The second order scattering fading (SOSF) channel is a versatile generalization of the Rician fading model. Besides a line of sight (LOS) component and a Rayleigh-diffused scattering component, it also incorporates a double-Rayleigh scattering component. In this letter, we present an exact closed-form formula for the generalized moment generating function (MGF) of the signal-to-noise ratio in SOSF channels, as well as for its moments. This new result allows for the evaluation of important performance metrics in wireless communication systems, such as the amount of fading and energy detection, for which results in the literature are unavailable because of the complicated nature of this fading model. Strikingly, we observe that whereas the amount of fading is monotonic with respect to the fading parameters <inline-formula><tex-math notation="LaTeX">\alpha</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">\beta</tex-math></inline-formula>, this is not the case for the energy detection performance under strong LOS conditions.