  We investigate the feasibility of UV lasing without inversion at a wavelength
of $253.7$ nm utilizing interacting dark resonances in mercury vapor. Our
theoretical analysis starts with radiation damped optical Bloch equations for
all relevant 13 atomic levels. These master equations are generalized by
considering technical phase noise of the driving lasers. From the Doppler
broadened complex susceptibility we obtain the stationary output power from
semiclassical laser theory. The finite overlap of the driving Gaussian laser
beams defines an ellipsoidal inhomogeneous gain distribution. Therefore, we
evaluate the intra-cavity field inside a ring laser self-consistently with
Fourier optics. This analysis confirms the feasibility of UV lasing and reveals
its dependence on experimental parameters.
