130_notes.dvi

(Frankie) #1

Thus we have a large effective spin-spin interaction entirely due to electron repulsion. There is
a large difference in energy between the singlet and triplet states. This is due to the exchange
antisymmetry and the effect of the spin state on the spatial state(as in ferromagnetism).


The first diagram below shows the result of our calculation. All states increase in energy due to the
Coulomb repulsion of the electrons. Before the perturbation, thefirst excited state is degenerate.
After the perturbation, the singlet and triplet spin states split significantly due to the symmetry of
the spatial part of the wavefunction. We designate the states with the usual spectroscopic notation.


In addition to the large energy shift between the singlet and triplet states,Electric Dipoledecay
selection rules


∆ℓ = ± 1

∆s = 0

cause decays from triplet to singlet states (or vice-versa) to be suppressed by a large factor (compared
to decays from singlet to singlet or from triplet to triplet). This caused early researchers to think
that there were two separate kinds of Helium. The diagrams below shows the levels for ParaHelium
(singlet) and for OtrhoHelium (triplet). The second diagrams showsthe dominant decay modes.

Free download pdf