  The cross-section for the lowest order $2\rightarrow2$ elastic scattering
between two charged scalars under external magnetic field mediated via a
neutral scalar, has been computed in strong as well as weak magnetic field
limits. This has been done by applying the optical theorem where the
cross-section is expressed in terms of the imaginary parts of different
one-loop graphs contributing to the forward scattering amplitudes. The
modification in the amplitudes due to the external magnetic field has been done
by means of replacing the charged scalar propagators with the Schwinger
proper-time ones. Significant modifications of the cross-sections with respect
to the vacuum cross-section are observed due to the external magnetic field.
