Approximate symmetries in the singly excited states of helium

Consideration of R(4) as the degeneracy group for the singly excited states of helium allows the assignment of R(4) irreducible representations (irreps) to these states. Induction of these irreps onto the irreps of SU(4) and U(4) provides a sufficient number of invariants to define the energy levels. Empirical equations allow all of the singlet states to be related to the first ionization energy and the Rydberg constant, to a good approximation. Empirical equations can also be derived for the triplet states, but their relation to the ionization energy and/or the Rydberg constant is not obvious.