Some properties of Stark states of hydrogenic atoms and ions

Abstract

The motivation for this work is the problem of providing accurate values of the atomic transition matrix elements for the Stark components of Rydberg–Rydberg transitions in atomic hydrogen and hydrogenic ions, for use in spectral line broadening calculations applicable to cool, low-density plasmas, such as those found in H II regions. Since conventional methods of calculating these transition matrix elements cannot be used for the high principal quantum numbers now easily attained in radio astronomical spectra, we attempt to show that the recurrence relation (ladder operator) method recently employed by Watson (2006 J. Phys. B: At. Mol. Opt. Phys. 39 1889–97) and Hey (2006 J. Phys. B: At. Mol. Opt. Phys. 39 2641–64) can be taken over into the parabolic coordinate system used to describe the Stark states of the atomic (ionic) radiators. The present method is therefore suggested as potentially useful for extending the work of Griem (1967 Astrophys. J. 148 547–58, 2005 Astrophys. J. 620 L133–4), Watson (2006), Stambulchik et al (2007 Phys. Rev. E 75 016401(9 pp) on Stark broadening in transitions between states of high principal quantum number, to physical conditions where the binary, impact approximation is no longer strictly applicable to both electron and ion perturbers. Another possible field of application is the study of Stark mixing transitions in ‘ultracold’ Rydberg atoms perturbed by long-range interactions with slow atoms and ions. Preparatory to the derivation of recurrence relations for states of different principal quantum number, a number of properties and recurrence relations are also found for states of identical principal quantum number, including the analogue in parabolic coordinates to the relations of Pasternack (1937 Proc. Natl Acad. Sci. USA 23 91–4, 250) in spherical polar coordinates.

New clues to the impact broadening mystery in radio recombination lines

“…As was found for the observations below ∼ 3 GHz, the 6 GHz data also show an unexplainable line narrowing. This mysterious result has since been examined by several authors (Hey 2006(Hey , 2007(Hey , 2009Watson 2006;Oks 2004;Griem 2005;Gigosos et al 2007;Gavrilenko and Oks 2007;Gordon 2008;von Prochazka et al 2010) but all attempts to explain it as an impact narrowing for quantum numbers above n = 200 and above ∆n = 8 have been unsuccessful. Although the reduced impact broadening below 3 GHz might be explainable by variable density models, this is unlikely to be the explanation for the decrease seen at 6 GHz since these observations were all made with the same telescope, the same beamwidth, and near the same frequency.…”

Classical calculation of the lifetimes and branching ratios for radiative decays of hydrogenic atoms

“…The quantum mechanical solutions of the hydrogen atom in parabolic coordinates have been described in detail in Ref. [16]. For the Rydberg-Stark problem we use the parabolic coordinates defined as ξ ± = x 2 + y 2 + z 2 ± z , ξ 0 = arctan (y/x) .…”

“…Further studies of the relationship between the quantum states in these representations are found in Refs. [16,20]. A discussion of features of the lifetimes of m = 0 vs m = 0 Stark states was given in Ref.…”

“…The densities are defined using the solutions given in Ref. [16]. The classical distributions were generated from histograms for the two coupled oscillators for which the phase δ was varied uniformly and weights according to the values of ξ ± were applied to the data for a meaningful comparison.…”

Stark effect of high-nhydrogen-like transitions: quasi-contiguous approximation

“…However, radiative transitions originating from high-n levels of hydrogen or hydrogen-like ions have a complex structure of the Stark effect, which poses a few calculational challenges. While effective and accurate methods for evaluating the atomic transition matrix elements are now readily available [10], the complexity due to the large number of different atomic states involved in such a transition remains an impeding factor in applying computer simulation methods employing directly solving the timedependent Schrödinger equation for Stark broadening of highn transitions in plasmas. The fast growth of the computational requirements with n makes such calculations unfeasible for, say n 20, using present personal computers.…”