Finding the Hamiltonian for the Be Atom without Nuclear Terms

[rovert]

I have a problem that uses the QM Hamiltonian for the berylium atom, but I am having trouble finding this Hamiltonian using the Born-Oppenheimer approximation (leaving out the nuclear-nucler and nucler-electron terms).
Any know how to get this?

 

[dextercioby]

It's not difficult. How many electrons does this atom have ? Can you treat the nucleus as a point particle charge ? Are you requires to use the spins of the electrons?

Daniel.

P.S. You can't leave out the nuclear-electron interaction terms.

 

[rovert]

Be has 4 electrons. Yes, they are assumed point charges. Electron spin should be included. Does it start with H=(-ћ2/2m)∑…? That is where I thought I should start, but am stuck after that. I have never seen a Hamiltonian developed for a many-electron atom.

 

[dextercioby]

You just have to add all possible terms: KE for the 4 electrons, KE for the nucleus, then Coulomb interaction for the 4 electrons among each other , Coulomb interaction for the 4 electrons with the nucleus and finally spin terms: spin-orbit interaction for the electrons and spin-spin interactions for the electrons, that is, of course, if you neglect nuclear spin.

Daniel.

 

[rovert]

Thanks for your help. I think I've got it now. Since I can make the Born-Oppenheimer approximation, I can leave KE for the nucleus out (basically ignore the nucleus all together) which I know is a HUGE assumption to make, but that is what the problem instructs.