The hyperfine interaction in the lithium atom by the extended Hartree-Fock method

The hyperfine splitting term (f) is calculated for both Hartree-Fock (HF) and extended Hartree-Fock (EHF) wave functions for the lithium atom. The EHF wave function is generated from a linear combination of products of spin and space functions. The spin functions are eigen-functions of S² and S[subscript z] and the total wave function is required to satisfy the Pauli principle. A variational principle is used to give three coupled integrodifferential equations that are solved numerically by Numerov's method. For the EHF approximation the total energy is found to be -14.89496 and (f) = 2.400. For the HF approximation the total energy is -14.86544 and (f) = 2.097. The HF results agree very well with the best previous investigation where the single particle orbitals are expanded in terms of an analytical series. This energy from the EHF approximation is better than that of any previous investigation, and the (f) value found is believed to be the true EHF (f) value since it does not depend on a particular choice of basis functions as do previous results. A method of including correlation functions in wave functions is discussed and an integrodifferential equation for the correlation function for the helium atom is derived