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Physica A Statistical Mechanics and its Applications

A novel complete treatment of the time-evolution of a spontaneously decaying atomic state in relativistic QED

JOSIP SEKE

Published Apr 1, 1997• 5 citations
Publisher
DOI
10.1016/s0378-4371(96)00462-1

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It is shown that the application of a self-consistent projection-operator method, developed recently by the author, makes a complete treatment of the spontaneously decaying atomic state in relativistic QED possible. In a new physical real-transition interaction picture (in which the unobservable interaction of the free electron with the vacuum radiation field is eliminated) explicit finite analytic results for the non-Markovian time evolution and the radiative line shape in the case of relativistic Lyman-α spontaneous emission are obtained.
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.