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

Abstract

TIMEDEL implements the time-delay method of determining resonance parameters from the characteristic Lorentzian form displayed by the largest eigenvalues of the time-delay matrix. TIMEDEL constructs the time-delay matrix from input K-matrices and analyses its eigenvalues. This new version implements multiresonance fitting and may be run serially or as a high performance parallel code with three levels of parallelism. TIMEDEL 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 timedelay: the program 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. Resonances are identified by peaks in the largest few eigenvalues of the time-delay matrix. Reasons for the new version:2 TIMEDEL 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:TIMEDEL 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:TIMEDEL can be run from a user-supplied file for K-matrices or can be implemented to generate these as required. Additional comments:TIMEDEL has been implemented as part of the UKRMol suite of codes [7]. Running time:The actual time spent in TIMEDEL is short: however adaptive grid run times are dominated by the job-dependent time taken to generate the K-matrices (in user supplied routines). The parallelization framework over related calculations, energy sub-ranges and K-matrix generation compensates for this.

UKRmol+: A suite for modelling electronic processes in molecules interacting with electrons, positrons and photons using the R-matrix method

“…Another way of determining the energy and width of resonances is by fitting the largest eigenvalues of the time-delay matrix. TIMEDEL [64] (and it's parallel implementation TIMEDELn [65], not distributed with the UKRmol+ suite, but available for download) can either use existing K-matrices or call RSOLVE to calculate K-matrices for an adaptive energy grid in order to calculate time-delays (an alternative version of a couple of subroutines is provided with the UKRmol-out suite for use with TIMEDELn for this purpose). Finally, for ionic targets the K-matrices generated can be fed into MCQD [66] which computes (complex) multichannel quantum defects at each threshold in the calculation.…”

UKRmol+: a suite for modelling of electronic processes in molecules interacting with electrons, positrons and photons using the R-matrix method

“…Another way of determining the energy and width of resonances is by fitting the largest eigenvalues of the time-delay matrix. TIMEDEL [62] (and it's parallel implementation TIMEDELn [63], not distributed with the UKRmol+ suite, but available for download) can either use existing K-matrices or call RSOLVE to calculate K-matrices for an adaptive energy grid in order to calculate time-delays (an alternative version of a couple of subroutines is provided with the UKRmol-out suite for use with TIMEDELn for this purpose). Finally, for ionic targets the K-matrices generated can be fed into MCQD [64] which computes (complex) multichannel quantum defects at each threshold in the calculation.…”

reskit: A toolkit to determine the poles of an S-matrix

“…This technique is particularly effective for overlapping resonances. Computational implementations of the technique are available [8,9]. We note that a number of approaches, not based on scattering methods, have been developed for the identification of resonances.…”