The Size of p-Branes

We obtain form factors for scattering of gravitons and anti-symmetric tensor particles off Dirichlet $p$-branes in Type II superstring theory. As expected, the form factor of the -1-brane (the D-instanton) exhibits point-like behavior: in fact it is saturated by a single dilaton tadpole graph. In contrast, $p$-branes with $p>-1$ acquire size of order the string scale due to quantum effects and exhibit Regge behavior. We find their leading form factors in closed form and show that they contain an infinite sequence of poles associated with $p$-brane excitations. Finally, we argue that the $p$-brane form factors for scattering of R-R bosons will have the same stringy features found with NS-NS states.