Doing a paper on the strong nuclear force --

[xdrgnh]

I'm doing a paper on the strong nuclear force for a nuclear physics class. I want to give a good quantitative account for it. I'm very familiar with Lagrangian field theory but not so much with QFT or QCD. I don't have time to learn all of the ins and outs of QFT and for this paper and for this class I don't need to know. What I';m looking for specifically is just the Lagrangian for the strong nuclear before between one proton and one neutron. If I can describe quantitatively the strong attraction in deuterium (H 2) that would be excellent.

 

[Orodruin]

This can be done on very many different levels. Have you started by looking up what the Yukawa potential is?

 

[xdrgnh]

Yes I have I do plan on talking about that. But I would really like to discuss the Lagrangian Density for the interaction between one proton and one neutron.

 

[Orodruin]

There is a Lagrangian density for Yukawa theory on the Wikipedia Yukawa potential page.
However, note that this is generally not what an elementary particle physicist will consider the strong force, which is an SU(3) gauge theory. The interaction between protons and neutrons which emerge from this force are much weaker than the strong force itself in a similar fashion to electromagnetic van der Waals' interactions between neutral molecules being weaker than that between ions.

 

[xdrgnh]

I'm pretty familiar with group theory. Do you know if the representation of the strong force between a single proton and neutron represented using SU(3) gauge theory simple enough to be explained to a class of undergrad seniors in mechanical and nuclear engineering?

 

[Orodruin]

The force between nucleons is based upon the exchange of pions rather than gluons, which are the SU(3) gauge bosons. I would not try to explain this other than very superficially to undergrads.

 

[ChrisVer]

If it's a presentation, then I'd recommend (I don't know what your supervisor did) that you'd avoid inserting information and stuff that you are unable to understand (due to lacking of QFT background - especially for effective theories).

However, to get an insight (since it's not my business to tell you what to do or how), you can look here:
http://www.scholarpedia.org/article/Nuclear_Forces#The_meson_theory_of_nuclear_forces
eg. it has the lagrangian L_{\pi NN} (for pion-nucleon-nucleon) in Fig5.

For the Deuterium interactions you can also look into nuclear physics books, which work for example with semi-theoretical+experimental potentials (there are many terms in the nuclear potentials however I think the deuterium is quite simple -at least when dealt with pedagogically)