  In this paper, the partial-wave expansion method is applied to describe the
difference-frequency pressure generated in a nonlinear scattering of two
acoustic waves with an arbitrary wavefront by means of a rigid sphere.
Particularly, the difference-frequency generation is analyzed in the nonlinear
scattering with a spherical scatterer involving two intersecting plane waves in
the following configurations: collinear, crossing at right angles, and
counter-propagating. For the sake simplicity, the plane waves are assumed to be
spatially located in a spherical region which diameter is smaller than the
difference-frequency wavelength. Such arrangements can be experimentally
accomplished in vibro-acoustography and nonlinear acoustic tomography
techniques. It turns out to be that when the sphere radius is of the order of
the primary wavelengths, and the downshift ratio (i.e. the ratio between the
fundamental frequency and the difference-frequency) is larger than five,
difference-frequency generation is mostly due to a nonlinear interaction
between the primary scattered waves. The exception to this is the collinear
scattering for which the nonlinear interaction of the primary incident waves is
also relevant. In addition, the difference-frequency scattered pressure in all
scattering configurations decays as $r^{-1} \ln r$ and $1/r$, whereas $r$ is
the radial distance from the scatterer to the observation point.
