Maxwell relaxation time for the transverse mode in simple liquids

A microscopic expression for the Maxwell relaxation time for the transverse mode in simple liquids has been derived on the basis of the generalized Langevin equation developed by Mori. For this, it is assumed that the correlation function of the second random force is a function of $t^2$. The derived expression does not involve any adjustable parameter and leads to a correct result for the shear-viscosity coefficient. Numerical predictions for the relaxation time in liquid argon are compared with other existing estimates. It is found that the present results are comparatively much better than some other existing estimates.