Nuclear Force equations.

1. Jun 7, 2004

Reflector

Where can I get the equations that describe the strong nuclear force between quarks/protons/neutrons? Are they not freely available? Thanks.

2. Jun 7, 2004

Tom Mattson

Staff Emeritus
It's not a simple equation, like Newton's law of gravitation or Coulomb's law for electrostatics. It's a whole theory called Quantum Chromodynamics (QCD). It's freely available all right, but the problem is that no one knows how to solve it. Check it out here.

3. Jun 7, 2004

you cant solve the equations. They can only be reduced to a system of equations with too many variables and too little equations, kind of like general relativity.

4. Jun 7, 2004

Tom Mattson

Staff Emeritus
No, that's not it. The problem is that gauge theories can only be solved perturbatively, and with QCD the running coupling constant is on the order of unity, so the perturbation series doesn't converge.

'Too many variables with too few equations' is not the problem with GR, either. In the case of GR, the equations are not exactly solvable because of their nonlinearity.

5. Jun 7, 2004

Reflector

Those equations in the link look too complicated for me. I was looking for something similar to the gravitational Force. Maybe I'm wasting my time anyway, I don't know. I have this theory but it didn't work out the way I wanted. Say, you have a right triangle and you expect on one side two values (say L) to have equal length (ie. L-L)... but instead you find that the second value is actually 10 x the value of the first value (ie 10L-L). Can it still be solved according to a logarithm function?

6. Jun 8, 2004

Tom Mattson

Staff Emeritus

The problem is that there isn't one. Newton's law of gravitation and Coulomb's law for electrostatics are classical (not quantum) relations, and they are applicable for sufficiently strong field intensities and sufficiently large distances. With QCD, there is only the short-range interaction, and there is no regime in which a classical approximation would be valid.

I'm at a loss as to how a logarithm would enter into the analysis at all.

7. Jun 8, 2004

Reflector

I thought that the logarithm dealt with 10-1 ratios. I don't know how else to make sense of the observation... plus having a logarithm may have something to do with dark matter... how there's like a 10-1 ratio of it compared with normal matter. I don't know. This was an ambitious attempt to link the strong force with gravity, and getting the 10-1 ratio instead of a 1-1 ratio has to mean something...

8. Jun 8, 2004

Tom Mattson

Staff Emeritus
It does: An increase by one power of ten, is an increase by 1 on a log scale. But exactly what analysis do you plan to do on a right triangle with logarithms? Right triangles are solved with trig functions, not logs.

What observation? Being mistaken about the length of a side of a triangle by a factor of 10? That doesn't imply that you need logarithms, it implies that you need glasses. :rofl:

There is no connection between logarithms and dark matter.

Well, I don't think you're putting any pressure on the string theorists just yet. I think you should keep studying physics to get the fundamentals down first.

9. Jun 9, 2004

arivero

Reflector, maybe you are looking for a force equation coming from a potential. Part of the problem is that it is not granted that you are going to be able to have a relativistic invariant potential for any force. The more effective trick is called Born approximation, and lets you to get a potential which approaches the real force.

Secondly, please take into account that the strong force between protons and neutrons is simply a residual of SU(3) force between quarks. So you need more more approximations. A very popular one is the OBE, One-Boson-Exchange approximation, where particles interact exchanging a nuclear boson, for instance a pion. Also empirical models are used, not coming from the fundamental theory.

Last, the whole colective of nucleons in a nucleus add to form a kind of well potential; this is approached with saxon-wood potential, or even with a square well.

10. Jun 9, 2004

Olias

Do the Words:Magnitude + Scale mean anything?

If so the wrong turning you took is evident

11. Jun 10, 2004

Alem2000

Hi, I wanted to as Tom a question. I havnt completed the introductory physics courses yet but since I saw the equation for the strong nuclear force I was wondering what the string theory equations look like. If you could please post them I would be greatful.

12. Jun 10, 2004

Alem2000

....and if I may add. What exactly can be done with the strong nuclear force equations...im confused, if they cant be solved than how are they relavant? Please keep in mind I am a beginner!

13. Jun 15, 2004

arivero

They (QCD+QED) are used in accelerator experiments, where only two particles are involved; there they are very accurate.

In the nucleus, they are only basis to create approximate models (One Boson Exchange etc) which in turn are reapproximated.

14. Jun 16, 2004

Tom Mattson

Staff Emeritus
Have a look at this:

String Theory in Lagrangian Formulation

15. Jun 16, 2004

Tom Mattson

Staff Emeritus
They can be approximately solved in certain regimes. The problem with QCD is that, for "normal" energies, the coupling constant is on the order of "1". This contrasts with the situation in QED, in which the coupling constant is 1/137, which means that graphs with a large number of vertices (and hence higher powers of the coupling constant) are supressed. Such is not the case with higher order QCD graphs.

But, at low energies, QCD can be approximated with Lattice QCD, in which spacetime is discretized (note: this is not quantum general relativity). And at high energies, the coupling constant drops down below "1", making a perturbation expansion possible. Both lattice QCD and perturbative QCD (pQCD) give good results in their appropriate regimes.

Confused? Me too....

16. Jun 16, 2004

Alem2000

Oh dont you worry Tom Mattson...I sure am confused...but also enamored! I cant waight to learn this stuff..not string theory but about the strong and weak nuclear forces.

The math I saw..what is it...i saw integrals and I think derivatives(or did I?). What is the mathmatics used in strings....and by the way thanks for posting that.

17. Jun 17, 2004

heardie

the math used is hardcore - looks like alot of tensor calculus to me