckee May 1 '13 at 12:47
@dmckee, yes your right –  Dario Alexander May 1 '13 at 13:02

This is a plot where the incoming pion beam is varied and the total interaction cross section is measured , showing higher scattering cross section at the resonances, as the beam kinetic energy is varied. The interactions are measured by looking how many pions are left in the beam direction after the beam has passed has passed the target. The difference is due to their having interacted , from elastic scattering and changing the angle to creating more particles , they are missing in the count.

This is related. explaining how similar plots can be made after the interaction: In particle physics E_k is the kinetic energy of an outgoing pion from a pi proton scattering.Such plots are usually constructed by scattering a beam of pions with fixed energy and looking at two body interactions with the protons at rest, identifying the outgoing proton and pion by ionization. One would have plotted the invariant mass distribution and then the resonances would have been easily labeled.

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But what does the cross-section at some energy tell us, isnt the probability of scattering always 1, the pion has to come out somewhere? And first you say the beam kinetic energy is varied, then you say E_k is the kinetic energy of the outgoing pion, which is it ? –  I am very happy May 1 '13 at 10:13
I will edit for clarity. –  anna v May 1 '13 at 10:21
The pion when it interacts, even with a simple elastic scatter gets off the beam direction . Have a look capone.mtsu.edu/phys3110/Homework/HW/Extra_12_A/… to see how a pion disappears from a beam line . The crossection gives the probability of interaction –  anna v May 1 '13 at 10:32
@user: It is, perhaps, helpful to know that there was already a history of doing this kind of (inclusive) scattering measurement on nuclei (with considerable success). This is one of the basic tools in the particle physics tool box, even if we mostly reach for more sophisticated ones these days. –  dmckee May 1 '13 at 12:51