Finite Range of Strong Interactions and Analyticity Properties in Momentum Transfer

We investigate how the finite range of strong interactions can be stated in terms of an experiment. It is found that it is equivalent to the fact that the probability of any process generated by strong interactions should decrease exponentially as a function of the impact parameter $a$. This impact parameter is defined by a translation of the initial wave packet in a direction normal to its mean velocity in the center-of-mass system. Because of the spreading of wave packets with time, it is necessary to consider wave-packets whose width in configuration space increases like $\sqrt{a}$. It is then shown that this property is equivalent to the analyticity of all absorptive parts due to different channels as functions of the momentum transfer inside an ellipse. Such analyticity properties are also valid for the amplitude of a two-body channel. The ellipse does not shrink to the physical region when the energy tends to infinity.