Martin Plummer

R-matrix calculations of low-energy electron collisions with methane

R-matrix calculations are performed for electron collision with CH4 at energies between 0.02 and 15 eV using a series of different ab initio models for both the target and the full scattering system. A target model similar to the standard multi-reference configuration interaction used in electronic structure calculations is found to give the best results. Results are presented for elastic scattering, with particular emphasis on the Ramsauer–Townsend miminum, and for rotational excitation, momentum transfer and electron impact dissociation. Extensive comparisons are made with previous studies.

The importance of an accurate target wavefunction in variational calculations for (e+–H2) scattering

Using the complex Kohn method, we have calculated variational values of phase shifts and the annihilation parameter, Zeff, for the elastic scattering of positrons by molecular hydrogen. Our results are sensitive to small changes in the accuracy of the wavefunction representing the target hydrogen molecule. We have developed a systematic approach to demonstrate that, at low positron energies, there are particular forms of the Kohn trial wavefunction for which the results of variational calculations are not reliable, even when the target wavefunction accounts for as much as 96.8% of the correlation energy of H2. We find that reliable results can be recovered if our calculations are extended to admit more sophisticated target wavefunctions accounting for 99.7% of the correlation energy. Remaining discrepancies between theory and experiment are briefly discussed.

Low-energy behaviour of e?O scattering calculations

We report on calculations of low-energy e–O scattering using the R-matrix method. We compare cross sections for elastic scattering and excitation with experiment and recent theoretical values. We calculate elastic cross sections for the 3Pe ground state and cross sections for excitation to and between the 1De and 1Se states. We present detailed comparisons of elastic differential cross sections with experiment. We compare our approach using orthogonal orbitals with an approach using non-orthogonal orbitals. We investigate noticeable differences in results from different calculations towards the low-energy limit. We discuss the use of long-range polarization pseudostates and issues of convergence of results for an open-shell neutral atom for which exact target states are not available.

Mapping application performance to HPC architecture

Abstract A suite of application benchmarks, designed to be broadly representative of UK HPC usage, has been developed to stress a broad range of architectural features of large scale parallel HPC resources. A generic methodology to investigate application performance and scaling characteristics has been defined, resulting in a detailed understanding of the performance of these applications. This methodology is transferable to other applications and systems: it is of practical value to developers and users who are aiming for optimal utilisation of HPC resources. An understanding of the performance characteristics of a range of large-scale HPC resources has been obtained using low-level synthetic benchmarks. A relatively simple, qualitative mechanism to assess and predict application performance on current and future architectures using synthetic benchmark results together with application performance analysis results is explored.

Terascale materials modelling on high performance system HPCx

We describe the HPCx UoE Ltd national computing resource HPCx Phase 2 as used in 2004 and 2005. We describe the work of the HPCx ‘terascaling team’ and how this work in collaboration with scientists and code developers allows for efficient exploitation of large-scale computational resources to produce new science as described in the rest of this volume. We emphasize the need for scientists and code developers to have an understanding of the peculiarities of the national and international facilities they use to generate their data. We give some examples of successful application code optimization in materials chemistry on HPCx. We introduce HPCx Phase 2A which entered service in November 2005.

Helium–antihydrogen scattering at low energies

We calculate cross sections for helium-antihydrogen scattering for energies up to 0.01 atomic unit. Our calculation includes elastic scattering, direct antiproton-alpha particle annihilation and rearrangement into He + ¯ p and ground- state positronium. Elastic scattering is calculated within the Born-Oppenheimer approximation using the potential calculated by Strasburger et al (2005 J. Phys. B: At. Mol. Opt. Phys. 38 3091). Matrix elements for rearrangement are calculated using the T-matrix in the distorted wave approximation, with the initial state represented by Hylleraas-type functions. The strong force, leading to direct annihilation, was included as a short-range boundary condition in terms of the strong-force scattering length.

Anomaly-free singularities in the generalized Kohn variational method

We have carried out an analysis of singularities in Kohn variational calculations for low-energy (e+–H2) elastic scattering. Provided that a sufficiently accurate trial wavefunction is used, we argue that our implementation of the Kohn variational principle necessarily gives rise to singularities which are not spurious. We propose two approaches for optimizing a free parameter of the trial wavefunction in order to avoid anomalous behavior in scattering phase shift calculations, the first of which is based on the existence of such singularities. The second approach is a more conventional optimization of the generalized Kohn method. Close agreement is observed between the results of the two optimization schemes; further, they give results which are seen to be effectively equivalent to those obtained with the complex Kohn method. The advantage of the first optimization scheme is that it does not require an explicit solution of the Kohn equations to be found. We give examples of anomalies which cannot be avoided using either optimization scheme but show that it is possible to avoid these anomalies by considering variations in the nonlinear parameters of the trial function.

Low‐energy scattering of antihydrogen by helium and molecular hydrogen

In this paper, we describe in detail calculations that we have carried out of cross sections for rearrangement processes in very low‐energy helium+antihydrogen (H) scattering that result in He+p+Ps or Hep+e+ or αp+Ps−. The interaction between the leptons is taken into account very accurately. Results are presented for all three processes. A description is also given of a preliminary calculation of elastic and antiproton annihilation cross sections for very low‐energy H2+H scattering.

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)

Calculation of the resonant contribution to using close-coupled equations for positron–molecule scattering

In a previous paper (2010 Phys. Rev. A 82 042702; 2014 Phys. Rev. A 89 069901(E)), one of us (EAGA) calculated the resonant contribution to , the effective number of electrons available for annihilation by a positron with wave number k 0, in the scattering of a heavy positron by H2. The mass of the positron was increased just sufficiently for a bound state to occur. This calculation was carried out using the Kohn variational method. An alternative method is to use the close-coupled equations for the system under consideration. We compare our results with those obtained by Gribakin and Lee (2006 Phys. Rev. Lett. 97 193201). There is a resonant contribution to from the vibrationally excited quasibound state which may be described by a Breit–Wigner resonance formula arising naturally from the close-coupling analysis if a certain additional assumption is made. There is also a separate resonant contribution to from the open channel function influenced by the quasibound state, and a cross term. It is shown that the contribution from the quasibound state is very similar to the expression for the resonant contribution obtained by Gribakin and Lee. Comparison is made with other treatments, for example, the close-coupling calculation of Nishimura and Gianturco (2003 Phys. Rev. Lett. 90 183201).