Calculation of The Relaxation Times for An Inhomogeneous ESR Line

A method for separately determining the longitudinal, T₁, and transverse, T₂, relaxation times from the saturation curve of an inhomogeneously broadened slow-passage ESR absorption line is presented. It imposes no restriction on the relative values of the spin packet (Lorentzian) and Gaussian widths conforming with the overall inhomogeneous width. It gives a simple way of calculating T₂=2/(spin-packet width) through the deconvolution of a non-saturated experimental spectrum and then, in a direct and elegant way, the T₁ is calculated once the amplitude of the microwave magnetic field, H₁, for which the saturation curve of the absorption line reaches its maximum, is known. In addition, algebraic relations for T₁ and T₂ are given for the case of inhomogeneous broadening which, in the limit of Gaussian distribution width to 0, reduce to the homogeneous case. These algebraic relations give the spectroscopist the possibility of a direct calculation of T₁ once a saturation curve up to its maximum has been obtained.