Photoionization and Electron-Ion Recombination of n = 1 to Very High n-Values of Hydrogenic Ions

Abstract

Single electron hydrogen or hydrogenic ions have analytical forms to evaluate the atomic parameters for the inverse processes of photoionization and electron-ion recombination (H I + hν↔ H II + e) where H is hydrogen. Studies of these processes have continued until the present day (i) as the computations are restricted to lower principle quantum number n and (ii) to improve the accuracy. The analytical expressions have many terms and there are numerical instabilities arising from cancellations of terms. Strategies for fast convergence of contributions were developed but precise computations are still limited to lower n. This report gives a brief review of the earlier precise methodologies for hydrogen, and presents numerical tables of photoionization cross sections (σPI), and electron-ion recombination rate coefficients (αRC) obtained from recombination cross sections (σRC) for all n values going to a very high value of 800. σPI was obtained using the precise formalism of Burgess and Seaton, and Burgess. αRC was obtained through a finite integration that converge recombination exactly as implemented in the unified method of recombination of Nahar and Pradhan. Since the total electron-ion recombination includes all levels for n = 1 −∞, the total asymptotic contribution of n=801−∞, called the top-up, is obtained through a n−3 formula. A FORTRAN program “hpxrrc.f” is provided to compute photoionization cross sections, recombination cross sections and rate coefficients for any nl. The results on hydrogen atom can be used to obtain those for any hydrogenic ion of charge z through z-scaling relations provided in the theory section. The present results are of high precision and complete for astrophysical modelings.

Atomic radiative data for oxygen and nitrogen for solar photospheric studies

“…Photoionization cross sections for the 2s 2 2p 4 3 P 2 ground level (left panels), as well as the 2s 2 2p 3 3s 5 S o 2 (middle panels) and 2s 2 2p 3 3s 5 P 1 (right panels) levels. The results of the present calculation, also reported in Bergemann et al (2021), are depicted by the top panels, and the results of Nahar (2021) and the OP (Cunto et al 1993) 1 .19 ± 0.10 1.73 ± 0.14 Musielok et al (1995) 1 .15 ± 0.13 1.14 ± 0.14 1.67 ± 0.19 2.55 ± 0.31 Recommended 1.38 ± 0.15 1.14 ± 0.12 2.03 ± 0.0.22 2.55 ± 0.27…”

“…5d4f, 2s2p 2 4f6l (l = 0 − 2), 2s2p 2 4f5f, 2s2p 2 5p 2 , 2s2p 2 5p5d, 2s2p 2 5p6l (l = 0 − 2), 2s2p 2 5p5f, 2s2p 2 5d 2 , 2s2p 2 5d6l (l = 0 − 2), 2s2p 2 5d5f, 2s2p 2 6s6l (l = 0 − 2), 2s2p 2 6s5f, 2s2p 2 6p 2 , 2s2p 2 6d 2 , 2s2p 2 6d5f, 2p 3 3snl (n = 4 → 6, l = 0 − 2) 2p 3 3s4f, 2p 3 3s5f, 2p 3 3p 2 , 2p 3 3p3d, 2p 3 3pnl (n = 4 → 6, l = 0 − 2), 2p 3 3p4f, 2p 3 3p5f, 2p 3 3d 2 , 2p 3 3dnl (n = 4 → 6, l = 0 → 2), 2p 3 4s4f, 2p 3 4s5f, 2p 3 4p 2 , 2p 3 4p4d, 2p 3 4snl (n = 4 → 6, l = 0 → 2), 2p 3 4pnl (5 = 4 → 6, l = 0 → 2), 2p 3 4p4f, 2p 3 4p5f, 2p 3 4d 2 , 2p 3 4dnl (5 = 4 → 6, l = 0 → 2), 2p 3 4d4f, 2p 3 4d5f, 2p 3 5snl (5 = 4 → 6, l = 0 − 2), 2p 3 5s4f, 2p 3 5s5f, 2p 3 5p4f, 2p 3 5d4f, 2p 3 4f6l (l = 0 → 2), 2p 3 4f5f, 2p 3 5p 2 , 2p 3 5p5d, 2p 3 5p6l (l = 0 − 2), 2p 3 5p5f, 2p 3 5d 2 , 2p 3 5d6l (l = 0 − 2), 2p 3 6d 2 , 2p 3 6d5f 2p 3 5d5f, 2p 3 6s6l (l = 0 − 2), 2p 3 6s5f, 2p 3 6p 2 , 2p 3 6p6d, 2p 3 6p5f, (middle panels), and 2s 2 2p 3 3s 5 P 1 (right panels) levels. The results of the present calculation, also reported in Bergemann et al (2021), are depicted by the top panels, and the results of Nahar (2021) and the OP (Cunto et al 1993) are presented in the middle and bottom panels, respectively.…”

Simulation and experimental results of plasma opening switch operation with inductive and electron beam diode loads in different plasma regimes

“…The plasma density of H-plasma and C-plasma are (1.6 ± 0.5) × 10 19 m −3 and (2.8 ± 0.6) × 10 19 m −3 with velocities measured using plasma transit times at two locations axial to the plasma gun are (4.54 ± 0.25) cm/μs and (1.81 ± 0.18) cm/μs respectively. The first peak in the density waveform in figure 4 is the H-plasma cloud and the second peak is the C-plasma cloud because the hydrogen has a lower mass and higher velocity compared to the carbon ions [25] and as the hydrogen ion has a single proton, it rapidly recombines with the electrons compared to carbon ions [23,27,28]. These plasma parameter measurement experiments are carried out on a single plasma gun in the vacuum chamber by removing the cathode electrode.…”

Photoejection from Various Systems and Radiative-Rate Coefficients

“…It is very important to try other approximations in addition to the R-matrix approach. Very recently, Nahar [46] has carried out very detailed and accurate calculations of photoionization cross sections and electron-ion recombination of n = 1 to very high n values of hydrogenic ions. Since hydrogen is very abundant in the universe, the results of this calculation are of immense importance in applications to solar-and astrophysics.…”