False Vacuum Decay Induced by Particle Collisions

The semiclassical formalism for numerical calculation of the rate of tunneling transitions induced by N particles with total energy E of order or higher than the height of the barrier is developed. The formalism is applied to the induced false vacuum decay in the massive four-dimensional $-\lambda {\varphi }^4$ model. The decay rate, as a function of E and N, is calculated numerically in the range $0.4\text{lsim}E\mathrm{/}{E}_{sph}\text{lsim}3.5$ and $0.25\text{lsim}N\mathrm{/}{N}_{sph}\text{lsim}1.0$, where $E_{sph}$ and $N_{sph}$ are the energy and the number of particles in the analog of the sphaleron configuration. The results imply that the ``two-particle’’ cross section of the false vacuum decay is exponentially suppressed at least up to energies of order $10E_{sph}$. At $E\sim E_{sph}$, this exponential suppression is estimated as about 80% of the zero energy suppression.