The differential cross-section for the emission of M shell fluorescence X-rays from Pt, Au and Hg by 5.96 keV photons at seven angles ranging from 50 degrees to 110 degrees have been measured. The differential cross-section is found to decrease with increase in the emission angle, showing an anisotropic spatial distribution of M shell fluorescence Xrays. The present results contradict the predictions of Cooper and Zare (Cooper, J., Zare, R.N., 1969. Atomic Collisions Processes, vol. XIC. Gordon and Breach, New York. p.317) that after photoionization of inner shells, the vacancy state has equal population of magnetic substates and that the subsequent X-ray emission is isotropic, but confirm the predictions of the calculations of Flugge, Mehlhorn and Schmidt that the atomic inner-shell vacancies produced after photoionization are aligned and X-ray emission from the filling of vacancies in states with J > 1/2 is anisotropic. The vacancies were created by the 5.96 keV gamma-rays from an Fe-55 source and the M X-rays were measured using a Si(Li) detector. (C) 2000 Elsevier Science Ltd. All rights reserved.