# Difference between cross section and probability of interaction

When I read some textbooks I find that the definition of cross section is the probability. Of incident neutron interact with a matter .but I find many other (cross section of fission, scattering, absorption..) And I find another definition of probability of interaction in distance $$l$$ which is given by

$$P(l)=1-e^{\frac{l}{\lambda}}$$

Where $$\lambda=\frac{1}{\Sigma}$$ And $$\Sigma$$ is the macroscopic cross section $$\Sigma=N \sigma$$, $$N$$ is the density of nuclear and $$\sigma$$ is the croos section

My question is what is the difference between the two definition?and if we want to know if an incident particle is interact with nuclear who is the better and give experiment result?

For example if we send neutron into $$Po^{209}$$ what is all the cross section that we should take it into consideration

## 1 Answer

The problem seems to be that the word cross section is used for different things in different fields and maybe even falsely by some people. I'm personally used to the definition in particle physics, where the cross section has the units of an area and has to be multiplied with multiple other quantities which describe the experiment (e.g. beam flux and target density) to gain a reaction rate which may be nearest to a probability. Therefore people may call it a probability.

The definition your formulas are coming from is different. It comes from the "Absorption cross section". If you just search for "cross section" on Wikipedia, it will give you a range of different meanings.

For your example I would guess you are looking for the neutron cross section which has it's own article.

• If we throw a neutrons to Po and use the formula above and say that 5% of particle are interact and 95% are pas is that true (or the formula use to other thing – Abdallahchaibeddrraa Mar 29 '20 at 15:35
• I have no idea from where you have your numbers, but I would say that you should NOT use above formula, as it is from a different definition of a cross section. – Paul G. Mar 29 '20 at 15:42
• So can you give the true formula to know the probality of interact neutron with material – Abdallahchaibeddrraa Mar 29 '20 at 16:05
• Like I said, you will find it, if you search "Neutron cross section" on Wikipedia. – Paul G. Mar 29 '20 at 16:24
• $V=\sigma vdt$ do you mean this formula – Abdallahchaibeddrraa Mar 29 '20 at 16:46