How do we determine the magnitude of the nuclear force acting on the nucleus of an atom?
Are you talking about the strong force ? Do you want to know the strength of the interaction, or how it is determined ? The strong force does not act "on the nucleus"; it acts between the nucleons. It has a coupling constant (a dimensionless number indicative of the strength of the interaction) that's about 137 times larger than that of the EM interaction (the fine structure constant). This number has been determined numerically, by techniques such as Lattice QCD. (Simplistically speaking : you assume a coupling constant and calculate a hadron mass; if you get the experimentally determined mass you are done; else tweak the coupling constant and try again)
Yes I am talking about the strong force. I want to primarly know how the strength of the interaction is determined say in a carbon atom.
Here's one explanation -
Why is the range of the strong force so small? Production and destruction of the messenger mesons violates the law of conservation of mass & energy! However, if the messenger particle has a very short lifetime, and so exists only within a very small space, the particle can exist within the limitations set by the uncertainty principle. Particles like this are called virtual particles.
more at http://antoine.frostburg.edu/chem/senese/101/quantum/faq/electron-confinement-to-nucleus.shtml
Just as an addendum. The strong force is mediated by gluons which have no (or a very small) rest mass, depending on what formalism you are using to describe them. The nuclear force (which binds together atomic nuclei) is the socalled residual strong force, mediated by the pions. These pions are the lightest mesons : ie quark anti-quark combinations. A pion indeed has the necessary rest mass.
But the main reason for this short-ranged activity is the fact that QCD (the theory describing the strong interaction) is NON-LINEAR. This means that gluons can interact with BOTH quarks and other gluons. each gluon carries colourcharge which needs to be conserved throughout QCD-interactions.
Check out : http://hyperphysics.phy-astr.gsu.edu/hbase/particles/expar.html
There is something that should have been said first IMHO : it is remarquable that the nucleus is very well decribed using classical models. Indeed, the seemingly crude "liquid drop model", which is empirical, provides one with a fairly succesful formula for computing the mass of the nucleus [tex](A,Z)[/tex] with [tex]Z[/tex] protons and [tex]N=A-Z[/tex] neutrons. This formula is commonly known as the "Weizsaker formula" :
The various terms have a simple interpretation in terms of the liquid drop model. Only the last two are not-so-obvious. Indeed, the very last term is rather non intuitive at all.
For more see for instance this intro to nuclear physics. Once you understand the various terms, you are ready to evaluate most energetical quantities of interest for practically all nuclei.
Now I agree with you Marlon, it must also be said that we do know a lot about the fundamental theory underlying this nuclear interaction, namely the strong interaction with gauge group QCD. But for pedagogical reasons, and also because it happened this way historically, one should mention first the so-succesful classical models, and only later come to the QCD, which anyway we always model and never solve. All of this depends crucially on the non-linearity of QCD which is equivalent to the non-commutativity of the gauge group, as you mentionned.
In any case, my message is :
Q : "how is the strength of the interaction determined ?"
A : "Through very efficient models"
Let us also consider the experiments from which we determine masses and energies, and also "size" of the subatomic particles.
Adding to what Marlon mentioned - there are two phenonemon - the attraction between nucleons with in the nucleus, and the attraction of quarks within the nucleons.
From the hyperphysics page cited by Marlon - "The strong interaction was modeled by Yukawa as involving an exchange of pions, and indeed the pion range calculation was helpful in developing our understanding of the strong force."
Pion Range of Strong Force - http://hyperphysics.phy-astr.gsu.edu/hbase/forces/exchg.html#c4
Exchange forces in general - http://hyperphysics.phy-astr.gsu.edu/hbase/forces/exchg.html#c1
Thank you all for your help
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