Applications of<i>B</i>-splines in atomic and molecular physics

Bachau, H.; Cormier, Éric; Decleva, P.; Hansen, J E; Martín, Fernando

doi:10.1088/0034-4885/64/12/205

Cited by 669 publications

(648 citation statements)

References 505 publications

(803 reference statements)

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“…If there are n B-Spline basis functions of the order k, the total number of knot points is n+k. B-Spline function is a powerful tool for fitting a smooth function [22], and it has been widely used in computational physics. Figure 1 shows an example where the input smooth function is accurately reconstructed by seven B-spline basis functions, by optimizing the knot points and the expansion coefficients.…”

Section: B Expanding Unknown Functions Using B-splinementioning

confidence: 99%

“…The IR phase and/or amplitude can be assumed to be known or unknown depending on the nature of the measurement. We chose to expand the unknown amplitude and/or phase of the XUV and the IR fields in terms of the so-called B-spline basis functions [22]. Such expansions are commonly used in representing a smooth function with minimum number of unknowns.…”

Section: Introductionmentioning

confidence: 99%

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Phase-retrieval algorithm for the characterization of broadband single attosecond pulses

Xi-nan

Hui

et al. 2017

Phys. Rev. A

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Recent progress in high-order harmonic generation with few-cycle mid-infrared wavelength lasers has pushed light pulses into the water window region and beyond. These pulses have the bandwidth to support single attosecond pulses down to a few tens of attoseconds. However, the present available techniques for attosecond pulse measurement are not applicable to such pulses. Here we report a phase-retrieval method using the standard photoelectron streaking technique where an attosecond pulse is converted into its electron replica through photoionization of atoms in the presence of a time-delayed infrared laser. The iterative algorithm allows accurate reconstruction of the spectral phase of light pulses, from the extreme-ultraviolet (XUV) to soft X-rays, with pulse durations from hundreds down to a few tens of attoseconds. At the same time, the streaking laser fields, including short pulses that span a few octaves, can also be accurately retrieved. Such well-characterized single attosecond pulses in the XUV to the soft X-ray region are required for time-resolved probing of inner-shell electronic dynamics of matter at their own timescale of a few tens of attoseconds.

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Section: B Expanding Unknown Functions Using B-splinementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Phase-retrieval algorithm for the characterization of broadband single attosecond pulses

Xi-nan

Hui

et al. 2017

Phys. Rev. A

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“…In order to calculate vibrationally-resolved cross sections, we have evaluated (bound and continuum) electronic wave functions using the static-exchange and the time-dependent DFT methods [4], developed by Decleva and colla borators, for different molecular geometries along the totally symmetric stretching mode. This mode is the most affected by the structural rearrangement accompanying core ionization [1,2].…”

Section: Synopsismentioning

confidence: 99%

Vibrationally Resolved B 1s Photoionization Cross Section of BF₃

et al. 2015

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SynopsisWe present a study of the vibrationally resolved B 1s photoionization cross section of the BF 3 mo lecule. A co mb ination of h igh-resolution photoelectron spectroscopy measurements and of state-of-the-art calcu lations shows the evolution of the photon energy dependence of the cross section from a co mplete trapping of the photoelectron wave (lo w energ ies) to oscillat ions due to intramolecular scattering [1,2]. These diffract ion pa tterns allow to access structural information of both the neutral mo lecule and the core -hole species generated upon photoabsoption [3].The advent of third-generation synchrotron radiation facilities, in combination with high energy-resolution detection techniques , has opened the way for the investigation of vibrationally-resolved inner-shell photoionization in small molecules, where an electron is emitted from a 1s orbital of a first-row atom. We present a study on B 1s photoionization of BF 3 , comparing experimental results with full firstprinciple calculations and showing that the most relevant features can be understood by means of simple models.In order to calculate vibrationally-resolved cross sections, we have evaluated (bound and continuum) electronic wave functions using the static-exchange and the time-dependent DFT methods [4], developed by Decleva and colla borators, for different molecular geometries along the totally symmetric stretching mode. This mode is the most affected by the structural rearrangement accompanying core ionization [1,2]. Our theoretical results are in good agreement with experimental measurements from SOLEIL synchrotron and, at high energies, qualitatively agree with a first-Born approximation model.We have found that the relative cross sections show clear oscillations in the high-energy region as a function of photoelectron mome ntum which are due to an intramolecular scattering mechanism: in its way out of the molecule, the photoelectron is diffracted by the surrounding atomic centers, encoding the geometry of the molecule [1,2,3]. Very close to the photoionization threshold a complete trapping of the photoelectron is observed, manifesting itself as an emission angle dependent shape resonance feature [1,2].

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“…The cases of stationary and time-dependent theories are discussed separately. For the former, interested readers are referred to two review articles [12,13].…”

Section: Summary Of Existing Theoriesmentioning

confidence: 99%

“…In this approximation, the positions of the two nuclei are fixed and, therefore, only electronic degrees of freedom are considered. Currently, the fixed-nuclei approximation, very often in combination with density functional theory for the description of the electronic continuum, provides a practical framework to study ionization of polyatomic molecules (see [13][14][15] and references therein). This is a reasonable approximation when one is not interested in the vibrational analysis of a molecular property (e.g., to evaluate total photoabsorption rates or total electron yields).…”

Section: Summary Of Existing Theoriesmentioning

confidence: 99%

Molecular ionization and dissociation using synchrotron radiation and ultrashort laser pulses

Martín¹

2007

J. Phys.: Conf. Ser.

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Abstract. An overview of recent theoretical progress to accurately describe non dissociative and dissociative ionization of molecules exposed to synchrotron radiation and ultrashort uv/xuv laser pulses is presented. The success of recent theoretical approaches rely on their ability to account for both the electronic and nuclear degrees of freedom. This is essential to describe the delicate interplay between the electronic motion and the molecule's vibration, especially in those cases where ionization occurs in a time scale comparable to that of the vibrational motion. Some of the most successful applications and the new physics that has emerged by comparing with recent kinematically complete experiments on H2 and D2 will be discussed. IntroductionMolecular ionization is one of the most elementary processes that occurs in the upper atmosphere [1] and in interstellar molecular clouds [2]. Since in molecules the absorbed energy is shared between electronic and nuclear degrees of freedom, the remaining molecular ion can be left in an excited vibrational or dissociative state. This is at variance with atomic ionization where the energy is entirely absorbed by the electrons. In early pictures of molecular ionization, the nuclear motion was either ignored or described in terms of the Franck-Condon (FC) approximation, in which electronic processes occurring at the equilibrium position of the nuclei are weighted by the squared overlap between the initial and final vibrational states. With the advent of kinematically complete experiments [3,4], in which the momenta of all charged particles is determined, new phenomena with an intrinsic molecular origin have been discovered (see, e.g., [5][6][7][8][9][10][11]). Also the above pictures have been revealed to be incomplete. In this manuscript, the important role of nuclear dynamics in molecular ionization produced by synchrotron radiation and ultrashort pulses will be demonstrated by means of recent ab initio theoretical calculations that account for all electronic and vibrational degrees of freedom.In particular, recent results for electron angular distributions from fixed-in-space molecules will be analyzed and compared with kinematically complete photoionization experiments using synchrotron radiation. These include double and single photoionization of H 2 (D 2 ). The range of excess photon energies considered goes from a few to several hundreds of eV. Also, multiphoton ionization of molecules by vuv ultrashort pulses will be discussed. In particular, the new physics that can be expected by varying pulse duration and intensity will be analyzed.

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Applications ofB-splines in atomic and molecular physics

Cited by 669 publications

References 505 publications

Phase-retrieval algorithm for the characterization of broadband single attosecond pulses

Phase-retrieval algorithm for the characterization of broadband single attosecond pulses

Vibrationally Resolved B 1s Photoionization Cross Section of BF₃

Molecular ionization and dissociation using synchrotron radiation and ultrashort laser pulses

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Applications ofB-splines in atomic and molecular physics

Cited by 669 publications

References 505 publications

Phase-retrieval algorithm for the characterization of broadband single attosecond pulses

Phase-retrieval algorithm for the characterization of broadband single attosecond pulses

Vibrationally Resolved B 1s Photoionization Cross Section of BF3

Molecular ionization and dissociation using synchrotron radiation and ultrashort laser pulses

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Vibrationally Resolved B 1s Photoionization Cross Section of BF₃