Scattering Factors for Atomic Lithium from Correlated and Independent Particle Model Wavefunctions

The natural orbital (NO) expansion of a highly accurate Hylleraas‐type wavefunction (99.90% of the correlation energy) is used for the determination of correlated x‐ray scattering factors for the ${}^{2}S$ ground state of the lithium atom. Correlated electron scattering amplitudes are also obtained within the first Born approximation. For purposes of comparison, scattering factors for this system were computed from various independent particle model (IPM) wavefunctions. Calculations based on the best density (BD) and symmetry‐adapted best density (SABD) determinants for Li yielded better approximations to the correlated (NO) scattering factor values than did those based on conventional IPM's. The latter included restricted and spin‐polarized Hartree–Fock (RHF and SPHF) functions. The accuracy of x‐ray scattering factors and electron scattering amplitudes is seen to depend on the value of the scattering variable $\mu$ . Although relative differences between the correlated and various HF values never exceed 1% for any given value of $\mu$ , these differences can be attributed almost entirely to “one‐electron” rather than to “pure correlation” effects.