Born method in the problem of entry of a term into the continuum through a sloping boundary

In the framework of the quantum variant of the Demkov–0sherov model, various cases of the position of a sloping boundary of the continuum and a term of the system are considered. The problem is solved by the Born method, i.e., the principal terms of the asymptotic: behaviors of different characteristics with respect to the parameter $\sqrt{m_e/M}$ ($m_e$ is the electron mass and $M$ is the reduced mass of the atoms) are studied.