Gauge-invariant treatment of the exponential decay of an unstable atomic state

JOSIP SEKE

Maurice M. Lévy

K.J.F. Gaemers, T.D. Visser

JOSIP SEKE

It is shown that the application of a self-consistent projection-operator method, developed recently by the author, makes possible a complete and gauge-invariant treatment of spontaneously decaying atomic state. All the shortcomings of the Weisskopf-Wigner gauge-dependent method (Markov approximation and the neglect of virtual transition, retardation and electron-spin effects) are removed. After deriving a gauge-invariant equation of motion for the decaying state, a new physical interaction picture (in which the unobservable interaction of the free electron with the vacuum radiation field is eliminated) is introduced. In this new interaction picture, apart from a natural solution of the renormalization problem, explicit finite analytic results for the whole non-Markovian Lyman- alpha spontaneous decay are derived. Furthermore, a quasi-Lorentzian expression for the radiative line shape containing the correct (complete) finite non-relativistic frequency shift, stemming from the Lamb shifts of both levels 1S and 2P, is calculated.

JOSIP SEKE, A. V. SOLDATOV, Nikolay N. Bogolubov

A recent paper by Facchi and Pascazio, in which the advantage of numerical evaluations of deviations from exponential decay was pointed out, makes a revisitation of the subject necessary. All the more, since the above-mentioned authors have not estimated the error bounds (being absolutely necessary in any calculation) for their results. On the contrary, the accuracy of all results presented in this paper is proved by error estimates. Moreover, for the first time, the power of the simple iteration method in calculating both the exponential and non-exponential time evolution of an unstable atomic state is demonstrated.