The Radiative Recombination Coefficients of the Hydrogen Atom.

Boardman, William J.

doi:10.1086/190101

Cited by 21 publications

(12 citation statements)

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“…In addition, we explored three different numerical methods to compute the photoionization and photorecombination rates: the approximations (valid for small values of the energy of the ejected electron) given by Burgess (1958); the polynomial expressions given by Karzas & Latter (1961) and Boardman (1964); and the numerical subroutines provided by Storey & Hummer (1991). The second and third approaches were found to give identical results for all levels up to n max = 30.…”

Section: Basic Equationsmentioning

confidence: 99%

Lines in the cosmic microwave background spectrum from the epoch of cosmological hydrogen recombination

Rubiño-Martín

Chluba

Sunyaev

2006

Monthly Notices of the Royal Astronomical Society

108

165

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We compute the spectral distortions of the cosmic microwave background (CMB) arising during the epoch of cosmological hydrogen recombination within the standard cosmological (concordance) model for frequencies in the range 1–3500 GHz. We follow the evolution of the populations of the hydrogen levels including states up to principle quantum number n= 30 in the redshift range 500 ≤z≤ 3500. All angular momentum substates are treated individually, resulting in a total number of 465 hydrogen levels. The evolution of the matter temperature and the fraction of electrons coming from He ii are also included. We present a detailed discussion of the distortions arising from the main dipolar transitions, for example Lyman and Balmer series, as well as the emission due to the two‐photon decay of the hydrogen 2s level. Furthermore, we investigate the robusteness of the results against changes in the number of shells considered. The resulting spectral distortions have a characteristic oscillatory behaviour, which might allow experimentalists to separate them from other backgrounds. The relative distortion of the spectrum exceeds a value of 10−7 at wavelengths longer than 21 cm. Our results also show the importance of detailed follow‐up of the angular momentum substates, and their effect on the amplitude of the lines. The effect on the residual electron fraction is only moderate, and mainly occurs at low redshifts. The CMB angular power spectrum is changed by less than 1 per cent. Finally, our computations show that if the primordial radiation field is described by a pure blackbody, then there is no significant emission from any hydrogen transition at redshifts greater than z∼ 2000. This is in contrast to some earlier works, where the existence of a ‘pre‐recombination’ peak was claimed.

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Section: Basic Equationsmentioning

confidence: 99%

Lines in the cosmic microwave background spectrum from the epoch of cosmological hydrogen recombination

Rubiño-Martín

Chluba

Sunyaev

2006

Monthly Notices of the Royal Astronomical Society

108

165

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“…The "Stobbe formulae" are useful for these (Bearden, 1966 Bergeron and Collin-Souffrin (1974), and by Weisheit (1974). Dalgarno and McCray (1972) and Shull (1979) , Bates and Dalgarno (1962), Boardman (1964), Glasco and Zirin (1964), and Burgess (1964). Similar values for helium have been given by Burgess and Seaton (1960) and by Robbins (1968,1970).…”

Section: B Quasars As Observed Opticallymentioning

confidence: 99%

The emission lines of quasars and similar objects

1979

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Much of our information about quasars is derived from their emission-line spectra. The analysis of such spectra has become an intricate subject which differs considerably from traditional, low-density nebular astrophysics. This review is intended to explain our present understanding of the situation, including some aspects of galactic nuclei whose luminosities are more modest than quasars. Quasars line-emitting regions are probably photoionized (even if supplementary heating processes also occur). So fax, models have been constructed which include ionization and thermal equilibria, the transfer of resonance-line and related photons, and the likely effects of absorption and scattering by dust grains. From comparisons between emission-line intensities produced in these models and observed quasars spectra, it appears that certain densities and pressures and size scales occur in or around quasars. The relative abundances of elements are not very far from solar values, although it is suspected that heavy elements -carbon, nitrogen, and oxygen in particular -are moderately "overabundant" in quasars. The emission-line intensities also provide indirect information about quasars ultraviolet and soft-x-ray continua; there are hints that photons with energies between 20 and 300 eV -which are not directly observable -may even represent the peak of the luminous output of a typical quasar. Finally, some gas-dynamical questions, while extremely important, are very difficult to answer, because of a lack of observables. CONTENTS 715

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“…Analytical representation of the radial wave functions of discrete R nl (r) and the continuum R pl (r) states for the hydrogen atom can be found in textbooks [8,11]. Then, radial integrals of the type Equation ( 13) are usually calculated employing the Gordon formula, as can be seen, for example, in [13][14][15]. The expression ( 12) is written for the first term in Equation ( 8) and easily adapts to the second one.…”

Section: Thermal Vertex Correction To the Recombination Processmentioning

confidence: 99%

“…The corrections to the partial spontaneous and stimulated recombination coefficients (∆α nl and ∆α β nl , respectively), partial ionization coefficient (∆β nl ), that we are interested in can also be calculated using Equations ( 1), ( 17), ( 19)- (21). The corresponding numerical results for the 1s and 2s states in the hydrogen atom are given in Table 3 separately for each of the three summands in Equation (14). It should be noted here that the calculations are well converged upon the summation over the intermediate spectrum m, which were carried out by the direct summation of each individual state ml < ε to m = 100.…”

Section: Recombination and Ionization Coefficientsmentioning

confidence: 99%

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

Triaskin

Zalialiutdinov

Anikin

2021

Atoms

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In the present paper, the correction of the recombination and ionization processes of the hydrogen atom due to the thermal interaction of two charges was considered. The evaluation was based on a rigorous quantum electrodynamic (QED) approach within the framework of perturbation theory. The lowest-order radiative correction to the recombination/ionization cross-section was examined for a wide range of temperatures corresponding to laboratory and astrophysical conditions. The found thermal contribution was discussed both for specific states and for the total recombination and ionization coefficients.

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The Radiative Recombination Coefficients of the Hydrogen Atom.

Cited by 21 publications

References 0 publications

Lines in the cosmic microwave background spectrum from the epoch of cosmological hydrogen recombination

Lines in the cosmic microwave background spectrum from the epoch of cosmological hydrogen recombination

The emission lines of quasars and similar objects

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

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