  We use the semiclassical formalism based on singular solutions in complex
time to compute scattering rates for multiparticle production at high energies.
In a weakly coupled $\lambda \phi^4$ scalar field theory in four dimensions, we
consider scattering processes where the number of particles $n$ in the final
state approaches its maximal value $n \to E/m \gg 1$, where $m$ is the particle
mass. Quantum corrections to the known tree-level amplitudes in this regime are
characterised by the parameter $\lambda n$ and we show that they become large
at sufficiently high multiplicities. We compute full amplitudes in the large
$\lambda n$ limit on multiparticle mass thresholds using the thin-wall
realisation of the singular solutions in the WKB approach. We show that the
scalar theory with spontaneous symmetry breaking, used here as a simplified
model for the Higgs sector, leads to exponentially growing multi-particle rates
within our regime which is likely to realise the high-energy Higgsplosion
phenomenon. We also comment on realisation of Higgsplosion in dimensions lower
than four.
