Duncan A Little

An ab initio study of singlet and triplet Rydberg states of N2

Potential energy curves for electronically excited states of molecular nitrogen are calculated using three different ab initio procedures. The most comprehensive of these involves the use of scattering calculations, performed at negative energy using the UK molecular R-matrix method. Such calculations are used to characterize all the Rydberg states of N2 with n ⩽ 6 and l ⩽ 4 as well as many higher states including some Rydberg states associated with the first excited A 2Πu state of N. Many of these states are previously unknown. The calculations are performed at a dense grid of internuclear separations allowing the many avoided crossings present in the system to be mapped out in detail. Extensive comparisons are made with the previously available data for excited states of N2.

Electron-impact resonant vibrational excitation and dissociation processes involving vibrationally excited N-2 molecules

Resonant vibrational excitation cross sections and the corresponding rate coefficients for electron–N2 collisions occurring through the resonant state are reviewed. New calculations are performed using accurate potential energy curves for the N2 electronic ground state, taken from the literature, and for the resonant state, obtained from R-matrix calculations. The calculations are extended to resonant excitation processes involving the N2 ground state vibrational continuum, leading to dissociation. Electron-impact dissociation is found to be significant from higher vibrational levels. Accurate analytical fits for the complete set of the rate coefficients are provided. The behavior of the dissociative cross sections is investigated for rotationally excited N2 molecules, with J = 50, 100 and 150, and for different vibrational levels.

An R-matrix study of singlet and triplet continuum states of N2

A systematic calculation of the positions and widths of the resonances converging on the first two excited states of N (A and B ) is presented. A closely-spaced grid of geometries is used to give continuous resonance curves without the need for curve fitting. Three methods, fitting the eigenphase sum, the time-delay method and the R-matrix specific QB method, are tested. Fits to the longest three time-delays are found to give the most reliable and complete determination of the resonance parameters. The low excitation energies of the A and B ion states results in complex resonance features with many avoided crossings leading to pronounced structures in both the resonance curves and the associated widths. The resonance curves likely to be important for dissociative recombination are identified. Their positions generally agree well with the calculations of Guberman, although in some cases their widths are narrower. Full data on all curves is provided.

Low-energy collisions between electrons and BeH+: Cross sections and rate coefficients for all the vibrational states of the ion

Abstract We provide cross sections and Maxwell rate coefficients for reactive collisions of slow electrons with BeH + ions on all the eighteen vibrational levels ( X 1 Σ + , v i + = 0 , 1 , 2 , … , 17 ) using a Multichannel Quantum Defect Theory (MQDT)—type approach. These data on dissociative recombination, vibrational excitation and vibrational de-excitation are relevant for magnetic confinement fusion edge plasma modeling and spectroscopy, in devices with beryllium based main chamber materials, such as the International Thermonuclear Experimental Reactor (ITER) and the Joint European Torus (JET). Our results are presented in graphical form and as fitted analytical functions, the parameters of which are organized in tables.

Theoretical study of ArH+ dissociative recombination and electron-impact vibrational excitation

Cross sections are presented for dissociative recombination and electron-impact vibrational excitation of the ArH+ molecular ion at electron energies appropriate for the interstellar environment. The R-matrix method is employed to determine the molecular structure data, i.e. the position and width of the resonance states. The cross sections and the corresponding Maxwellian rate coefficients are computed using a method based on the Multichannel Quantum Defect Theory. The main result of the paper is the very low dissociative recombination rate found at temperatures below 1000K. This is in agreement with the previous upper limit measurement in merged beams and offers a realistic explanation to the presence of ArH+ in exotic interstellar conditions.

Multiple core hole formation by free-electron laser radiation in molecular nitrogen

We investigate the formation of multiple-core-hole states of molecular nitrogen interacting with a free-electron laser pulse. We obtain bound and continuum molecular orbitals in the single-center expansion scheme and use these orbitals to calculate photo-ionization and Auger decay rates. Using these rates, we compute the atomic ion yields generated in this interaction. We track the population of all states throughout this interaction and compute the proportion of the population which accesses different core-hole states. We also investigate the pulse parameters that favor the formation of these core-hole states for 525 eV and 1100 eV photons.

Interaction of molecular nitrogen with free-electron-laser radiation

We compute molecular continuum orbitals in the single center expansion scheme. We then employ these orbitals to obtain molecular Auger rates and single-photon ionization cross sections to study the interaction of N2 with Free-Electron-Laser (FEL) pulses. The nuclei are kept fixed. We formulate rate equations for the energetically allowed molecular and atomic transitions and we account for dissociation through additional terms in the rate equations. Solving these equations for different parameters of the FEL pulse, allows us to identify the most efficient parameters of the FEL pulse for obtaining the highest contribution of double core hole states (DCH) in the final atomic ion fragments. Finally we identify the contribution of DCH states in the electron spectra and show that the DCH state contribution is more easily identified in the photo-ionization rather than the Auger transitions.

TIMEDELn: A programme for the detection and parametrization of overlapping resonances using the time-delay method

Abstract TIMEDELn implements the time-delay method of determining resonance parameters from the characteristic Lorentzian form displayed by the largest eigenvalues of the time-delay matrix. TIMEDELn constructs the time-delay matrix from input K-matrices and analyses its eigenvalues. This new version implements multi-resonance fitting and may be run serially or as a high performance parallel code with three levels of parallelism. TIMEDELn takes K-matrices from a scattering calculation, either read from a file or calculated on a dynamically adjusted grid, and calculates the time-delay matrix. This is then diagonalized, with the largest eigenvalue representing the longest time-delay experienced by the scattering particle. A resonance shows up as a characteristic Lorentzian form in the time-delay: the programme searches the time-delay eigenvalues for maxima and traces resonances when they pass through different eigenvalues, separating overlapping resonances. It also performs the fitting of the calculated data to the Lorentzian form and outputs resonance positions and widths. Any remaining overlapping resonances can be fitted jointly. The branching ratios of decay into the open channels can also be found. The programme may be run serially or in parallel with three levels of parallelism. The parallel code modules are abstracted from the main physics code and can be used independently. New version programme summary Programme Title: TIMEDELn Programme Files doi: http://dx.doi.org/10.17632/wmv4f42xnz.1 Licencing provisions: MIT Programming language: FORTRAN Journal reference of previous version: Computer Phys. Comms. , 114 , 236–242 (1998). Does the new version supersede the previous version?: Yes Nature of problem: TIMEDELn detects and parametrizes resonances, including overlapping resonances when provided with the K-matrix of the scattering problem. Solution method: Resonances are identified by peaks in the largest few eigenvalues of the time-delay matrix. Reasons for the new version: TIMEDELn includes a new procedure for fitting multiple overlapping resonances. It has also been parallelized to allow studies of complex systems (atoms and molecules) and generation of bulk data. Summary of revisions: TIMEDELn analyses the largest eigenvalues of the time-delay matrix and identifies those with resonance features which are then separated and fitted [6]. It has been modularized with calls to external libraries and user supplied routines abstracted for ease of modification. It has been parallelized, with a choice of a specific module allowing multi-level parallel structures or serial execution if preferred. It can run bulk simulations of ‘similar but different’ calculations (for example, varying fixed-nuclear geometries). Restrictions: When ‘target’ energies are calculated or supplied, the energy of the incident particle (electron) is currently defined with respect to the lowest supplied target energy (the ground state), although an expert user or developer would be able to modify this. Unusual features: TIMEDELn can be run from a user-supplied file for K-matrices or can be implemented to generate these as required. External routines/libraries: Lapack [1], Minpack [2], options for alternatives (e.g. NAG [3]), option for MPI [4] Additional comments: TIMEDELn has been implemented as part of the UKRMol suite of codes [7]. [1] E. Anderson et al., LAPACK Users’ Guide, third edition, (Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1999) http://www.netlib.org/lapack/ [2] LMDIF1 and dependencies, MINPACK Fortran numerical library (University of Chicago, Argonne National Laboratory, USA, 1999), http://www.netlib.org/minpack/ [3] NAG Fortran Library Mark 25 (Numerical Algorithms Group, Oxford, UK, 2015), http://www.nag.co.uk/numeric/fl/FLdescription.asp/ [4] The Message Passing Interface, standards for MPI are available from the MPI Forum, http://www.mpi-forum.org/ [5] D.T. Stibbe and J. Tennyson, Computer Phys. Comms. , 114 , 236–242 (1998). [6] D.A. Little and J. Tennyson, J. Phys. B: At. Mol. Opt. Phys. , 47 , 105204 (2014). [7] J.M. Carr, P.G. Galiatsatos, J.D. Gorfinkiel, A.G. Harvey, M.A. Lysaght, D. Madden, Z. Masin, M. Plummer, J. Tennyson, H.N. Varambhia, Eur. Phys. J. D , 66 , 58 (2012)