We present a computational and theoretical framework for solving the Schrodinger equation (SE) for the two-center Coulomb problem in prolate spheroidal coordinates when the energy of the SE is positive. A general and robust computer code has been produced that calculates the separation constants, spheroidal harmonic expansion coefficients, regular quasi-radial two-center Coulomb wave functions, and two- center Coulomb phase shifts. These quantities can be calculated over a range of internuclear separations, angular momentum projections, and continuum electron momenta. A representative set of results are presented and compared with previous calculations, excellent agreement is found in many cases while significant disagreements are found in others. Program summary Program title: spheroidal-cw CPC Library link to program files: https://doi .org /10 .17632 /nf5gw7vjnh .1 Code Ocean capsule: https://codeocean .com /capsule /7638744 Licensing provisions: MIT Programming language: Fortran 90 Nature of problem: A robust and accurate computer code for calculating Coulomb wave functions in prolate spheroidal coordinate is necessary for the calculation of cross sections for photonionization, and electron and positron scattering on charged diatomic targets. Solution method: The angular solution is expanded in a series of spherical harmonics leading to the diagonalization of a pentadiagonal matrix. The eigenvectors contain the expansion coefficients and the eigenvalues are the separation constants which, unlike the SE in spherical coordinates, are also functions of the energy. The radial two-center Coulomb wave functions are started using a power series solution and then propagated using a linear multistep method. An asymptotic expansion is used to calculate the two-center Coulomb phase shift, and to normalize the radial wave function. Additional comments including restrictions and unusual features: Two-center Coulomb radial wave functions and phase shifts can be accurately calculated for internuclear separations from 0.001 to 60.0 a0, angular momentum projection |m| from 0 to 44, momentum k from 0.01 to 100.0 a.u., and a combined nuclear charge Z(+ )from 1 to 12. (C) 2022 Elsevier B.V. All rights reserved.

We use the adiabatic-nuclei molecular convergent close-coupling method to perform calculations of 0.01--1000 eV electrons scattering on the $c^{3}\mathrm{\ensuremath{\Pi}}_{u}$, $a^{3}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$, $B^{1}\mathrm{\ensuremath{\Sigma}}_{u}^{+}$, $C^{1}\mathrm{\ensuremath{\Pi}}_{u}$, and $EF^{1}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$ states of ${\mathrm{H}}_{2}$ in the $v=0$ vibrational level. Elastic, superelastic, ionization, and grand-total cross sections are presented, as well as cross sections for excitation of the $n=2$--3 singlet and triplet states of ${\mathrm{H}}_{2}$ (where $n$ is the atomic-limit principle quantum number). Comparison with available theoretical results is made. Good agreement is found with the recent $R$-matrix results [J. Phys. B 53, 245203 (2020)] for most of the exchange and dipole-forbidden transitions, but not for the dipole-allowed transitions. The sources of disagreement were found to be an unconverged partial-wave expansion and the utilization of the fixed-nuclei approximation (as opposed to adiabatic-nuclei) in the $R$-matrix calculations.

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.

The feasibility of producing the molecular antihydrogen anion (H) over bar (-)(2) in the laboratory is investigated. Utilizing reaction rates calculated here involving the interaction of laser excited-state antihydrogen atoms held in magnetic minimum traps, key processes are identified that could lead to anion production, as well as competing effects leading to anti-atom loss. These are discussed in the context of present-day and near-future experimental capabilities.

Vibrational excitations of H-2(X (1)Sigma(+)(g), nu(i) = 0 - 14) are investigated via the electron-impact excitation of the B E-1(u)+, C (1)Pi(u), B' E-1(u)+, D (1)Pi(u,) and E, F (1)Sigma(+)(g) states followed by radiative cascade to the vibrational bound and free (continuum) levels of the electronic ground state. The adiabatic-nuclei convergent close-coupling formalism is utilized to calculate cross sections from threshold to 500 eV. Results are in qualitative agreement with previous calculations, however absolute values differ significantly.

Figure 1: Cross sections for excitation of the bound (top) and dissociative (bottom) vibrational levels of the H2 X Σg state following electronic excitation and radiative decay. Electron-impact excitation of the singlet states of H2 will either lead to dissociation through the excited singlet spectrum, or radiative decays to the vibrational levels of the ground electronic state. Decays to bound levels are one of the dominant processes by which vibrationally-excited H2 is formed in plasmas, which is of considerable importance as excitation cross sections depend strongly on the initial vibrational state of the molecule. Cascades to continuum levels, on the other hand, are an important process for dissociation of H2. As with many vibrationally-dependent processes in e-H2 scattering, the previously available theoretical data has been almost entirely produced using the impact-parameter method, which is known to be inaccurate except at high incident energies [1]. The present calculations [2], which have been performed using the adiabatic-nuclei convergent closecoupling method, are a significant improvement in accuracy over the previous theoretical data. In Fig. 1 we present the cross sections for electron-impact excitation and radiative decay to the bound and continuum (dissociative) vibrational levels from all vi = 0–14 initial vibrational levels of H2. There is a strong dependence on the initial vibrational state, particularly for the decays leading to dissociation, where there is a significant enhancement in the cross section for scattering on the higher levels.

Above the threshold for excitation of the electronic singlet manifold, the dominant mechanism for exciting vibrational levels in the ground electronic state is electronic excitation followed by radiative cascade. Calculations of these processes require a fully vibrationally resolved description of the scattering problem, with an accurate account of electronic channel coupling over a large range of internuclear separations. Previous calculations are limited to those performed using the semi-classical impact-parameter method [3], which is known to yield cross sections up to two times larger than convergent close-coupling (CCC) results for electronic excitation [4]. Using a spheroidal-coordinate formulation of the molecular CCC method, we have performed fully quantum-mechanical calculations of excitation-radiative decay (ERD) leading to vibrational excitation of H2, over the range of energies from 10 to 300 eV.

We present convergent close-coupling (CCC) calculations of electron-impact dissociation of vibrationally-excited molecular hydrogen into neutral fragments. This work follows from our previous results for dissociation of molecular hydrogen in the ground vibrational level [Scarlett et al., Eur. Phys. J. D 72, 34 (2018)], which were obtained from calculations performed in a spherical coordinate system. The present calculations, performed utilizing a spheroidal formulation of the molecular CCC method, reproduce the previous dissociation cross sections for the ground vibrational level, while allowing the extension to scattering on excited levels.

Submitted for the GEC19 Meeting of The American Physical Society Towards a self-consistent approach to model cool hydrogen plasma emission MARK ZAMMIT, JAMES COLGAN, Los Alamos National Laboratory, JEREMY SAVAGE, DMITRY FURSA, IGOR BRAY, Curtin University, CHRISTOPHER FONTES, DAVID KILCREASE, PETER HAKEL, JEFFERY LEIDING, EDDY TIMMERMANS, Los Alamos National Laboratory — Cool (molecular) plasmas are ubiquitous throughout the Universe. As far as we are aware, all opacity and emissivity studies of molecular plasmas are conducted utilizing data or codes taken from several different sources. To this end, we are developing a fully generalizable self-consistent approach to model cool hydrogen (H2 and H + 2 ) plasmas opacity and emissivity. Here we present results of cool hydrogen plasmas emission, and a preliminary investigation of the plasma effects in low-temperature hydrogen plasmas using an equation of state model. Mark Zammit Los Alamos National Laboratory Date submitted: 03 Jun 2019 Electronic form version 1.4

We present time-of-flight differential cross-section measurements and convergent close-coupling calculations of differential cross sections for the electron-impact excitation of the X- 1 Sigma(+)(g) -> b (3)Sigma(+)(u) transition in molecular hydrogen. A part of this work was recently published [M. Zawadzki et al., Phys. Rev. A 97, 050702(R) (2018)]. In this work, agreement between theory and experiment is excellent overall, and marks a transition in electron-molecule scattering where differential scattering of excitation is found to be in such precise agreement. We also present total electron-impact excitation differential cross sections for H-2 for which agreement between theory and experiment is found to be excellent.

We present calculations of vibrationally resolved cross sections for excitation of the B (1)Sigma(+)(u), C (1)Pi(u), B' (1)Sigma(+)(u), D (1)Pi(u), and E, F (1)Sigma(+)(g) 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.

We report cross sections for electron-impact dissociative excitation of the B-1 Sigma(+)(u), C-1 Pi(u), D-1 Pi(u), B'(1)Sigma(+)(u) and E,F-1 Sigma(+)(g) singlet states of molecular hydrogen from all nu(i) = 0-14 vibrational levels of the ground X-1 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.

The electron impact X-1 sigma(+)(g) -> b(3) sigma(+)(u) transition in molecular hydrogen is one of the most important dissociation pathways to forming atomic hydrogen atoms, and is of great importance in modeling astrophysical and industrial plasmas where molecular hydrogen is a substantial constituent. Recently, it has been found that the convergent close-coupling (CCC) cross sections of Zammit et al. [Phys. Rev. A. 95, 022708 (2017)] are up to a factor of 2 smaller than the currently recommended data. We have determined normalized differential cross sections for excitation of this transition from our experimental ratios of the inelastic to elastic scattering of electrons by molecular hydrogen using a transmission-free time-of-flight electron spectrometer, and find excellent agreement with the CCC calculations. Since there is already excellent agreement for the absolute elastic differential cross sections, we establish benchmark differential and integrated cross sections for the X-1 sigma(+)(g) -> b(3)sigma(+)(u) transition, with theory and experiment being essentially in complete agreement.

We present convergent close-coupling calculations of electron-impact dissociation of the ground state of molecular hydrogen into neutral fragments over the range of impact energies from 6 to 300 eV. The calculations account for dissociative excitation, excitation radiative decay dissociation, and predissociation through all bound electronic triplet states, and singlet states up to the D′ 1Πu state. An estimate is given for the contribution from the remaining bound electronic singlet states. Our results are in agreement with the recommended data of Yoon et al. [J. Phys. Chem. Ref. Data 37, 913 (2008)] in the low (6–12 eV) and high (60–70 eV) energy regions, but somewhat lower at the intermediate energies.

M. Zawadzki,1 R. Wright,2 G. Dolmat,2 M. F. Martin,2 L. Hargreaves,2 D. V. Fursa,3 M. C. Zammit,4 L. H. Scarlett,3 J. K. Tapley,3 J. S. Savage,3 I. Bray,3 and M. A. Khakoo2,* 1Atomic Physics Division, Department of Atomic, Molecular, and Optical Physics, Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland 2Department of Physics, California State University, Fullerton, California 92831, USA 3Curtin Institute for Computation and Department of Physics, Astronomy and Medical Radiation Sciences, Curtin University, Perth, Western Australia 6102, Australia 4Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

The calculation of hot planetary atmosphere-like opacities are of fundamental importance in the modeling of radiation transport, energy deposition, heating rates, and hydrodynamic simulations. We summarize the Los Alamos National Laboratory molecular opacity efforts in these research areas, and introduce new codes currently under development to calculate molecular opacities. We also present some preliminary results of one of these codes, and investigate the isotopic effects of H-2(+) and its isotopologue D-2(+) We find a large isotopic effect for the state-resolved photodissociation (PD) cross sections and the LTE-averaged PD cross section at low material temperatures. Below the material temperature of T-mat approximate to 2000 K, we show that isotopic effects should be taken into account to obtain LTE-averaged PD cross sections accurate to better than approximate to 10-20%.