  In this paper the perturbation theory with the frequency of transition in
atom as perturbation parameter is constructed. The estimation of the reminder
term of series of this perturbation theory is given. With the help of this
perturbation theory we have found an exact asymptotics of eigenvalues of
complete hamiltonian in the limit of high quantum numbers. It is shown that the
counter-rotating terms keep a leading term but absolutely change a second term
of this asymptotic.
