  Recently, Jarah has constructed the kink form factor relevant to the
scattering of an ultrarelativistic meson with an arbitrary nonrelativistic
scalar kink. However the formula was only applied to the Sine-Gordon model,
where the form factor was long ago determined by Weisz using integrability. In
this paper, using various known analytic results for the (1+1)-dimensional real
scalar $\Phi^4$ model and a kink wave packet construction, we analytically
calculate the leading quantum correction to the form factor of the $\Phi^4$
kink. We discuss its properties in general and also in the ultra-relativistic
meson case and provide a numerical check of our results.
