The position of the F band peak is determined in additively coloured CaF$_2$, SrF$_2$ and BaF$_2$ by the Faraday rotation method. However, in additively coloured crystals, the F band is normally overlaid by absorption due to higher F aggregate centres and a determination of the spin orbit coupling constant in the excited $^2$P state of the F centre is not feasible since a precise knowledge of the F band optical density is required. It is found that trapped electron centres are produced by X-irradiation at 77 $^\circ$K of undoped SrF$_2$ and BaF$_2$ crystals and hydrogen doped CaF$_2$, SrF$_2$ and BaF$_2$ crystals and the spin orbit coupling is determined for these centres. Paramagnetic resonance measurements show (Bessent, Hayes, Hodby & Smith 1968) that the trapped electron centres are closely related to the normal F centres found in additively coloured crystals. Wavefunctions obtained from a point ion model (Bennett & Lidiard 1965) are used to calculate the spin orbit coupling for the $^2$P state of the F centre in CaF$_2$, SrF$_2$ and BaF$_2$. For comparison with theory it is assumed that the spin orbit coupling for the irradiation induced trapped electron centres is not appreciably different from that for normal F contres and we obtain good agreement between theory and experiment.