Paul-Antoine Hervieux - Academia.edu (original) (raw)
Papers by Paul-Antoine Hervieux
Physical Review A, Sep 2, 2014
We present experimental and theoretical results on single-and multiple-electron capture, and frag... more We present experimental and theoretical results on single-and multiple-electron capture, and fragmentation, in C 6+ + C 60 collisions at velocities in the v col = 0.05 − 0.4 a.u. range. We use time-of-flight mass spectrometry and coincidence detection of charged fragments to separate pure target ionization from processes in which the C 60 target is both ionized and fragmented. The coincidence technique allows us to identify different types of fragmentation processes such as C q+ 60 → C q+ 58 + C 2 and C q+ 60 → C (q−1)+ 58 + C + 2. A quasimolecular approach is employed to calculate charge transfer and target excitation cross sections. First-order time-dependent perturbation and statistical methods are used to treat the postcollisional processes: the calculated rate constants for C 2 and C + 2 emission from the excited and charged fullerene are then used to evaluate the fragmentation dynamics. We show that the target ionization cross section decreases with the induced target charge state and the impact energy. C 2 emission from C q+ 60 is found to dominate when q 2 while C + 2 emission dominates when q 5, in agreement with the present and previous experimental results.
Physical Chemistry Chemical Physics
Can we observe site-sensitivity after X-ray core-ionisation of a symmetric molecule composed of t... more Can we observe site-sensitivity after X-ray core-ionisation of a symmetric molecule composed of the same heavy atom such as the carbon cage adamantane? We investigate this question using electron-ion coincidence spectroscopy and theoretical methods.
APS Division of Atomic, Molecular and Optical Physics Meeting Abstracts, Apr 1, 2017
Bulletin of the American Physical Society, 2018
There exists a broad landscape of positronium (Ps) formation studies by implanting positron beams... more There exists a broad landscape of positronium (Ps) formation studies by implanting positron beams on atoms, molecules, polymers, solids, liquids, surfaces/films, metal-organic-frameworks and embedded nanostructures. Recently, ground state Ps formation studies using the C 60 molecule as a target have been carried out [1,2]. Due to the dominant electron capture from the fullerene shell region and the spatial dephasing across the shell-width, a powerful diffraction effect was found to underpin the process of Ps formation in C 60. In the current work, we access excited state Ps formations from both C 60 and C 240 fullerenes. Results reveal significant structures in the cross section as a function of both the impact energy and the Ps level-structures that arise from positron-fullerene shortrange interactions. Fullerenes are modeled by a local-density approximation (LDA) approach [3] and the Ps formation is treated by the continuum distorted-wave finalstate (CDW-FS) approximation [4]. The work may motivate application of the Ps formation spectroscopy to gas phase nanoparticles and access fullerene-level-as well as Ps-level-differential measurements. [1] Hervieux et al.,
Physical Review A, 2015
This combined experiment-theory study demonstrates that the surface plasmon resonance in C60 alte... more This combined experiment-theory study demonstrates that the surface plasmon resonance in C60 alters the valence photoemission quantum phase, resulting in strong effects in the photoelectron angular distribution and emission time delay. Electron momentum imaging spectroscopy is used to measure the photoelectron angular distribution asymmetry parameter that agrees well with our calculations from the time-dependent local density approximation (TDLDA). Significant structure in the valence photoemission time delay is simultaneously calculated by TDLDA over the plasmon active energies. Results reveal a unified spatial and temporal asymmetry pattern driven by the plasmon resonance, and offers a sensitive probe of electron correlation. A semiclassical approach facilitates further insights into this link that can be generalized and applied to other molecular systems and nanometer-sized metallic materials exhibiting plasmon resonances.
Zeitschrift f�r Physik D Atoms, Molecules and Clusters, 1997
We present a statistical fragmentation study of doubly charged alkali (Li, Na, K) and antimony cl... more We present a statistical fragmentation study of doubly charged alkali (Li, Na, K) and antimony clusters. The evaporation of one charged trimer is the most dominant decay channel (asymmetric fission) at low excitation energies. For small sodium clusters this was quite early found in molecular dynamical calculations by Landman et al. [1]. For doubly charged lithium clusters, we predict Li + 9 to be the preferential dissociation channel. As already seen experimentally a more symmetric fission is found for doubly charged antimony clusters. This different behavior compared to the alkali metal clusters is in our model essentially due to a larger fissility of antimony. This is checked by repeating the calculations for Na ++ 52 with a bulk fissility parameter set artificially equal to the value of Sb.
Physical Review A, 2000
Positronium formation in the transfer-excitation reaction of positrons impacting on singlet and t... more Positronium formation in the transfer-excitation reaction of positrons impacting on singlet and triplet metastable He(1s2s) is studied at intermediate and high impact energies within the framework of a four-body version of the continuum distorted wave-final state model. Cross sections for selective final states of the residual target as well as total cross sections and polarization fraction of the 2pϪ1s multiplet line of He ϩ are computed by using a partial-wave technique. For 2p final states of He ϩ cross sections exhibit interference patterns.
Physical Review A, 2002
We have evaluated electron capture and excitation cross sections in collisions of H+ with isoelec... more We have evaluated electron capture and excitation cross sections in collisions of H+ with isoelectronic Naq+20+q clusters (q=-1,0,+1) in the impact energy range 40-500 eV. The theoretical method includes the many-electron aspect of the problem and makes use of realistic cluster potentials obtained with density-functional theory and a spherical jellium model. As expected, electron capture decreases monotonically with cluster charge, but the corresponding mechanism does not follow a common pattern. Excitation cross sections are very similar in the three cases investigated here.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2000
ABSTRACT Positronium formation in positron-He(1s2) and positron-alkaline-earth metals is studied ... more ABSTRACT Positronium formation in positron-He(1s2) and positron-alkaline-earth metals is studied at high-enough impact energies. The importance of simultaneous excitation of the target is analysed in comparison with the case where the residual target relaxes to its fundamental state. A four-body version of the continuum-distorted-wave-final-state model is introduced to describe this two-electron process, where in the case of alkaline-earth metals, the core formed by the target nucleus and the inner-shell electrons is assumed to remain frozen during the collision. Cross sections of electron capture for selective final states and total cross sections are calculated to illustrate our analysis.
Journal of Physics B: Atomic, Molecular and Optical Physics, 1997
The electron capture process with the formation of positronium atoms in the ground state in colli... more The electron capture process with the formation of positronium atoms in the ground state in collisions of high-energy positrons impacting on hydrogenic ions also in the ground state is studied theoretically. Contributions from double-step mechanisms in the collision process at high impact energies are discussed. Scaling laws for the theoretical differential and total cross sections valid at sufficiently high impact energies and nuclear charge of the target are obtained.
Physical Review A, 2013
Ionization mechanisms of C 60 molecules irradiated by a short intense 800-nm laser pulse are stud... more Ionization mechanisms of C 60 molecules irradiated by a short intense 800-nm laser pulse are studied. Angleresolved photoelectron spectra show above-threshold ionization (ATI) patterns with a low peak contrast and a remarkably smooth angular distribution. The results are interpreted by combining two theoretical models. A time-dependent Schrödinger equation (TDSE) calculation based on the B-spline method that explicitly takes into account the molecular potential mimics the single-active-electron response while a statistical model accounts for the many-electron effects. We show that the latter are responsible for the loss of contrast in the ATI peaks. The smooth angular distribution arises in the TDSE calculation as a result of the high angular momentum of the C 60 ground electronic state and therefore is a manifestation of the atomic behavior of the molecule.
Journal of Physics: Conference Series, 2020
Synopsis Cross-sections computation of the formation of antihydrogen’ atoms or ions resulting fro... more Synopsis Cross-sections computation of the formation of antihydrogen’ atoms or ions resulting from two consecutive collisions between positronium atoms and antiprotons is a central issue of GBAR’s experiment. In [2] cross-section calculations using a perturbative approach, have been undertaken, for the charge exchange three- and four-body reactions (1) and (2). In the present study, we investigate the influence of a laser field on these two reactions. We show that under special irradiation conditions, antihydrogen’ atom or ion formation cross-sections may be increased by the presence of the laser field.
Springer Proceedings in Physics, 2014
A classical model based on the anharmonic Drude-Voigt model and the Maxwell’s equations is develo... more A classical model based on the anharmonic Drude-Voigt model and the Maxwell’s equations is developed for modeling ultrafast nonlinear coherent magneto-optical experiments performed on ferromagnetic thin films. Our theoretical predictions of the Faraday angles are in good agreement with available experimental data.
Physical Review A, 2003
We present a combined theoretical and experimental study of dissociative charge transfer in colli... more We present a combined theoretical and experimental study of dissociative charge transfer in collisions of slow Li 31 2ϩ clusters with Cs atoms. We provide a direct quantitative comparison between theory and experiment and show that good agreement is only found when the experimental time-of-flight and initial cluster temperature are taken into account in the theoretical modeling. This model explains evaporation as resulting from a collisional energy deposit due to cluster electronic excitation during charge transfer. We discuss in detail the basic mechanisms that are responsible for the charge-transfer reaction and different approximations to evaluate the energy deposit.
Journal of Physics A: Mathematical and Theoretical
The pseudo- PT symmetric Dirac equation is proposed and analyzed by using a non-unitary Foldy–Wou... more The pseudo- PT symmetric Dirac equation is proposed and analyzed by using a non-unitary Foldy–Wouthuysen transformations. A new spin operator PT symmetric expectation value (called the mean spin operator) for an electron interacting with a time-dependent electromagnetic field is obtained. We show that spin magnetization—which is the quantity usually measured experimentally—is not described by the standard spin operator but by this new mean spin operator to properly describe magnetization dynamics in ferromagnetic materials and the corresponding equation of motion is compatible with the phenomenological model of the Landau–Lifshitz–Gilbert equation (LLG).
Bulletin of the American Physical Society, 2018
Bulletin of the American Physical Society, 2017
Due to the dominant electron capture by positrons from the molecular shell and the spatial dephas... more Due to the dominant electron capture by positrons from the molecular shell and the spatial dephasing across the shell-width, a powerful diffraction effect universally underlies the positronium (Ps) formation from C 60. This results into trains of resonances in the Ps formation cross section as a function of the positron beam energy [1], producing structures in recoil momenta in analogy with classical single-slit diffraction fringes in the configuration space. C 60 is modeled by a jellium-based local-density approximation (LDA) method [2] and the Ps formation is treated by the continuum distorted-wave final-state (CDW-FS) approximation [3]. The work may motivate application of the Ps formation spectroscopy to gas-phase nanoparticles and also the access target-level-as well as Ps-level-differential measurements. [1] Hervieux et al (submitted), arXiv:1610.00335 [physics.atm-clus]; [2] Choi et al (submitted),
Journal of Physics: Conference Series, 2020
Synopsis We present a theoretical approach to calculate the cross sections for the ionization of ... more Synopsis We present a theoretical approach to calculate the cross sections for the ionization of molecules by single electron impact. It is based on the First Born approximation (FBA), describing the ejected electron by a distorted wave (DW). The cross sections are calculated for an average molecular orientation with the proper average method. Single-center molecular wave functions are generated using Gaussian making this method easily applicable to any molecule. We show the calculated cross sections of some molecular targets of varying complexity.
Physica Scripta, 1997
ABSTRACT Formation of positronium atoms in ground state in collisions of high velocity positrons ... more ABSTRACT Formation of positronium atoms in ground state in collisions of high velocity positrons impacting on highly charged hydrogenic atoms (ions) also in ground state is theoretically studied. Differential and total cross sections are obtained by using a distorted wave model derived from a quantum three-body formalism. Scaling laws for differential and total cross sections valid at high impact energies are presented.
Dans ce travail, nous avons etudie l'ionisation simple d'agregats metalliques a couches f... more Dans ce travail, nous avons etudie l'ionisation simple d'agregats metalliques a couches fermees. Nous avons mene nos etudes dans le cadre de modele du jellium spherique dans lequel la structure ionique est ignoree. Nous avons traite le systeme de fermions (electrons delocalises) d'une part, dans l'approximation de la densite locale et d'autre part, dans l'approximation de la densite locale dependant du temps TDLDA qui tient compte des correlations dynamiques. L'etude des sections efficaces doublement differentielles dans l'approximation TDLDA pour differents moments de transfert nous a permis de montrer l'importance des effets collectifs et d'identifier trois regions d'energie transferee. A basse energie, nous avons observe le phenomene d'interference entre l'ionisation directe et les excitations discretes. autour de 6 eV, on observe le plasmon de volume qui correspond a une resonance collective des electrons delocalises dans tout ...
Physical Review A, Sep 2, 2014
We present experimental and theoretical results on single-and multiple-electron capture, and frag... more We present experimental and theoretical results on single-and multiple-electron capture, and fragmentation, in C 6+ + C 60 collisions at velocities in the v col = 0.05 − 0.4 a.u. range. We use time-of-flight mass spectrometry and coincidence detection of charged fragments to separate pure target ionization from processes in which the C 60 target is both ionized and fragmented. The coincidence technique allows us to identify different types of fragmentation processes such as C q+ 60 → C q+ 58 + C 2 and C q+ 60 → C (q−1)+ 58 + C + 2. A quasimolecular approach is employed to calculate charge transfer and target excitation cross sections. First-order time-dependent perturbation and statistical methods are used to treat the postcollisional processes: the calculated rate constants for C 2 and C + 2 emission from the excited and charged fullerene are then used to evaluate the fragmentation dynamics. We show that the target ionization cross section decreases with the induced target charge state and the impact energy. C 2 emission from C q+ 60 is found to dominate when q 2 while C + 2 emission dominates when q 5, in agreement with the present and previous experimental results.
Physical Chemistry Chemical Physics
Can we observe site-sensitivity after X-ray core-ionisation of a symmetric molecule composed of t... more Can we observe site-sensitivity after X-ray core-ionisation of a symmetric molecule composed of the same heavy atom such as the carbon cage adamantane? We investigate this question using electron-ion coincidence spectroscopy and theoretical methods.
APS Division of Atomic, Molecular and Optical Physics Meeting Abstracts, Apr 1, 2017
Bulletin of the American Physical Society, 2018
There exists a broad landscape of positronium (Ps) formation studies by implanting positron beams... more There exists a broad landscape of positronium (Ps) formation studies by implanting positron beams on atoms, molecules, polymers, solids, liquids, surfaces/films, metal-organic-frameworks and embedded nanostructures. Recently, ground state Ps formation studies using the C 60 molecule as a target have been carried out [1,2]. Due to the dominant electron capture from the fullerene shell region and the spatial dephasing across the shell-width, a powerful diffraction effect was found to underpin the process of Ps formation in C 60. In the current work, we access excited state Ps formations from both C 60 and C 240 fullerenes. Results reveal significant structures in the cross section as a function of both the impact energy and the Ps level-structures that arise from positron-fullerene shortrange interactions. Fullerenes are modeled by a local-density approximation (LDA) approach [3] and the Ps formation is treated by the continuum distorted-wave finalstate (CDW-FS) approximation [4]. The work may motivate application of the Ps formation spectroscopy to gas phase nanoparticles and access fullerene-level-as well as Ps-level-differential measurements. [1] Hervieux et al.,
Physical Review A, 2015
This combined experiment-theory study demonstrates that the surface plasmon resonance in C60 alte... more This combined experiment-theory study demonstrates that the surface plasmon resonance in C60 alters the valence photoemission quantum phase, resulting in strong effects in the photoelectron angular distribution and emission time delay. Electron momentum imaging spectroscopy is used to measure the photoelectron angular distribution asymmetry parameter that agrees well with our calculations from the time-dependent local density approximation (TDLDA). Significant structure in the valence photoemission time delay is simultaneously calculated by TDLDA over the plasmon active energies. Results reveal a unified spatial and temporal asymmetry pattern driven by the plasmon resonance, and offers a sensitive probe of electron correlation. A semiclassical approach facilitates further insights into this link that can be generalized and applied to other molecular systems and nanometer-sized metallic materials exhibiting plasmon resonances.
Zeitschrift f�r Physik D Atoms, Molecules and Clusters, 1997
We present a statistical fragmentation study of doubly charged alkali (Li, Na, K) and antimony cl... more We present a statistical fragmentation study of doubly charged alkali (Li, Na, K) and antimony clusters. The evaporation of one charged trimer is the most dominant decay channel (asymmetric fission) at low excitation energies. For small sodium clusters this was quite early found in molecular dynamical calculations by Landman et al. [1]. For doubly charged lithium clusters, we predict Li + 9 to be the preferential dissociation channel. As already seen experimentally a more symmetric fission is found for doubly charged antimony clusters. This different behavior compared to the alkali metal clusters is in our model essentially due to a larger fissility of antimony. This is checked by repeating the calculations for Na ++ 52 with a bulk fissility parameter set artificially equal to the value of Sb.
Physical Review A, 2000
Positronium formation in the transfer-excitation reaction of positrons impacting on singlet and t... more Positronium formation in the transfer-excitation reaction of positrons impacting on singlet and triplet metastable He(1s2s) is studied at intermediate and high impact energies within the framework of a four-body version of the continuum distorted wave-final state model. Cross sections for selective final states of the residual target as well as total cross sections and polarization fraction of the 2pϪ1s multiplet line of He ϩ are computed by using a partial-wave technique. For 2p final states of He ϩ cross sections exhibit interference patterns.
Physical Review A, 2002
We have evaluated electron capture and excitation cross sections in collisions of H+ with isoelec... more We have evaluated electron capture and excitation cross sections in collisions of H+ with isoelectronic Naq+20+q clusters (q=-1,0,+1) in the impact energy range 40-500 eV. The theoretical method includes the many-electron aspect of the problem and makes use of realistic cluster potentials obtained with density-functional theory and a spherical jellium model. As expected, electron capture decreases monotonically with cluster charge, but the corresponding mechanism does not follow a common pattern. Excitation cross sections are very similar in the three cases investigated here.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2000
ABSTRACT Positronium formation in positron-He(1s2) and positron-alkaline-earth metals is studied ... more ABSTRACT Positronium formation in positron-He(1s2) and positron-alkaline-earth metals is studied at high-enough impact energies. The importance of simultaneous excitation of the target is analysed in comparison with the case where the residual target relaxes to its fundamental state. A four-body version of the continuum-distorted-wave-final-state model is introduced to describe this two-electron process, where in the case of alkaline-earth metals, the core formed by the target nucleus and the inner-shell electrons is assumed to remain frozen during the collision. Cross sections of electron capture for selective final states and total cross sections are calculated to illustrate our analysis.
Journal of Physics B: Atomic, Molecular and Optical Physics, 1997
The electron capture process with the formation of positronium atoms in the ground state in colli... more The electron capture process with the formation of positronium atoms in the ground state in collisions of high-energy positrons impacting on hydrogenic ions also in the ground state is studied theoretically. Contributions from double-step mechanisms in the collision process at high impact energies are discussed. Scaling laws for the theoretical differential and total cross sections valid at sufficiently high impact energies and nuclear charge of the target are obtained.
Physical Review A, 2013
Ionization mechanisms of C 60 molecules irradiated by a short intense 800-nm laser pulse are stud... more Ionization mechanisms of C 60 molecules irradiated by a short intense 800-nm laser pulse are studied. Angleresolved photoelectron spectra show above-threshold ionization (ATI) patterns with a low peak contrast and a remarkably smooth angular distribution. The results are interpreted by combining two theoretical models. A time-dependent Schrödinger equation (TDSE) calculation based on the B-spline method that explicitly takes into account the molecular potential mimics the single-active-electron response while a statistical model accounts for the many-electron effects. We show that the latter are responsible for the loss of contrast in the ATI peaks. The smooth angular distribution arises in the TDSE calculation as a result of the high angular momentum of the C 60 ground electronic state and therefore is a manifestation of the atomic behavior of the molecule.
Journal of Physics: Conference Series, 2020
Synopsis Cross-sections computation of the formation of antihydrogen’ atoms or ions resulting fro... more Synopsis Cross-sections computation of the formation of antihydrogen’ atoms or ions resulting from two consecutive collisions between positronium atoms and antiprotons is a central issue of GBAR’s experiment. In [2] cross-section calculations using a perturbative approach, have been undertaken, for the charge exchange three- and four-body reactions (1) and (2). In the present study, we investigate the influence of a laser field on these two reactions. We show that under special irradiation conditions, antihydrogen’ atom or ion formation cross-sections may be increased by the presence of the laser field.
Springer Proceedings in Physics, 2014
A classical model based on the anharmonic Drude-Voigt model and the Maxwell’s equations is develo... more A classical model based on the anharmonic Drude-Voigt model and the Maxwell’s equations is developed for modeling ultrafast nonlinear coherent magneto-optical experiments performed on ferromagnetic thin films. Our theoretical predictions of the Faraday angles are in good agreement with available experimental data.
Physical Review A, 2003
We present a combined theoretical and experimental study of dissociative charge transfer in colli... more We present a combined theoretical and experimental study of dissociative charge transfer in collisions of slow Li 31 2ϩ clusters with Cs atoms. We provide a direct quantitative comparison between theory and experiment and show that good agreement is only found when the experimental time-of-flight and initial cluster temperature are taken into account in the theoretical modeling. This model explains evaporation as resulting from a collisional energy deposit due to cluster electronic excitation during charge transfer. We discuss in detail the basic mechanisms that are responsible for the charge-transfer reaction and different approximations to evaluate the energy deposit.
Journal of Physics A: Mathematical and Theoretical
The pseudo- PT symmetric Dirac equation is proposed and analyzed by using a non-unitary Foldy–Wou... more The pseudo- PT symmetric Dirac equation is proposed and analyzed by using a non-unitary Foldy–Wouthuysen transformations. A new spin operator PT symmetric expectation value (called the mean spin operator) for an electron interacting with a time-dependent electromagnetic field is obtained. We show that spin magnetization—which is the quantity usually measured experimentally—is not described by the standard spin operator but by this new mean spin operator to properly describe magnetization dynamics in ferromagnetic materials and the corresponding equation of motion is compatible with the phenomenological model of the Landau–Lifshitz–Gilbert equation (LLG).
Bulletin of the American Physical Society, 2018
Bulletin of the American Physical Society, 2017
Due to the dominant electron capture by positrons from the molecular shell and the spatial dephas... more Due to the dominant electron capture by positrons from the molecular shell and the spatial dephasing across the shell-width, a powerful diffraction effect universally underlies the positronium (Ps) formation from C 60. This results into trains of resonances in the Ps formation cross section as a function of the positron beam energy [1], producing structures in recoil momenta in analogy with classical single-slit diffraction fringes in the configuration space. C 60 is modeled by a jellium-based local-density approximation (LDA) method [2] and the Ps formation is treated by the continuum distorted-wave final-state (CDW-FS) approximation [3]. The work may motivate application of the Ps formation spectroscopy to gas-phase nanoparticles and also the access target-level-as well as Ps-level-differential measurements. [1] Hervieux et al (submitted), arXiv:1610.00335 [physics.atm-clus]; [2] Choi et al (submitted),
Journal of Physics: Conference Series, 2020
Synopsis We present a theoretical approach to calculate the cross sections for the ionization of ... more Synopsis We present a theoretical approach to calculate the cross sections for the ionization of molecules by single electron impact. It is based on the First Born approximation (FBA), describing the ejected electron by a distorted wave (DW). The cross sections are calculated for an average molecular orientation with the proper average method. Single-center molecular wave functions are generated using Gaussian making this method easily applicable to any molecule. We show the calculated cross sections of some molecular targets of varying complexity.
Physica Scripta, 1997
ABSTRACT Formation of positronium atoms in ground state in collisions of high velocity positrons ... more ABSTRACT Formation of positronium atoms in ground state in collisions of high velocity positrons impacting on highly charged hydrogenic atoms (ions) also in ground state is theoretically studied. Differential and total cross sections are obtained by using a distorted wave model derived from a quantum three-body formalism. Scaling laws for differential and total cross sections valid at high impact energies are presented.
Dans ce travail, nous avons etudie l'ionisation simple d'agregats metalliques a couches f... more Dans ce travail, nous avons etudie l'ionisation simple d'agregats metalliques a couches fermees. Nous avons mene nos etudes dans le cadre de modele du jellium spherique dans lequel la structure ionique est ignoree. Nous avons traite le systeme de fermions (electrons delocalises) d'une part, dans l'approximation de la densite locale et d'autre part, dans l'approximation de la densite locale dependant du temps TDLDA qui tient compte des correlations dynamiques. L'etude des sections efficaces doublement differentielles dans l'approximation TDLDA pour differents moments de transfert nous a permis de montrer l'importance des effets collectifs et d'identifier trois regions d'energie transferee. A basse energie, nous avons observe le phenomene d'interference entre l'ionisation directe et les excitations discretes. autour de 6 eV, on observe le plasmon de volume qui correspond a une resonance collective des electrons delocalises dans tout ...