Hey, sorry for the late reply! Zettili says the second excited state is ##\phi_{2,0,0}\left(r_{1}\right)\phi_{2,0,0}\left(r_{2}\right)\chi_{\text{singlet}}##.
If it's of any help, he says the ground state energy is ##2E_{1}=-27.2Z^{2}## eV, the first excited energy is ##E_{1}+E_{2}=-17Z^{2}##...