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When introducing the hydrogenic atomic orbitals, it is said that the 2s and 2p orbitals are degenerate. I have also read that for atoms with more than one electron, like He, the 2s and 2p are NOT degenerate.
How does the addition of a second electron in the 1s orbital change the energy of the 2s and 2p orbitals?
Let's imagine triplet $\ce{He}$, hence one electron in the 1s. The other electron could not be in the 1s, too (it would have to have opposite spin, thus, singlet $\ce{He}$). It is in either the 2s or one of the 2p orbitals.$^{1}$ Among other things, the Coulomb interaction with the 1s orbital/electron will affect their orbital energies. Given that the 1s and 2s have the same symmetry, but each of the 2p have a symmetry different from them, it is reasonable to assume that the Coulomb interaction between 1s and 2s would be different from the one of 1s and 2p.$^{2}$ Thus, the orbital energies are different.
$^{1}$ Though I would think that the electron density would always be spherically symmetric for the isolated atom.
$^{2}$ This can also be calculated when assuming some parameters for the helium orbitals (which can be calculated exactly for the one-electron case).
