Why is there no constant magnetic dipole-dipole interaction?

[Gavroy]

In my opinion, there should be a magnetic-dipole-dipole interaction between 2 1s-hydrogen atoms, but i could not find anything that confirms this.

first of all i discovered this equation here:

http://en.wikipedia.org/wiki/Magnetic_dipole–dipole_interaction

the potential energy $$U = - \frac{ \mu_0 } {4 \pi r_{jk}^3 } \left( 3 (\bold{m}_j \cdot \bold{e}_{jk}) (\bold{m}_k \cdot \bold{e}_{jk}) - \bold{m}_j \cdot \bold{m}_k \right)$$

but an electron in a hydrogen atom with arbitrary l has always a electro magnetic dipole moment(http://en.wikipedia.org/wiki/Electron_magnetic_dipole_moment#Example:_Hydrogen_atom )and therefore this whole term should therefore be different from zero?

so one could evaluate the first term energy correction by using pertubation theory and would probably get a result different from zero. but actually, i guess that somewhere i am completely wrong, cause i never heard anything of such a correction?

 

[Vanadium 50]

What is l(l+1) for the 1S state?

 

[Gavroy]

oh, you are so right.

but what is with the l=1 state? e.g. 2 hydrogen atoms in a 2p-state?

 

[DrDu]

In principle, there is a magnetic interaction also for the 1S states due to the spin's magnetic moment. However, it is magnitudes smaller than the singlet-triplet splitting which is due to different symmetry of the orbital part of the molecular wavefunction.

 

[Gavroy]

ok, thank you,
so does this mean - or do you think- that this equation is correct?