QED model of the radiation escape from matter

Abstract

A simple model based on QED is presented for the estimation of contribution of the excited level few-photon decays to the radiation escape from the matter in the epoch of the cosmological hydrogen recombination. It is shown that apart from the widely studied two-photon decays, some specific 3-photon decays can contribute on the level of 0.1% accuracy, required by the recent astrophysical observations. I. INTRODUCTIONTheory of the cosmological hydrogen recombination became one of the most intensively discussed fundamental physics problems in the last decade. The interest comes from the accurate measurements of the asymmetry in the temperature and polarization distribution of the Cosmic Microwave Background (CMB) [1], [2]. The launching of the Planck Surveuor which enables to perform these measurements with accuracy 0.1% makes the situation even more intriguing.The modern theory of the cosmological hydrogen recombination starts from the papers by Zel'dovich, Kurt and Sunyaev [3] and by Peebles [4]. It was argued that the bound-bound one-photon transitions from the upper levels to the lower ones did not permit the hydrogen atoms to reach their ground states: each photon released in such transition in one atom was immediately absorbed by another atom. These reabsorption processes did not allow the radiation to "escape" the interaction with the matter. As it was first established in [3], [4] the two-photon 2s-1s transition presents the main channel for the radiation "escape" and formation of the CMB. This transition also led to the final hydrogen recombination. Hence, the recent properties of the CMB are essentially defined by the two-photon processes during the cosmological recombination epoch.In [5] the importance of the two-photon decays from excited states with n > 2 for the detailed analysis of the properties of CMB was noted. Over the past few years the theory of cosmological recombination was essentially detalized by many authors. In particular, in [5], [6] it was demonstrated that the two-photon transitions ns → 1s(n > 2) and nd → 1s can also give a sizeable contribution to the radiation "escape". There is a difference between the decay of ns(n > 2), nd states and the decay of the 2s state. This difference is due to the presence of cascade transitions as the dominant decay channels in the cases of ns(n > 2) and nd levels. For the 2s level the cascade transitions are absent. The cascade photons can be effectively reabsorbed and therefore the problem of separation of the "pure" two-photon emission from the cascade photons arises in connection with the "escape" probability. This problem was intensively discussed during the last decade [7]- [12]. As it was proved in [11] the separation of the "pure" two-photon emission for the ns(n > 2) and nd levels is an ambiguous procedure. First this ambiguity was established for the two-photon transitions with cascades in the highly charged ions [13]. To reach the level of accuracy 0.1% for the theoretical description of the properties of the CMB many effects should be taken ...

Theory of the multiphoton cascade transitions with two photon links: comparison of quantum electrodynamical and quantum mechanical approaches

“…To present an illustration of the proper choice of the cascade regularization we will evaluate an absorbability of the twophoton emission presented by the frequency distribution for the two-or three-photon transitions. A similar property was first introduced in [33] and employed in [45,46] to characterize the probability of absorption of the radiation emitted by one atom and absorbed by another atom. In our case this means the probability for the two-photon radiation emitted by one atom to be absorbed in the one-photon absorption lines of another atom.…”

“…It is convenient to begin with the absorbability X 2γ 2s−1s of two-photon emission, to compare it with the absorbability of the other two-photon transitions. We define X 2γ as [46]…”