Finite-energy bounds on the total cross section of strongly inelastic interaction between spinless particles

An explicit analytic expression is found for the unitary maximum of the total cross section $\sigma_t$ in terms of $a\equiv\sigma_e/\sigma_t$ and $b$, where $\sigma_e$ is the elastic cross section and $b$ is the forward slope of the imaginary part of the scattering amplitude. The basic assumptions are: 1) the scattering amplitude can be expanded in Legendre polynomials, 2) unitarity, and 3) strong (in the sense $a<2/3$) inelasticity of the scattering.