  We report the first closed, analytical expression for the scattering angle of
an electron bunch ponderomotively scattered from a counter-propagating,
ultra-intense laser pulse, also accounting for radiation reaction (RR). The
found formulation depends nontrivially on the laser intensity, pulse duration,
beam waist, and energy of the electron bunch. For various laser and bunch
parameters the proposed formula is in excellent quantitative agreement with
full, relativistic test particle simulations in a realistic electromagnetic
field configuration of a focused laser pulse. We also demonstrate how in the
radiation dominated regime a simple rescaling of our model's input parameters
yields excellent quantitative agreement with numerical simulations based on the
Landau-Lifshitz model. Finally, we discuss how the model can be applied for an
in-situ characterization of current and future ultra-high power laser systems,
but also to experimentally probe fundamental properties of RR during
ultra-intense laser electron interaction.
