Rayleigh-normal scale mixture ($RZ\sim \mathrm{Laplace}(0,1)$)

An independent unit-scale Rayleigh distribution variable $R$ and standard normal distribution variable $Z$ give $RZ$ with Laplace distribution of density $e^{-|x|}/2$. Indeed its characteristic function is $\mathbb{E}{e}^{-t^2{R}^2/2}=1/(1+t^2)$.