1 . I n t r o d u c t i o n D e s p i t e t h e f a c t t h a t a v a s t body o f e x p e r i m e n t a l d a t a h a s b e e n c o l l e c t e d d u r i n g t h e l a s t y e a r s o n t h e measurement o f t h e e l e c t r o n induced X-she l l i o n i z a t i o n c r o s s s e c t i o n oK , t h e r e a r e s t i l l no d a t a f o r many e l e m e n t s a t a l l , o r f o r c e r t a i n e l e m e n t s o n l y i n a v e r y s m a l l e n e r g y i n t e r v a l , and sometimes t h e y a r e a l s o v e r y c o n t r a d i c t o r y . S i n c e t h e knowl e d g e o f oK is n o t o n l y o f t h e o r e t i c a l i n t e r e s t b u t a l s o o f t e n u s e f u l i n many b r a n c h e s o f b a s i c and a p p l i e d r e s e a r c h , i t seems t o b e d e s i r a b l e t o e v a l u a t e t h e d a t a and combine t h e r e l i a b l e v a l u e s i n o r d e r t o d e r i v e uppott potted by the Deutsche ForschungsgemeinechaZt Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987978 C9-488 JOURNAL DE PHYSIQUE a formula that describes aK for all elements and energies. For this purpose we have evaluated the available measurements concerning their consistency with regard to the fluorescence yields and a unique error assignment and selected for various elements (Z=6,7,8,10, 18,22,28,29,47,50 and 79) spread although not for all elements over an impact energy range of I„ < E0 < 2 GeV , where I„ denotes the K-shell binding energy. 2. The Formula To the evaluated set of data, obtained as pointed out above, we fitted a three-parameter formula, which was derived from the two-parameter relativistic Bethe expression [1], Besides the general E and Z dependence it had to obey in addition several conditions:(i) for non relativistic energies the formula should agree with the predictions of the exact expression of the Bethe formula [2]/(2) the cross section should vanish for Eo = I„ and (iii) the slope of the cross section has to be zero at its maximum, which occurs at about E„ j 4I„ . The fitting procedure will be explained in detail in a forthcoming paper [3]. We thus obtained the semi-empirical formula in barn aR = aFi(Z,g)[F2(B) +bF3(Z,6) + F„(Z)F5(Z,6) ] (1)