  We prove that the entanglement created in the low-energy scattering of two
particles in two dimensions is given by a universal coefficient that is
independent of the interaction potential. This is strikingly different from the
three dimensional case, where it is proportional to the total scattering cross
section. Before the collision the state is a product of two normalized
Gaussians. We take the purity as the measure of the entanglement after the
scattering. We give a rigorous computation, with error bound, of the leading
order of the purity at low-energy. For a large class of potentials, that are
not assumed to be spherically symmetric, we prove that the low-energy behaviour
of the purity, $\mathcal P$, is universal. It is given by $\mathcal P= 1-
\frac{1}{(\ln (\sigma/\hbar))^2} \mathcal E$, where $\sigma$ is the variance of
the Gaussians and the entanglement coefficient, $\mathcal E$, depends only on
the masses of the particles and not on the interaction potential. The
entanglement depends strongly in the difference of the masses. It takes its
minimum when the masses are equal, and it increases rapidly with the difference
of the masses.
