Effect of Self-Energy Terms in the Bethe-Salpeter Equation

The Bethe-Salpeter equation is solved in the ladder-graph approximation to the ${\phi }^3$ theory with the inclusion of certain self-energy diagrams. The self-energy graphs are included to force the resultant cross sections to satisfy the unitarity condition ${\sigma }_{\mathrm{total}}\ge {\sigma }_{\mathrm{elastic}}$. It is found that the inclusion of these effects can substantially change both the elastic and inelastic cross sections.