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In this paper the five-fold differential cross section for the (e, 2e) reaction is derived using a relativistic plane-wave Born approximation. It is shown that (e, 2e) reactions with electron impact energies of a few MeV should provide a sensitive test of the wavefunctions of the inner shells of heavy elements. Calculations are presented for the K shells of gold and thorium using relativistic and non-relativistic Hartree-Fock theories. These show that relativistic effects are significant in thedoi:10.1088/0022-3700/15/18/025 fatcat:jkfsamve5jcxlmrh7tyxmogow4