The talk is aimed at giving insights from the ongoing research into multiparticle scattering in the real scalar field theory. The object of the research is the unbroken $\lambda \phi^4$ theory in the case of weak coupling. The research aims are to obtain semiclassical suppression exponents for the processes few $ \to N$, where $N$ is a semiclassically large ($\sim 1/\lambda$) final number of particles, and "few" is a few-particle initial state.
Since in the semiclassical limit solutions of the saddle-point equations (which replace classical field equations in semiclassics) become singular for considered boundary value problem (they have a discontinuity in the energy), this singular behaviour can be represented through the term with a delta-like source $j$ in the action. In this approach, properties of the saddle-point solutions are recovered in the limit $j\to 0$. In our research, we start from source-dominated solutions which we can describe analytically and then take the limit $j\to 0$ by solving lattice saddle-point equations with Newton-Raphson method for every new smaller amplitude of the source, step by step.
During the talk, I would like to describe our research and show the first obtained results.