Interpretation of single-particle singularity in multiple scattering processes

It is shown that the total probability of the process of multiple scattering that takes place through single-particle intermediate states is proportional to not only the product $VT$ of the volume and the interaction time but also the product of the integrals $\int d\rho$, where $\rho=r/k$ is the ratio of the distance between the centers of two successive collisions to the momentum of the corresponding intermediate particle.