Abstract A method is proposed, which primarily determines screening constants for incomplete atomic shells from the experimental ionization potentials of spin-paired Pauli-type orbitals. The method is complimentary and in addition to the standard Sommerfeld approach, which derives screening constants from X-ray spin doublet term differences. Atomic photoelectric absorption cross sections are computed from screened hydrogen-like eigenfunctions for low atomic number elements Z = 6 to 15, using a range of incident photon energies between 1 and 30 keV. Comparison with experiment and alternate more exact theories shows, that improved cross sections are obtained for the more important incomplete L-shell contributions. X-ray photoelectric mass absorption coefficients for low Z elements (Z= 6 to 15), employing 33 characteristic X-ray energies {NiKα (0.852 keV) to AgKβ (24.942 keV)}, are given.