Fast Padé transform in the theory of resonances: exact solution of the harmonic inversion problem

Belkić, Dževad; Belkić, Karen

doi:10.1088/0953-4075/44/12/125002

Cited by 7 publications

(3 citation statements)

References 20 publications

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“…The cross-sections have been also calculated within the firstorder Born approximation with initial and final wavefunctions verifying CB1. This approach can be interpreted as an extension to the case of the ionization of molecular targets of the CB1 model introduced by Belkić et al [46,47] for studying the electron capture from atomic targets. In order to represent the multi-centered nature of the target (H 2 O molecule in vapor phase), the electronic populations of the target have been described by means of molecular orbitals constructed from a linear combination of atomic orbitals in a selfconsistent field approximation [48].…”

Section: Cb1 Approximationmentioning

confidence: 99%

Double differential distribution of electron emission in the ionization of water molecules by fast bare oxygen ions

Bhattacharjee

Biswas

Bagdia

et al. 2016

J. Phys. B: At. Mol. Opt. Phys.

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The doubly differential distributions of low-energy electron emission in the ionization of water molecules under the impact of fast bare oxygen ions with energy of 48 MeV are measured. The measured data are compared with two quantum-mechanical models, i.e. the post and prior versions of the continuum distorted wave-eikonal initial state (CDW-EIS) approximation, and the first-order Born approximation with initial and final wavefunctions verifying correct boundary conditions (CB1). An overall excellent qualitative agreement is found between the data and the CDW-EIS models whereas the CB1 model showed substantial deviation. However, the detailed angular distributions display some discrepancies with both CDW-EIS models. The single differential and total cross-sections exhibit good agreement with the CDW-EIS models. The present detailed data set could also be used as an input for modeling highly charged ion induced radiation damage in living tissues, whose most abundant component is water. Similar measurements are also carried out for a projectile energy of 60 MeV. However, since the double differential cross-section data show similar results the details are not provided here, except for the total ionization cross-sections results.

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Section: Cb1 Approximationmentioning

confidence: 99%

Double differential distribution of electron emission in the ionization of water molecules by fast bare oxygen ions

Bhattacharjee

Biswas

Bagdia

et al. 2016

J. Phys. B: At. Mol. Opt. Phys.

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“…FT was unable to resolve a number of spectral peaks and, for those resolved, was unable to predict the correct height. Similar observations were made by Belkic et al [18] of FT when employed for quantitation of truncated 1D-NMR data. This, once again, can be observed in Figure 7.3 for the 1 H − 1 H COSY spectrum of HydroxyEthylPiperazine Ethane Sulfonic acid (HEPES).…”

Section: Resultssupporting

confidence: 84%

High-resolution multidimensional parametric estimation for nuclear magnetic resonance spectroscopy

Anjum¹

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<p>Nuclear Magnetic Resonance spectroscopy (NMR) is a powerful technique for rapid and efficient quantitation of compounds in chemical samples. NMR causes the nuclei in the molecules to resonate and various chemical arrangements appear as peaks in the Fourier spectrum of a free induction decay (FID). The spectral parameters elicited from the peaks serve as a fingerprint of the chemical components contained in the molecule. These fingerprints can be employed to understand the chemical structure. Signal acquired from a NMR spectrometer is ideally modelled as a superposition of multiple damped complex exponentials (cisoids) in Additive White Gaussian Noise (AWGN). The number as well as the spectral parameters of the cisoids need to be estimated for characterisation of the underlying chemicals. The estimation, however, suffers from numerous difficulties in practice. These include: unknown number of cisoids, large signal length, large dynamic range, large peak density, and numerous distortions caused by experimental artefacts. This thesis aims at the development of estimators that, in view of the above-mentioned practical features, are capable of rapid, high-resolution and apriori-information-free quantitation of NMR signals. Moreover, for the analytic evaluation of the performance of such estimators, the thesis aims to derive interpretable analytic results for the fundamental estimation theory tool for assessing the performance of an unbiased estimator: the Cramer Rao Lower Bound (CRLB). By such results, we mean those that analytically allow the determination, in terms of the CRLB, of the impact of the free model parameters on the estimator performance. For the CRLB, we report analytic expressions on the variance of unbiased parameter estimates of damping factors, frequencies and complex amplitudes of an arbitrary number of damped cisoids embedded in AWGN. In addition to the CRLB, analytic expressions for the determinant and the condition number of the associated Fisher Information Matrix (FIM) are also reported. Further results, in similar order, are reported for two special cases of the damped cisosid model: the Magnetic Resonance Relaxometry model and the amplitude-only model (employed in quantitative NMR - qNMR). Some auxiliary results for the above-mentioned models are also presented, i.e., on the multiplicity of the eigenvalues and the factorisation of the characteristic polynomial associated with their respective FIMs. These results have not been previously reported. The reported theoretical results successfully account for various physical and chemical phenomena observed in experimental NMR data, and quantify their impact on the accuracy of an unbiased estimator as a function of both model and experimental parameters, e.g., influence of prior knowledge, peak multiplicity, multiplet symmetry, solvent peak, carbon satellites, etc. For rapid, high-resolution and apriori-information-free quantitation of NMR signals, a sub-band Steiglitz-McBride algorithm is reported. The developed algorithm directly converts the time-domain FID data into a table of estimated amplitudes, phases, frequencies and damping factors, without requiring any previous knowledge or pre-processing. A 2D sub-band Steiglitz-McBride algorithm, for the quantitation of 2D NMR data in a similar manner, is also reported. The performance of the developed algorithms is validated by their application to experimental data, which manifests that they outperform the state-of-the-art in terms of speed, resolution and apriori-information-free operation.</p>

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“…We combine the CDW-EIS ionization probabilities with the experimental branching ratios of single to multiple vacancy production. Another possibility might be to combine the IPM with the CDW [30], which has also been used with success for ionization of multielectron targets.…”

Section: Theoretical Modelmentioning

confidence: 99%

Multiple ionization of argon by helium ions

Montanari

Miraglia

2016

J. Phys. B: At. Mol. Opt. Phys.

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We apply the continuum distorted-wave eikonal initial state and the independent electron model to describe the multiple ionization of Ar by He2+ and He+ in the energy range 0.1–10 Mev amu–1. Auger-like post collisional processes are included, which enhance the high energy multiple ionization cross sections via ionization of the inner shells. All Ar electrons (K, L and M-shells) have been included in these calculations. The results agree well with the experimental data at high energies, where the post-collisional ionization is the main contribution. At intermediate impact energies the description is also good though it tends to overestimate the triple and quadruple ionization data at intermediate energies. We analyze this by comparing the present results for He+2 in Ar, with previous ones for He+2 in Ne and Kr. It was found that the theoretical description improves from Ne to Ar and Kr, with the latter being nicely described even at intermediate energies. The present formalism is also tested for Ar inner shell and total ionization cross sections. In all the cases the results above 0.1 MeV amu–1 are quite reasonable, as compared with the experimental data available and with the ECPSSR values.

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Fast Padé transform in the theory of resonances: exact solution of the harmonic inversion problem

Cited by 7 publications

References 20 publications

Double differential distribution of electron emission in the ionization of water molecules by fast bare oxygen ions

Double differential distribution of electron emission in the ionization of water molecules by fast bare oxygen ions

High-resolution multidimensional parametric estimation for nuclear magnetic resonance spectroscopy

Multiple ionization of argon by helium ions

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