# Partial waves

Hi! I need an help on short thesis I'm writing for an exam.
It is about artificial radioactivitiy, and my professor has told me to treat the partial waves formalisms to calculate the cross-section of nuclear reactions.

He told me to start that section with: "Cross section is the most important tool for the study of nuclear reactions, especially artificial ones"...

I don't knowt why, and I have not been able to understand it. Who can explain me this sentence?
I think I've got the essential points of the formalisms. However, I am not sure about something:
is there a difference between cross section in different areas of Physics?

Sorry for the maybe stupid questions, but some courses at my uni has been a little muddling, and I can't find a book to put in order these important concepts.

Thank you for the possibile answers
Bye
Iorfus

Physics is all about forming (and hopefully solving) models of the world around us.
The choice you make will not change the result but will make all the difference in the amount of math you will need to do to solve the model (or in extreme cases whether you will be able to see your way through the math to solve it at all).

An example : It is quite possible to solve problems in electromagnetism by writing out all Maxwells equations in terms of partial differential equations in the Cartesian variables x,y,z and time and laboriously solving them, substituting one solution into the next and so on. Even for an elementary problem the work would be vast. Or you could chose the formalism of vectors and vector operators (div, grad, curl) and the leverage given by well known vector operator identities – the problem becomes manageable and perhaps even more important the physics separates clear from the math.

The definition of cross section is not different in different areas of physics ( except where specifically defined to be) its just the best formalism for the problem you are considering.

Just use the best tool for the job.

Hope this helps.

Regards

Sam

Thank you...I am ok for the last question!
If anyone could explain the sentence I wrote in my starting post, I would be completely ok!

The sentence is :"Cross section is the most important tool for the study of nuclear reactions, especially artificial ones".

However, thank you for the help. Bye!

Well its not my role to write your thesis but here is my, brief, take on the problem.

Bear with me we do get to answer the cross section question right at the heart of the argument.

Artificial radioactivity will largely be about neutron absorption by stable nuclei. There are more exotic charged particle interactions but I will leave these aside.

So we take a sample of an element and bombard it with neutrons of a given energy. The question we want to answer is what radioactive products do we form and in what proportion.

So lets form the model which is mercifully simple. Look up what isotopes are present in your target element in normal proportion, very few elements have only one naturally occurring isotope, this data is tabulated in many places.

Write down the reactions for each isotope if it absorbs a neutron.

Check if these reactions 'go' ie the reaction releases energy. Discard those which don't as they will not happen.

For each product nucleus look up its decay path(s) so you will know what radiation you will get.

But in what proportion will each product nucleus occur? The answer is in the ratio of cross sections for neutron absorption of the parent nuclei in the target at the energy of neutrons you are using.

Cross section gives a measurement of the probability that a particular reaction will occur.

You can take this a step further to calculate from the cross section how much of a particular product will be formed – but there are some subtleties in the calculation.

Hence we have used the model to solve the original question via cross sections.

Regards

Sam
PS If you really want to impress your Prof point out that neutron sources have a notoriously wide spread of energies and so precision measurements are difficult. One way around this is to use precisely controlled energy deuterons to sneak neutrons into nuclei – look up Oppenheimer Phillips polarisation.

Thank you very much!
Now I know why cross section is so important.
I assure you that I am not a bad student, however I am muddled by the confusion about these subjects.
Bye!

Ok...Thank you very much. Now I know how to introduce my discussion, and also how to end it! Bye!

Collisions are a valuable tool for doing nuclear and particle physics, especially particle physics. You have a lot of control of what particles you are shooting at what other particles, what energies they have, and sometimes even their spin orientations.

Needless to say, one has to look at what comes out, and a good tool for doing that is a partial-wave expansion. This is essentially a multipole expansion of the wavefunction. The outward waves get phase shifts relative to the non-scattered case, and these contribute to the cross section. Scattering: the Partial Wave Expansion

Thanks!!