Atomic collision data for hydrogen principal quantum numbers n ranging from 1 to 1500, relevant for conditions pertaining to the gaseous nebula W51 [7, 8]: T = 104 K, Ne = Nf = 2500 cm−3
Table 1. Atomic collision data for hydrogen principal quantum numbers n ranging from 1 to 1500, relevant for conditions pertaining to the gaseous nebula W51 [7, 8]: T = 104 K, Ne = Nf = 2500 cm−3. Listed for each value of n are the orbital period, the polarizability [19, 20, 51, 52] in atomic units, and thermally averaged dimensionless parameters for ion–induced dipole collisions, defined in equations (3) and (5). The last column lists the mean time interval between strong collisions. The data show clearly that, while curvature of the perturber trajectories is insignificant in a plasma of this kind for n > 40, the 'size' of the bound orbital is the limiting factor in determining the 'strong' collision cross-section for higher excited states. For the spectra of Bell et al [7, 8] the restriction imposed on the upper principal quantum number by collisions of this type lies significantly above the n-values of the measured recombination lines. A quantity in parentheses indicates the power of 10 by which the corresponding entry should be multiplied.
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.