Search

The low-energy electron-impact dissociation of molecular hydrogen has been a source of disagreement between various calculations and measurements for decades. Excitation of the ground state of ${\mathrm{H}}_{2}$ into the dissociative $b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$ state is now well understood, with the most recent measurements being in excellent agreement with the molecular convergent close-coupling (MCCC) calculations of both integral and differential cross sections [Zawadzki et al., Phys. Rev. A 98, 062704 (2018)]. However, in the absence of similar measurements for vibrationally excited or isotopically substituted ${\mathrm{H}}_{2}$, cross sections for dissociation of these species must be determined by theory alone. We have identified large discrepancies between MCCC calculations and the recommended $R$-matrix cross sections for dissociation of vibrationally excited ${\mathrm{H}}_{2}$, ${\mathrm{D}}_{2}$, ${\mathrm{T}}_{2}$, HD, HT, and DT [Trevisan et al., Plasma Phys. Contr. Fusion 44 1263 (2002); Plasma Phys. Contr. Fusion 44, 2217 (2002)], with disagreement in both the isotope effect and dependence on initial vibrational level. Here we investigate the source of the discrepancies, and discuss the consequences for plasma models, which have incorporated the previously recommended data.

A Monte Carlo simulation of electron energy deposition in a gas of molecular hydrogen has been conducted with the aim of producing an ab initio estimate of energy deposition parameters such as the mean energy per ion pair. A set of cross sections obtained using the molecular convergent close-coupling method were used as input. At high incident electron energies the mean energy per ion pair was calculated to be 36.3 eV, agreeing with the recommended value of 36.5 ± 0.3 eV. This represents the first fully ab initio calculation of the mean energy per ion pair using a self consistent data set.

Calculations of electron-impact excitation cross sections for molecular hydrogen have been performed using spherical- and spheroidal-coordinate formulations of the molecular convergent close-coupling method. We present a comparison and find good agreement between the results of these two techniques performed within the fixed-nuclei approximation for excitation from the ground X1Σg+ (v = 0) state of H2 to the B1Σu+ , C 1Πu, B′1Σu+ , D 1Πu, EF1Σg+ , b3Σu+ , c3Πu+ , a3Σu+ , e3Σu+ , h3Σg+ , and d 3Πu states. For the spheroidal-coordinate approach the adiabatic-nuclei method has been applied, allowing for a more reliable estimate of cross sections at near-threshold energies. Comparison of the adiabatic-nuclei cross sections with the corresponding fixed-nuclei cross sections is also presented.

We present a comprehensive set of vibrationally-resolved cross sections for electron-impact electronic excitation of the isotopologues of molecular hydrogen (D2, T2, HD, HT, and DT) initially in the ground electronic state. We apply the adiabatic-nuclei molecular convergent close-coupling (MCCC) method to calculate cross sections from threshold to 500 eV for excitation of all bound vibrational levels and dissociative excitation of the B 1 Σ u + , C 1 Π u , E F 1 Σ g + , B ′ 1 Σ u + , G K 1 Σ g + , I 1 Π g , J 1 Δ g , D 1 Π u , H 1 Σ g + , b 3 Σ u + , c 3 Π u , a 3 Σ g + , e 3 Σ u + , d 3 Π u , h 3 Σ g + , g 3 Σ g + , i 3 Π g , and j 3 Δ g electronic states from all bound vibrational levels of the ground electronic ( X 1 Σ g + ) state. Including the previously-published MCCC e-H2 cross sections (Scarlett et al., Atom. Data Nucl. Data Tables 137 (2021) 101361) the data set contains cross sections for over 60,000 electronic and vibrational transitions. The cross sections are presented in graphical form and provided as both numerical values and analytic fit functions in supplementary data files. The data can also be downloaded from the MCCC database at mccc-db.org .

Collisional radiative (CR) models for molecular hydrogen are of high relevance for performing qualitative and quantitative analysis of excited-state population densities measured in plasmas or predicting the dependence of plasma emission on parameter variations. Although the development of such models for H2 started decades ago, major uncertainties still exist regarding the most important set of input parameters, namely the cross sections for electron-impact excitation. The deviations between cross sections from different datasets are particularly pronounced in the energy region close to the threshold energy, strongly increasing the uncertainty of CR models applied to low-temperature plasmas. This paper presents experimental validation of a set of newly calculated non ro-vibrationally resolved electron-impact cross sections calculated for the triplet system of H2 using the molecular convergent close-coupling method in the adiabatic-nuclei formulation. These cross sections are implemented into a CR model based on the flexible solver Yacora. A first comparison of CR calculations with the different datasets to experimentally-determined population densities is performed at a planar ICP discharge for varying pressure (between 1 and 10 Pa) and RF power (between 700 and 1100 W). For the experimentally-accessible electron temperature and density range (2.5–10 eV and 1.8–3.3 × 1016 m−3, respectively), very good agreement between the model and experiment is obtained using the new data set, in contrast to previously used cross sections.

We present a comprehensive set of vibrationally-resolved cross sections for electron-impact electronic excitation of molecular hydrogen suitable for implementation in collisional-radiative models. The adiabatic-nuclei molecular convergent close-coupling method is used to calculate cross sections for excitation of all bound vibrational levels and dissociative excitation of the B 1 Σ u + , C 1 Π u , E F 1 Σ g + , B ′ 1 Σ u + , G K 1 Σ g + , I 1 Π g , J 1 Δ g , D 1 Π u , H 1 Σ g + , b 3 Σ u + , c 3 Π u , a 3 Σ g + , e 3 Σ u + , d 3 Π u , h 3 Σ g + , g 3 Σ g + , i 3 Π g , and j 3 Δ g electronic states from all v i = 0 –14 bound vibrational levels of the ground electronic ( X 1 Σ g + ) state. The data set consists of cross sections from threshold to 500 eV for over 5000 transitions, representing all possible electronic and vibrational transitions between the X 1 Σ g + state and the n = 2 –3 singlet and triplet states (where n refers to the united-atoms-limit principle quantum number). The cross sections are presented in graphical form and provided as both numerical values and analytic fit functions in supplementary data files. The data can also be downloaded from the MCCC database at http://mccc-db.org .

We report cross sections for electron-impact dissociative excitation of the $B{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$, $C{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}$, $D{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}$, ${B}^{\ensuremath{'}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$, and $E,F{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$ singlet states of molecular hydrogen from all ${v}_{i}=0--14$ vibrational levels of the ground $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$ state. Calculations are performed using the adiabatic-nuclei convergent close-coupling method formulated in prolate spheroidal coordinates from threshold to 500 eV. Agreement with previous calculations varies with transition and impact energy, ranging from excellent to poor. Agreement with available experiment is generally good.

We apply the adiabatic nuclei convergent close-coupling method to electron-impact dissociative excitation of ${\mathrm{H}}_{2}$ in the low-energy regime. Differential and integrated cross sections are presented for excitation of the $b^{3}\mathrm{\ensuremath{\Sigma}}_{u}^{+}$ state, the primary pathway to dissociation of ${\mathrm{H}}_{2}$ at low energies. Agreement with experiment is satisfactory. Results are also presented for the isotopologues ${\mathrm{D}}_{2}$, ${\mathrm{T}}_{2}$, HD, HT, and DT, which show a pronounced isotope effect near threshold in both the differential and integrated cross sections.

We report the electron impact integrated and differential cross sections for excitation to the $b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}, a{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}, c{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{u}, B{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}, E,F{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}, C{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}, e{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}, h{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}, d{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{u}, {B}^{\ensuremath{'}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}, D{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}, {B}^{\ensuremath{'}}{}^{\ensuremath{'}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$, and ${D}^{\ensuremath{'}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}$ states of molecular hydrogen in the energy range from 10 to 300 eV. Total scattering and total ionization cross sections are also presented. The calculations have been performed by using the convergent close-coupling method within the fixed-nuclei approximation. Detailed convergence studies have been performed with respect to the size of the close-coupling expansion and a set of recommended cross sections has been produced. Significant differences with previous calculations are found. Agreement with experiment is mixed, ranging from excellent to poor depending on the transition and incident energies.

We present calculations of vibrationally resolved cross sections for excitation of the , , , , and electronic states of molecular hydrogen. Here we apply the adiabatic nuclei convergent close-coupling method formulated in two-center prolate spheroidal coordinates. We find significant disagreement with previous calculations, where available.

A two-center close-coupling method that includes positronium (Ps) formation channels has been developed for positron scattering on molecular hydrogen. Calculations are performed within the fixed-nuclei approximation. Results for the grand total, Ps-formation, and direct ionization cross sections are presented. In general, good agreement with experiment is seen in all the calculated cross sections.

We have extended the convergent close-coupling method to investigate electron scattering from the vibrationally excited molecular hydrogen ion H${{}_{2}}^{+}$, within the Born-Oppenheimer approximation. Results are presented for proton-production and dissociative-ionization cross sections. The comparison with experiment is excellent across the energy range from near threshold to 1 keV.

An overview is given of the recently developed adiabatic-nuclei convergent closecoupling method for positron-molecule scattering. Fixed-nuclei single-centre calculations of positron-H2 scattering are presented. Particular emphasis is given to demonstrating convergence with increasing size of the basis and the projectile partial-wave expansion. Results are converged to within ±5%.