Recombination process for the hydrogen atom in the presence of blackbody radiation

Abstract

The process of recombination for the hydrogen atom in the heat bath creating the blackbody radiation is descibed within the frameworks of quantum electrodynamics. For this purpose the self-energy for unbound electron in the field of the nucleus is considered. The imaginary part of this self-energy is directly connected with the recombination cross-section. The same procedure is applied to the hydrogen atom in the field of blackbody radiation. This leads to the new thermal correction to the process of recombination for the hydrogen atom in the heat bath. This correction takes into account the finite lifetimes of atomic levels and appears to be important for special astrophysical studies.

Lowest-Order Thermal Correction to the Hydrogen Recombination Cross-Section in Presence of Blackbody Radiation

“…Recently, the influence of finite lifetimes on the stimulated transition rates in hydrogen and helium atoms was studied in [16][17][18], while this effect for bound-free transitions is described in detail in [1]. In the latter case, the numerical calculations become much more complicated when summing over nl for the recombination/ionization coefficients due to the presence of the Lorentz factor.…”

“…The theoretical prescription for electron recombination is precisely given within the framework of the quantum mechanical (QM) approach, which allows one to carry out the non-relativistic evaluation (based on the solution of the Schrödinger equation) for light atomic systems and easily extends to the relativistic case within the Dirac formalism. Recently, focusing on simple examples of the hydrogen atom, a rigorous derivation of the corresponding cross-section was obtained within the framework of quantum electrodynamics (QED) [1]. In particular, quantum mechanical results were obtained by considering a one-loop self-energy Feynman diagram.…”

“…In particular, quantum mechanical results were obtained by considering a one-loop self-energy Feynman diagram. In addition, in [1], it was demonstrated that the QED approach accommodates a thorough description of the effects induced by the blackbody radiation and, by excellence, strictly take into account the finite lifetimes of atomic levels.…”

“…Adopting the formalism developed in [1,6] for the vertex-type radiative thermal correction to a particular case of the radiative recombination process, we estimate the Feynman graphs shown in Figure 1. The process of electron transition from the initial state of the continuous spectrum i = ε to the bound state with the emission of a photon is considered here for the hydrogen atom placed in a heat bath.…”

“…where k is the momentum of the emitted photon, p ≡ | p| is the incident electron momentum and nl is the principal quantum number and orbital momentum of the bound atomic state, respectively. The corresponding QED derivation of the cross-section for the radiative recombination process using the one-loop self-energy correction can be found in [1].…”