Approach to equilibrium of the hydrogen atom at low temperatures

The dynamics of the approach to equilibrium of the hydrogen atom is investigated numerically through a Monte Carlo procedure. We show that, before approaching ionization, the hydrogen atom may live in a quasi-equilibrium state, characterized by aging, whose duration increases exponentially as the temperatures decreases. By analyzing the quasi-equilibrium state, we compute averages of physical quantities for the hydrogen atom. We have introduced an analytic approach that fits satisfactorily the numerical estimates for low temperatures. Although the present analysis is expected to hold for energies typically up to 5% of the ionization energy, it works well for temperatures as high as 7000K.