Models with non-Hermitian Hamiltonian and optical theorem

Abstract

The applicability of the optical theorem in the models with the non-Hermitian Hamiltonian is studied. By way of example we consider the $n\bar{n}$ transition in a medium followed by annihilation. It is shown that an application of optical theorem for the non-unitary $S$-matrix leads to the qualitative error in the result. The lower limit on the free-space $n\bar{n}$ oscillation time $\tau $ calculated by means of the model with Hermitian Hamiltonian lies in the range $10^{16}\; {\rm yr}>\tau >1.2\cdot 10^{9}\; {\rm s}$.