RASCAS simulations of single-scattering events in a H I medium with T = 100 K assuming isotropic angular redistribution and no recoil effect. Top: frequency redistribution, R(x_in, x_out), in Doppler units (x_out) of Lyman-α photons emitted at x_in after one single-scattering on a hydrogen atom. The solid coloured curves are the results from RASCAS assuming x_in = 0, 1, 2, 3, 4, 5, and 8, while the dashed black lines are the analytic solutions of Hummer (1962). Bottom: accuracy of R(x_in, x_out) from RASCAS compared to the solution of Hummer (1962) as a function of x_out. Here σ is the relative error between R(x_in, x_out) obtained from RASCAS and the solution of Hummer (1962), and σ_p is the relative Poisson error in each bin of x_out due the limited number of photons used in this simulation (). In each sub-panel, the solid black curves show the mean value of σ/σ_p.