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Atomic radiative and collisional data for high-n hydrogen transitions [7, 8] measured and analysed for the following plasma parameters pertaining to the gaseous nebula Orion A [7, 8]: Te = Tf = 104 K, Ne = Nf = 2.0 ×

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posted on 2013-08-19, 00:00 authored by J D Hey

Table 3. Atomic radiative and collisional data for high-n hydrogen transitions [7, 8] measured and analysed for the following plasma parameters pertaining to the gaseous nebula Orion A [7, 8]: Te = Tf = 104 K, Ne = Nf = 2.0 × 104 cm−3. Apart from the calibration lines (n, Δn) = (71, 1), (89, 2) in the notation of [56], the transitions fall within the rest frame frequency window 17.55 < f[GHz] < 17.70. The first line of the table lists the Holtsmark normal field-strength, the electron Debye length, the maximum allowable value of nΔn for the ion impact approximation to be valid, and the characteristic time for Holtsmark field-strength variations. In the second line the binary collision parameter g is listed for ion–atom interaction limited by the Debye shielding cut-off, the thermal (collisional–radiative) limit for LTE level populations (ncr), the maximum principal quantum number for dynamic electron–radiator interactions (n_{{\rm max}}^e), and the Inglis–Teller limit. Listed for each transition are the line strength S(n, n'), and for the upper level n': the atomic dipole polarizability \bar \alpha _{{\rm pol}}^{(4)} ( {n^{\prime} } ), the dimensionless \bar \eta-parameter (thermally averaged), the characteristic collision duration for the ion–induced dipole interaction (appendix C), and the two binary collision parameters (appendix B). The time-scales and collision parameters show that, while the conditions for the impact approximation are fulfilled for both electron and ion perturbers, collective effects of the quasi-static ion background should have an important effect on the binary ion–atom (elastic) interaction. Line broadening by the nearly elastic (Δn = 0) collisions may therefore be expected to fall below values calculated for atomic states unperturbed by the ion background.


Since highly excited atoms, which contribute to the radio recombination spectra from Galactic H II regions, possess large polarizabilities, their lifetimes are influenced by ion (proton)–induced dipole collisions. It is shown that, while these ion–radiator collisional processes, if acting alone, would effectively limit the upper principal quantum number attainable for given plasma parameters, their influence is small relative to that of electron impacts within the framework of line broadening theory. The present work suggests that ion–permanent dipole interactions (Hey et al 2004 J. Phys. B: At. Mol. Opt. Phys. 37 2543) would also be of minor importance in limiting the occupation of highly excited states. On the other hand, the ion–induced dipole collisions are essential for ensuring equipartition of energy between atomic and electron kinetic distributions (Hey et al 1999 J. Phys. B: At. Mol. Opt. Phys. 32 3555; 2005 J. Phys. B: At. Mol. Opt. Phys. 38 3517), without which Voigt profile analysis to extract impact broadening widths would not be possible. Electron densities deduced from electron impact broadening of individual lines (Griem 1967 Astrophys. J. 148 547; Watson 2006 J. Phys. B: At. Mol. Opt. Phys. 39 1889) may be used to check the significance of the constraints arising from the present analysis. The spectra of Bell et al (2000 Publ. Astron. Soc. Pac. 112 1236; 2011 Astrophys. Space Sci. 333 377; 2011 Astrophys. Space Sci. 335 451) for Orion A and W51 in the vicinity of 6.0 and 17.6 GHz are examined in this context, and also in terms of a possible role of the background ion microfield in reducing the near-elastic contributions to the electron impact broadening below the predictions of theory (Hey 2012 J. Phys. B: At. Mol. Opt. Phys. 45 065701). These spectra are analysed, subject to the constraint that calculated relative intensities of lines, arising from upper states in collisional–radiative equilibrium, should be consistent with those obtained from Voigt profile analysis. It is shown that the experimental technique yields an excellent temperature diagnostic for the H II regions. On the other hand, strong evidence is not obtained, from those spectra which satisfy the above constraint on intensity, to indicate that the electron impact broadening theory requires substantial correction. The main grounds for attempting a revision of theory to allow for the influence of the ion microfield during the scattering processes on the upper and lower states of each line thus still appear to have a stronger theoretical (Hey 2007 J. Phys. B: At. Mol. Opt. Phys. 40 4077) than experimental basis.