The centres generated by a moving dislocation retain their orientation when the dislocation moves away from them. The dichroism in the plastically deformed crystals might, therefore, be due to the alignment of point defects and not to the dislocations themselves. It is shown that the different dislocations forming the slip band cause the same orientation of point defects. The splitting of the creation energy of the centres due to the dislocation elastic field is considered. An expression is obtained to determine the orientation of the centres when the slip system is known. This approach is applied to the experimental results on the N_c band dichroism in LiF crystals which have been deformed after gamma -irradiation.