  In this paper we consider eigenvalues asymptotics of the energy operator in
the one of the most interesting models of quantum physics, describing an
interaction between two-level system and harmonic oscillator. The energy
operator of this model can be reduced to some class of infinite Jacobi
matrices. Discrete spectrum of this class of operators represents the perturbed
spectrum of harmonic oscillator. The perturbation is an unbounded operator
compact with respect to unperturbed one. We use slightly modified Janas-Naboko
successive diagonalization approach and some new compactness criteria for
infinite matrices. Two first terms of eigenvalues asymptotics and the
estimation of remainder are found.
