available energy region. However, as observed long ago\[19\], this is not the case. If one writes proton-proton total, inelastic and elastic cross sections in terms of the S-matrix at a given impact parameter of the collision, $S(b),$ as

$$\sigma_{in}=\int d^2b[1-S^2(b)]\eqno(2.3)$$

$$\sigma_{e\ell}=\int d^2b[1-S(b)]^2\eqno(2.4)$$

$$\sigma_{tot}=2\int d^2b[1-S(b)],\eqno(2.5)$$

then $S(b)$ depends on  b roughly as indicated in Fig.1. (We take S(b) to be real for simplicity.)

For small values of impact parameter $S(b)$ is near zero for proton-proton collisions already in the ISR and Fermilab fixed target energy regime. For proton-antiproton collisions $S(b)$ is quite small for $b<1 fm$ in the Fermilab energy regime. $S(b)$ near zero is a signal that unitarity corrections are large though they are not so easy to see in the total cross section because the radius of interaction is expanding and the growth of $\sigma_{tot}$ is mainly coming from that expansion. Monte Carlo simulations\[20\] of the dipole formulation\[21,22\] of the Balitsky, Fadin, Kuraev, Lipatov\[23,24\] equation for the academic case of heavy onium-heavy onium scattering show a similar phenomenon. For rapidities less than about 15 the BFKL equation is reliable for the total onium-onium cross section, however, for small impact parameter collisions important unitarity corrections are visible for rapidities of 