QED calculation ofE1M1 andE1E2 transition probabilities in one-electron ions with arbitrary nuclear charge

Labzowsky, L. N.; Shonin, A. V.; Solovyev, D.

doi:10.1088/0953-4075/38/3/010

Cited by 61 publications

(92 citation statements)

References 27 publications

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“…−1 , which fully agrees with the result of earlier computations (Breit & Teller 1940;Kipper 1950;Spitzer & Greenstein 1951;Klarsfeld 1969;Johnson 1972;Goldman & Drake 1981;Drake 1986;Goldman 1989;Labzowsky et al 2005). With the approximate formula for the non-resonant two-photon emission spectrum for the 2s-state as given in Appendix B, we obtain A 2s1s = 8.2297s…”

Section: The Two-photon Rate For the 2s-statesupporting

confidence: 90%

Two-photon transitions in hydrogen and cosmological recombination

Chluba

Sunyaev

2008

A&A

154

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We study the two-photon process for the transitions ns → 1s and nd → 1s in hydrogen up to large n. For n ≤ 20 we provide simple analytic fitting formulae to describe the non-resonant part of the two-photon emission profiles. Combining these with the analytic form of the cascade-term yields a simple and accurate description of the full two-photon decay spectrum, which only involves a sum over a few intermediate states. We demonstrate that the cascade term naturally leads to a nearly Lorentzian shape of the two-photon profiles in the vicinity of the resonances. However, due to quantum-electrodynamical corrections, the two-photon emission spectra deviate significantly from the Lorentzian shape in the very distant wings of the resonances. We investigate up to which distance the two-photon profiles are close to a Lorentzian and discuss the role of the interference term. We then analyze how the deviation of the two-photon profiles from the Lorentzian shape affects the dynamics of cosmological hydrogen recombination. Since in this context the escape of photons from the Lyman-α resonance plays a crucial role, we concentrate on the two-photon corrections in the vicinity of the Lyman-α line. Our computations show that the changes in the ionization history due to the additional two-photon process from high shell (n > 2) likely do not reach the percent-level. For conservative assumptions we find a correction ∆N e /N e ∼ −0.4% at redshift z ∼ 1160. This is numerically similar to the result of another recent study; however, the physics leading to this conclusion is rather different. In particular, our calculations of the effective two-photon decay rates yield significantly different values, where the destructive interference of the resonant and non-resonant terms plays a crucial role in this context. We also show that the bulk of the corrections to the ionization history is only due to the 3s and 3d-states and that the higher states do not contribute significantly.

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Section: The Two-photon Rate For the 2s-statesupporting

confidence: 90%

Two-photon transitions in hydrogen and cosmological recombination

Chluba

Sunyaev

2008

A&A

154

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“…Recently Labzowsky et al (2005) gave a value of A 2s1s = 8.2206 s −1 for the total transition rate, which to 0.1% agrees with a more simple calculation based on the method used by Spitzer & Greenstein (1951). In this paper we use this simplified approach and include induced effects in the calculation of the hydrogen two-photon decay rate within the context of cosmological hydrogen recombination.…”

Section: Induced 2s → 1s Two-photon Transition Of Hydrogen During Recsupporting

confidence: 74%

Induced two-photon decay of the 2s level and the rate of cosmological hydrogen recombination

Chluba

Sunyaev

2006

A&A

123

153

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Induced emission due to the presence of soft CMB photons slightly increases the two-photon decay rate of the 2s level of hydrogen defining the rate of cosmological recombination. This correspondingly changes the degree of ionization, the visibility function and the resulting primordial temperature anisotropies and polarization of the CMB on the percent level. These changes exceed the precision of the widely used Cmbfast and Camb codes by more than one order of magnitude and can be easily taken into account.

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“…From the theoretical point of view it would be surprising to find a value that deviates significantly from A 2s→1s = 8.2206 s −1 , derived from the most detailed computation (Labzowsky et al 2005). However, laboratory measurements of this transition rate are extremely challenging (O'Connell et al 1975;Krüger & Oed 1975;Cesar et al 1996).…”

Section: Measuring a 2s→1s With Planckmentioning

confidence: 94%

Planck2015 results

Ade

Aghanim

Arnaud

et al. 2016

A&A

9,473

226

3,990

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This paper presents cosmological results based on full-mission Planck observations of temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation. Our results are in very good agreement with the 2013 analysis of the Planck nominal-mission temperature data, but with increased precision. The temperature and polarization power spectra are consistent with the standard spatially-flat 6-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations (denoted "base ΛCDM" in this paper). From the Planck temperature data combined with Planck lensing, for this cosmology we find a Hubble constant, H 0 = (67.8 ± 0.9) km s −1 Mpc −1 , a matter density parameter Ω m = 0.308 ± 0.012, and a tilted scalar spectral index with n s = 0.968 ± 0.006, consistent with the 2013 analysis. Note that in this abstract we quote 68% confidence limits on measured parameters and 95% upper limits on other parameters. We present the first results of polarization measurements with the Low Frequency Instrument at large angular scales. Combined with the Planck temperature and lensing data, these measurements give a reionization optical depth of τ = 0.066 ± 0.016, corresponding to a reionization redshift of z re = 8.8+1.7 −1.4 . These results are consistent with those from WMAP polarization measurements cleaned for dust emission using 353-GHz polarization maps from the High Frequency Instrument. We find no evidence for any departure from base ΛCDM in the neutrino sector of the theory; for example, combining Planck observations with other astrophysical data we find N eff = 3.15 ± 0.23 for the effective number of relativistic degrees of freedom, consistent with the value N eff = 3.046 of the Standard Model of particle physics. The sum of neutrino masses is constrained to m ν < 0.23 eV. The spatial curvature of our Universe is found to be very close to zero, with |Ω K | < 0.005. Adding a tensor component as a single-parameter extension to base ΛCDM we find an upper limit on the tensor-to-scalar ratio of r 0.002 < 0.11, consistent with the Planck 2013 results and consistent with the B-mode polarization constraints from a joint analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP B-mode data to our analysis leads to a tighter constraint of r 0.002 < 0.09 and disfavours inflationary models with a V(φ) ∝ φ 2 potential. The addition of Planck polarization data leads to strong constraints on deviations from a purely adiabatic spectrum of fluctuations. We find no evidence for any contribution from isocurvature perturbations or from cosmic defects. Combining Planck data with other astrophysical data, including Type Ia supernovae, the equation of state of dark energy is constrained to w = −1.006 ± 0.045, consistent with the expected Corresponding author: G. Efstathiou, e-mail: gpe@ast.cam.ac.ukArticle published by EDP Sciences A13, page 1 of 63 A&A 594, A13 (2016) value for a cosmological constant. The standard big bang nucleosynthesis predictions for the helium and deuterium abundanc...

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QED calculation ofE1M1 andE1E2 transition probabilities in one-electron ions with arbitrary nuclear charge

Cited by 61 publications

References 27 publications

Two-photon transitions in hydrogen and cosmological recombination

Two-photon transitions in hydrogen and cosmological recombination

Induced two-photon decay of the 2s level and the rate of cosmological hydrogen recombination

Planck2015 results

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