# EM and Gravitational binding energy for quarks

1. Sep 2, 2010

### Kenai

Hi guys,

If I have a $$\Sigma$$ triplet of baryons, how do I calculate the EM and gravitational binding energy of these baryons? (assuming there is 1fm of distance between quarks and that each quark has 1/3 the mass of the $$\Sigma$$),

I guess I have to use the EM and Gravitational Potential Energies for this.

Will be ok using the Rydberg Energy Formula for thr EM binding energie?

$$E = \frac{1}{2} {\alpha}^2 (\mu {c}^2)$$

With $$\mu$$ being the reduced mass.

And what about the Gravitational thing? (just U = G m1m2 /r ?)

Thank you.

2. Sep 2, 2010

### bcrowell

Staff Emeritus
If you just want an order of magnitude estimate, then this will work, and the directly analogous equation for the electrical force will also work. If you want an accurate number, you'd have to devote the next decade if your life to learning to do numerical QCD calculations. The gravitational energy is of course negligible for any practical purpose.

3. Sep 4, 2010

### clem

The gravitational energy is negligible, and is never considered.
You can't use the Rydberg formula for the EM energy because the quarks are not held together by EM, but by strong forces.
There are three components to the energy differences:
!. Coulomb ~ qq'/r^2.
2. A spin dot spin magnetic term.
3. A spin dot spin QCD term.

They are all of comparable size ~ 1 MeV.