Evaluation of the Coulomb and exchange integrals for higher excited states of helium atom, taking into account the interaction between magnetic moments of the electrons

We have calculated the total energy of the helium atom in higher excited state. The Coulomb and exchange integrals are evaluated via spherical harmonics. The interaction of the magnetic moments of the electrons between them and also with the magnetic moments of the nucleus was taken into account through a cosine term in the Coulomb potential. The obtained results are in agreement with experimental data.