Cerenkov Line-like Radiation, The Extended and Improved Formulae System
  You & Cheng (1980) argued that, for relativistic electrons moving through a dense gas, the Cerenkov effect will produce peculiar atomic and/or molecular emission lines--Cerenkov lines. They presented a series of formulae to describe the new line-mechanism. Elegant experimental confirmation has been obtained by Xu. et al. in the laboratory which definitely verified the existence of Cerenkov lines. Owing to the potential importance in high energy astrophysics, in this paper we give a more detailed physical discussion of the emission mechanisms and improve the previous formulae system into a form which is more convenient for astrophysical application. Specifically, the extended formulae in this paper can be applied to other species of atoms and/or ions rather than hydrogen as in the previous paper, and also to X-ray astronomy. They can also be used for the calculation of a nonuniform plane-parallel slab of the emissive gas. 
J.H.You, Y.D. Xu, D.B.Liu, J.R.Shi, G.X.Jin