Helium energy level diagram for ground and first excited states

[MeiLai]

Consider a helium atom where both electrons are replaced by identical charged particles of spin-1. Ignoring the motion of the nucleus, the Hamiltonian is [see attachment 1]

Construct an energy level diagram ( qualitatively ) for this "atom", when both particles are in the n=1 state, and when one particle is in the n=1 state and the other is in the state (nlm)=(200). Do this by treating the term in the Hamiltonian as a perturbation. Write out the space and spin wavefunctions for each level in terms of the single particle hydrogenic wavefunctions [phi]nlm spin wavefunctions [chi]s,m-sub-s. Show the splitting qualitatively, and state the degeneracy of each level.

 

[kuruman]

The electrons have been replaced by particles of spin 1. Are these particles bosons or fermions? Should their wavefunctions be symmetric or antisymmetric under particle interchange? Also, you need to reconsider what kind of spin multiplicities you get when you add two spin 1 particles.