  A multiple scattering model of a quantum particle interacting with a random
Lorentz gas of fixed point scatterers is established in an Euclidean space of
arbitrary dimension. At the core of the model, the scattering amplitude for the
point scatterers is derived in detail, and expressed in terms of the scattering
length. The fundamental properties of the model, such as the cross section and
the scattering matrix, are calculated. In addition, the model is shown to
verify the optical theorem and thus probability conservation. Finally, the
differential and total cross sections are numerically computed in two
situations whether the Lorentz gas is smaller or larger than the mean free
path. A distinct Airy diffraction peak is obtained for a large enough number of
scatterers. This observation is related to the extinction paradox.
