Relativistic calculation of the two-photon decay rate of highly excited ionic states

Abstract

Based on quantum electrodynamics, we reexamine the two-photon decay of one-electron atoms.Special attention is paid to the calculation of the (two-photon) total decay rates which can be viewed as the imaginary part of the two-loop self-energy. We argue that our approach can easily be applied to the cases with a virtual state having an intermediate energy between the initial and the final state of the decay process leading, thus, to the resonance peaks in the two-photon energy distribution. In order to illustrate our approach, we obtain fully relativistic results, resolved into electric and magnetic multipole components, for the two-photon decay rates of the 3S 1/2 → 1S 1/2 transition in neutral hydrogen as well as in various hydrogen-like ions.

Two-photon approximation in the theory of electron recombination in hydrogen

“…However, accurate treatment of the recombination process from the particular excited level, as presented in this paper, also may be of interest. In particular, we demonstrate that the consequent QED treatment of the 3p level decay should include the two-photon contribution comparable with the widely discussed two-photon decay of the 3s level [23][24][25][26][27][28][29][30][31]. In this paper, we limit ourselves only to electric dipole transitions (in both one-and two-photon decays) and ignore n d → ns transitions, which are also important [6][7][8][9].…”

“…This approach was criticized later [8]. Another ("alternative") method which formally allows for the separate determination of the pure two-photon contribution in the case of two-photon transitions with cascades was developed in a series of works by Jentschura [25][26][27][28][29]. This approach contradicts the LPA results.…”

Correlated two-photon emission by transitions of Dirac-Volkov states in intense laser fields: QED predictions

“…The main problem with this regularization scheme is that the resulting scattering amplitude is not strictly gauge invariant, but the noninvariance induced by the small regularizing imaginary parts of the energies of the virtual states is moved to higher orders. We note that very similar questions concerning two-photon emission amplitudes for bound states have recently been discussed in [46,47,48,49,50]. As an alternative, we propose to multiply the rate with the regularizing…”

The two-photon approximation for the four-photon decay of the 4d excited state in hydrogenThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at École de Physique, les Houches, France, 30 May – 4 June, 2010.

“…Nevertheless, this scheme is not fully adequate; the main difficulty consists in interference between resonant and nonresonant photons. Recently a series of papers [10][11][12][13][14] was published where the author suggested an ''alternative'' approach for cascade separation. However, the procedure given in these works is not unique, and contains serious conceptual problems connected with the cascade definition and interference contributions to the total transition rate.…”