The Compton scattering of 59.54 keV gamma rays by an Al scatterer has been used as a primer source at scattering angles from 48 to 118degrees by using a Si(Li) detector, and this primer gamma ray has been send to absorbers including Gd, Th, Dy, Ho and Er. A new method has been developed to determine the K-shell absorption jump factor of elements and compounds. This method is based on simultaneous measurement of fluorescence radiation and scattered radiation, thus avoiding the problems with measuring the source strength and source-to-detector solid angle. In this method, the jump factor is effected from the scattering angle. Evident energies near to K-absorption edges of each lanthanide element have been determined for chosen angles, after the incident photon energy (59.5 keV) is exposed to Compton scattering from At (secondary source). The experimental absorption jump factors are compared with the theoretical estimates and literature experimental values. (C) 2003 Elsevier B.V. All rights reserved.