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The three-body continuum Coulomb problem is treated in terms of the generalized parabolic coordinates. Approximate solutions are expressed in the form of a Lippmann-Schwinger-type equation, where the Green’s function includes the leading term of the kinetic energy and the total potential energy, whereas the potential contains the non-orthogonal part of the kinetic energy operator. As a test of this approach, the integral equation for the (e −, e −, He++) system has been solved numerically by using the parabolic Sturmian basis representation of the (approximate) potential. Convergence of the expansion coefficients of the solution has been obtained as the basis set used to describe the potential is enlarged.

Atomic collisions have been very important for the development of our present understanding of the composition and behaviour of matter at the atomic level. They are also relevant in a wide range of applications; from physical chemistry to fusion reactors, from cancer treatment to research in astrochemistry. In the thesis we apply ab-initio methods to investigate the charge transfer processes when atoms enter in collision with other atoms and molecules. The focus of this work is concentrated in processes that due to their size are not amenable to the accurate methods used in atomic physics. Calculations are based on real time propagation using time-dependent density functional theory (TDDFT) a theory that uses an auxiliary set of non-interacting electrons with an interacting density to describe the state of the electrons in the system. In this work, the application of TDDFT is explored for atomic collisions in a set of problems of interest. First, we demonstrate that TDDFT can be applied in the simple case of a collision of a H+ with a He atom, with agreement with experimental results. Also we show the feasibility of simulate larger systems such as an atom of gold in collision with a butane molecule. When the particles involved in the collision has a velocity, the static ground state of the electrons associated to moving nuclei is not the ground state of the same nuclei in movement. The proper initialization of the wavefunctions is an issue. We introduce a velocity phase factor to account for the Galilean transformation from the static electronic ground state to the dynamic framework of the collision. Several alternatives are proposed in the case of multiple moving particles and a special discussion is devoted for the case of non-local pseudopotentials. Finally, a more challenging process was modelled, the collision of a 2 MeV Li+ impacting a C60 fullerene molecule. The capture cross-section was computed and compared with experimental data available for such process., (FSA - Sciences de l'ingénieur) -- UCL, 2013

The present study is focused on the clinical validation of two electron Monte Carlo (eMC) based treatment planning systems (TPS), Oncentra MasterPlan TPS (OMTPS) and XiO eMC. We present a new approach on the commissioning process based on, (a) homogeneous water phantom validation, (b) heterogeneous phantom validation with film measurements and, (c) Full MC validation. As a first step, MC models of electron beams (4, 8, 12 and 18 MeV) from an Elekta SL25 medical linear accelerator were build using the popular EGSnrc/BEAMnrc user MC code. The calculated dose distributions were benchmarked by a comparison with the measurements made in the water phantom for a wide range of open field sizes and insert combinations, at a single source to surface distance (SSD) of 100 cm. These BEAMnrc models were used to evaluate the accuracy of OMTPS (respectively XiO eMC) for two energies 4 and 12 MeV (respectively for 4, 8, 12 and 18 MeV) in a homogeneous water phantom. As a second step, the accuracy of both TPSs has been evaluated by comparing dose distributions in a heterogeneous phantom containing ribs structures. Dose distributions in the lung and non-lung tissue predicted from BEAMnrc simulation were compared with those computed with OMTPS and XiO eMC. In the case of OMTPS calculations, differences between BEAMnrc simulation and measurements range from 0.5%-2.0% between two ribs and 0.6%-1.0% below the ribs, whereas the range difference between OMTPS and measurements was the same (0.5-4.0%) in both areas. BEAMnrc models have been set as reference in the case of XiO eMC computation and the overall agreement between the two schemes lies under 2.5% for the most tested dose distributions at 8, 12 and 18 MeV and is better than the 4 MeV one. The present work demonstrates the added value of MC TPS compared to pencil beam algorithms. Results show that OMTPS and XiO eMC can predict dose perturbation induced by high-density heterogeneities for the electron beam energies investigated, excep, (MED 3) -- UCL, 2012

We study the charge transfer between colliding ions, atoms, or molecules, within time-dependent density functional theory. Two particular cases are presented, the collision between a proton and a Helium atom, and between a gold atom and a butane molecule. In the first case, proton kinetic energies between 16 keV and 1.2 MeV are considered, with impact parameters between 0.31 and 1.9 A ° . The partial transfer of charge is monitored with time. The total cross-section is obtained as a function of the proton kinetic energy. In the second case, we analyze one trajectory and discuss spin-dependent charge transfer between the different fragments.

We study both the above-threshold ionization spectrum and harmonics generation resulting from the interaction of atomic hydrogen with a UV pulse. Our calculations are based on the solution of the time-dependent Schrödinger equation in momentum space where the kernel of the non-local Coulomb potential is replaced by a sum of separable potentials, each of them supporting one bound state of atomic hydrogen. It is shown that the interaction of hydrogen with a field, the frequency of which corresponds to the 1s-2p transition, leads, quite unexpectedly, to the emission of very energetic electrons. © Published under licence by IOP Publishing Ltd.

In a previous publication, a procedure was proposed for unambiguously extracting the cross sections for double ionization and single ionization from a time-propagated wavepacket, and it was tested on the well-known case of one-photon double ionization of helium successfully. Here, we apply it to the two-photon process for which the numerically predicted double ionization cross section is not completely stabilized yet. Our results confirm the value obtained for this cross section by all but two active groups in the field, they definitely exonerate electron correlations in the final state from any responsibility in this splitting of the published data into two sets, they emphasize the need for a more careful account of reflection effects and propose a tentative explanation for an overestimation of the cross section in the J-matrix method. They also demonstrate the conceptual and computational advantages of the method proposed. (Some figures may appear in colour only in the online journal)

We present an ab initio approach to solving the time-dependent Schrodinger equation to treat electron-and photon-impact multiple ionization of atoms or molecules. It combines the already known time-scaled coordinate method with a high-order time propagator based on a predictor-corrector scheme. In order to exploit in an optimal way the main advantage of the time-scaled coordinate method, namely, that the scaled wave packet stays confined and evolves smoothly toward a stationary state, of which the squared modulus is directly proportional to the electron energy spectra in each ionization channel, we show that the scaled bound states should be subtracted from the total scaled wave packet. In addition, our detailed investigations suggest that multiresolution techniques like, for instance, wavelets are the most appropriate ones to represent the scaled wave packet spatially. The approach is illustrated in the case of the interaction of a one-dimensional model atom as well as atomic hydrogen with a strong oscillating field.

We apply the Jacobi matrix method to the Faddeev-Merkuriev differential equations in order to calculate the three-body wave function that describes the double continuum of an atomic two-electron system. This function is used to evaluate within the first-order Born approximation, the fully differential cross sections for (e, 3e) processes in helium. The calculations are performed in the case of a coplanar geometry in which the incident electron is fast and both ejected electrons are slow. Quite unexpectedly, the results obtained by reducing our double-continuum wave function to its asymptotic expression are in satisfactory agreement with all the experimental data of Lahmam-Bennani et al. [A. Lahaman-Bennani et al., Phys. Rev. A 59, 3548 (1999); A. Kheifets et al., J. Phys. B 32, 5047 (1999).] without any need for renormalizing the data. When the full double-continuum wave function is used, the agreement of the results with the experimental data improves significantly. However, a detailed analysis of the calculations shows that full convergence in terms of the basis size is not reached. This point is discussed in detail.

We consider the ionization of atomic hydrogen by a strong infrared field. By starting from the corresponding time-dependent Schrodinger equation in momentum space, we develop a model in which the kernel of the nonlocal Coulomb potential is replaced by a finite sum of separable potentials. Each separable potential supports one bound state of atomic hydrogen. Here, we consider only the 1s, 2s, and 2p states. In this way, the full three-dimensional Schrodinger equation reduces to a system of a few coupled one-dimensional linear Volterra integral equations. The objective of this first contribution is to give a detailed account of the model and to validate it in physical situations where the dynamics are well understood.

A spectral approach is used to evaluate energies and widths for a wide range of singlet and triplet resonance states of helium. Data for total angular momentum L=1,...4 is presented for resonances up to below the 5th single ionization threshold. In addition the expectation value of cos(theta_12) is given for the calculated resonances.

We present an ab initio approach to solving the time-dependent Schr¨odinger equation to treat electron- and photon-impact multiple ionization of atoms or molecules. It combines the already known time-scaled coordinate method with a high-order time propagator based on a predictor-corrector scheme. In order to exploit in an optimal way the main advantage of the time-scaled coordinate method, namely, that the scaled wave packet stays confined and evolves smoothly toward a stationary state, of which the squared modulus is directly proportional to the electron energy spectra in each ionization channel, we show that the scaled bound states should be subtracted from the total scaled wave packet. In addition, our detailed investigations suggest that multiresolution techniques like, for instance, wavelets are the most appropriate ones to represent the scaled wave packet spatially. The approach is illustrated in the case of the interaction of a one-dimensional model atom as well as atomic hydrogen with a strong oscillating field.

In this work, we investigate the role of the electronic correlations in the two-photon XUV single ionization-excitation and in the electron-impact ionization-excitation of the helium atom. In the two-photon process, we show by means of perturbative Floquet treatment that like for the sequential transition, the core resonances are present in the partial and total cross sections in a regime where two-photon double ionization is direct. We analyse the physical origin of these resonances. Concerning the electron-impact process, we use a first-order time-independent perturbative theory where the wave function of the initial and the final states includes the electronic correlation rigourously. In particular, we study the role of the exit channels leading to the autoionization of the atom. A detailed comparison between theoretical predictions and experimental data is presented and discussed. Interesting perspectives are given in the conclusion. We investigate the influence of the electron's anomalous magnetic moment on the process of relativistic Mott scattering in a powerful electromagnetic plane wave for which the ponderomotive energy is of the order of the magnitude of the electron's rest mass. For this purpose, we use the Coulomb-Dirac-Volkov and the Dirac-Volkov functions with the electron's anomaly to describe the initial and final states respectively. First-order Born differential cross sections of induced and inverse bremsstrahlung are obtained for linearly and circularly polarized laser light. Numerical calculations are carried out for various parameters values, (i.e. scattering angle, the nucleus charge, photon energy, electrical field) and are compared with results obtained by Li et al. [J. Phys. B: At. Mol. Opt. Phys. 37, 653 (2004)]. It is found that for parameters used in the present work, incorporating the anomaly of the electron in the initial and final states yields cross sections which are strongly modified whatever the scattering geometry as compared to, Dans ce travail, nous étudions le rôle des corrélations électroniques lors des processus d'ionisation-excitation de l'hélium par absorption de deux photons XUV d'une part, et d'autre part, par impact électronique. Dans le cas du processus photonique, nous montrons à l'aide d'un traitement de Floquet perturbatif, qu'à l'instar des transitions séquentielles, les résonances de coeur sont présentes dans les sections efficaces partielles et totales d'ionisation-excitation directes. Nous discutons l'origine physique de ces résonances. Dans le cas du processus électronique, nous effectuons un calcul perturbatif du premier ordre où les états initial et final sont décrits par des fonctions d'onde prenant en compte les corrélations électroniques de manière rigoureuse. Nous étudions en particulier, le rôle des canaux de sortie conduisant à l'autoionisation de l'hélium. Une comparaison détaillée de nos résultats avec d'autres résultats théoriques et des résultats expérimentaux disponibles est présentée et discutée. Ce travail ouvre les perspectives intéressantes qui sont reprises dans la conclusion. Nous étudions les effets de l'anomalie du moment magnétique (AMM) de l'électron dans la diffusion relativiste de Mott assistée par champ laser ultra intense pour lequel l'énergie pondéromotrice de l'électron est de l'ordre de la masse invariante de l'électron. A cet effet, nous utilisons les fonctions d'onde de Coulomb-Dirac-Volkov et de Dirac-Volkov avec AMM pour décrire respectivement les états initial et final. Nous calculons dans la première approximation de Born, les sections efficaces différentielles du processus de bremsstrahlung induit et inverse pour un champ laser polarisé linéairement et circulairement. Les calculs numériques sont effectués pour plusieurs paramètres cinématiques (angle de diffusion, charge du noyau, fréquence du photon, champ électrique) et ils sont comparés à ceux de Li et al. [J. Phys. B: At. Mol. Opt. Phys. 37, 653 (2004)]. Nous trouvons que pour les p, (PHYS 3) -- UCL, 2010

Mercury's internal structure is the most puzzling among the terrestrial planets and the BepiColombo space mission will play an important role in advancing our understanding of the structure, formation, and evolution of Mercury. Mercury possesses a slow rotation period of 58,6 days and revolves around the Sun in 88 days, revealing a 3:2 spin-orbit resonance. The planet exhibits an equatorial asymmetry from which a solar torque arises, which induces a periodic variation of the planet's rotation, or libration, with a period of 88 days. In the presence of a liquid core, the amplitude of the forced libration will be greatly enhanced compared to the amplitude in the case of a completely solidified planetary interior because a liquid core does not participate in the libration and the moment of inertia of the mantle is about half of the total moment of inertia of Mercury. Insight into Mercury’s deep interior will be obtained from observations from the “rotation experiment”, which will involve observations of the 88-day forced libration, the obliquity, and the gravity field of Mercury. The librations will be determined from the comparison of target surface positions at different times using an onboard camera. We have simulated repeated photographic measurements of selected target positions on the surface of Mercury in order to estimate the accuracy of the reconstruction of the orientation and rotational motion of the planet, as a function of the orbit of the spacecraft, different surface illuminations, the number of different targets considered and their locations on the surface of the planet. We show that the obliquity and libration can be retrieved through the rotation experiment to a precision level meeting or exceeding the minimum BepiColombo mission requirements., (PHYS 3) -- UCL, 2010

In this work, we present the mathematical derivation of the formulas to be used in the cross-correlation analysis, using the wavelet transform as a basis. Although we are using sismic waves as an example, we can also apply this formalism to other global geophysical quantities. First, we use the wavelet power spectrum and the wavelet cross-correlation between the various components in a station to detect the arrival time of body waves. secondaly, we use wavelet cross-correlation between stations to discriminate real sismic events from noise, comparing it with the method of coincidences between stations. We use the Morlet wavelet with correction term, in order to respect the admissibility condition. The analysis made on the data corresponding to the earthquakes of 12th and 23rd August 2008 and the recording of 2 hours of 3rd March 2009 shows that we detect much better the S-waves than P-waves, because of the direction of the latter. As we use also the wavelet modulus maxima which gives us the skeleton, we focus on the length of the ridges. We must take a long ridge length, because the energy and velocity spectra of the data analysed of Brabant Wallon are broad., (PHYS 3) -- UCL, 2010

Thanks to its high energy and luminosity, the Large Hadron Collider (LHC) at CERN can also be exploited as an high energy photon collider. In particular photoproduction offers interesting possibilities for the study of the electroweak sector up to TeV scale. After a brief presentation of cross sections for many photon-induced processes, prospects are discussed for the Higgs boson search as well as for the top quark physics. Although the studied final states possess striking characteristics, the separation of photon-induced processes from the overwhelming background of partonic interactions requires the use of advanced techniques. In this context, several tagging strategies are proposed, depending on the LHC luminosity. In order to realistically perform a simulation of the response of a multipurpose detector, a dedicated framework called DELPHES was designed. Using this fast simulation of a LHC-like detector, expected sensitivity on the tWb coupling measurement using several topologies resulting from the W associated single top photoproduction are presented. Finally, a more detailed estimate of the expected sensitivity of photoproduction for the most promising topology has been performed with the CMS simulation tools, which confirms the results obtained with DELPHES., (PHYS 3) -- UCL, 2010

The correlations between earthquake occurrence and the tides were investigated using 25,910 global earthquakes selected from the global Centroid Moment Tensor (CMT) catalog. One month tidal strain was computed for each earthquake at the focus. It included the solid earth tides as well as the ocean loading parts. Then, the cubic , compression, shear and Coulomb tidal stress was individually computed using PREM earth model. A tidal phase angle corresponding to each component was assigned to the individual event. Then the distributions of tidal phase angels were separately examined by the Schuster’s and Kolmogorov- Smirnov (KS) test. The none hypothesis tests of Tidal Triggering of Earthquakes (TTE) were started with the complete catalogue, then it was examined by different subsets separated according to the period, amplitude of the tidal stress at where the tidal phase angle was measured. The rupture types and the luni-solar difference zenith distance of earthquake were also considered. At the same time, two random time earthquake catalogues with the same focus mechanism solutions were also generated. They were simultaneously joined all tests which has been made with the true CMT catalogue. No obvious statistic evidences of the tidal triggering of earthquakes can be detected from the global catalogue. The chance to get the significant statistic values are nearly equal among the true and two random time catalogues for the majority tested subsets. The efficiency of the none hypothesis of TTE rejected by the Schuster’s test is decreasing when the size of the sample is increasing out our planet. It generated a tsunami wave which became a huge disaster for human beings and cost more than 230,000 lives 1. However, on the other hand, it is also a rare opportunity for scientists to know better about our planet from it since the complete process were recorded by the most digital instruments. Three months later, another big event shocked this area again. In this work, 16 Superc, (PHYS 3) -- UCL, 2010

A spectral approach of configuration interaction type is used to evaluate energies and widths for a wide range of singlet and triplet P-e resonance states of helium up to the eighth single ionization threshold. While the present data are in excellent agreement with existing theoretical results (below the N = 3-5 ionization threshold) obtained within an explicitly correlated approach, there are substantial differences with the energies, the widths, and the number of resonances obtained with the stabilization method.

We consider two-photon double ionization of helium with 100, 200, and 400 eV excess energy for the two ejected electrons, corresponding to photon energies of 89.5, 139.5, and 239.5 eV, respectively. We focus on the case of ultrashort pulses (two oscillations of the field) and develop an approach to calculate the two-photon transition matrix elements within the lowest order of the time-dependent perturbation theory. One of the major difficulties in calculating such amplitudes is the infinite summation over a complete set of intermediate states. In the subfemtosecond regime, however, this summation can be performed accurately by means of the closure approximation. This results in a simple expression for the two-photon amplitude that contains a dipole term and a quadrupole term. The dipole term can be clearly associated to a process in which each electron absorbs a photon whereas the quadrupole term is associated to a process in which one electron absorbs two photons and ejects the second one by collision. We analyze in detail how the relative weight of both processes influences the behavior of the electron energy and angular distributions. In particular we study how the shape of these distributions changes with the amount of electron correlations taken into account in both initial and final states. For 100 eV excess energy, our results for the electron energy distribution are compared with those obtained by solving the time-dependent Schrodinger equation. All these results unveil the crucial role of electron correlations in this transient regime of ionization which is neither sequential nor direct.

We investigate high-lying doubly excited nonautoionizing states of helium with total angular momentum L = 1,2, ...,9 with the help of a configuration interaction approach. We provide highly precise nonrelativistic energies of these states and discuss the properties of the wave functions with respect to the particle exchange operator.

The triply differential cross section of ionization excitation of helium, leaving the residual ion in the n = 2 excited states, is evaluated for the kinematics considered experimentally by Dupre et al. [J. Phys. B 25, 259 (1992)]. The interaction of the incident electron with the target is described at the first order, while the interaction of the ejected electron with the residual ion is treated very accurately within the formalism of the Jacobi matrix method. In the quasiphoton limit and for low ejected electron energies, the presence of series of doubly excited states, mainly below the n = 3 single ionization threshold in helium, makes the triply differential cross sections extremely sensitive to both the energy and the emission angle of the ejected electron. We show that the convolution of our results with a Gaussian energy profile, in which the full width at half-maximum corresponds to the energy resolution in the experiment, has a significant effect. Our results suggest that it is also important to account for the finite resolution on the measurement of the scattering angle when the experimental data are compared to the theoretical predictions. Comparison of our theoretical results convoluted both in energy and in angle with the experimental data demonstrates the importance of an accurate description of the helium spectrum. A possible two-step mechanism involving single ionization of the target followed by excitation of the core electron is proposed to explain the remaining discrepancies.

We consider the non-sequential double ionization of helium by two XUV photons. To gain further insight into the double-escape mechanism, we examine the interaction of helium with attosecond pulses. Such an interaction allows us to unveil the timescale on which the two electrons interact. By analysing the behaviour of the electron angular and energy distributions versus the pulse duration, we show that in the limit of ultrashort pulse durations, it becomes possible to disentangle the process in which each electron absorbs one photon from the process in which one electron absorbs both photons while ejecting the other electron by a collision. These results, which confirm the double-escape mechanism that we had proposed earlier (2008 J. Phys. B: At. Mol. Opt. Phys. 41 051001), are obtained using two different time-dependent theoretical approaches. The first one is based on Jacobi matrix calculations to extract the relevant information from the ionized wave packet. In the second one, we project the final wave packet on two Coulomb functions. We also develop a simple model based on time-dependent perturbation theory.

Part I: Recent calculations of ionization rate based on the numerical solution of the time-dependent Schrödinger equation (TDSE) in configuration space gave results in disagreement with the ionization rate obtained under the strong field approximation(SFA), is to say, assuming that the ionization is by tunneling. Moreover, recent experimental results, which clearly show among other things, (a) the presence of resonant structures in the region of low energy spectrum of emitted electrons and (b) interference figures for the distribution of moments of electrons emitted cannot be explained in the context of the SFA. These findings reinforce the idea that the electrons, at least those of low energies, are emitted by another process than the tunnel effect. Under these conditions, the influence of the Coulomb potential compared to the electric field remains high even in the strong field limit. To analyze the role of the Coulomb potential, we developed a new mathematical model that goes beyond the SFA as well as the efficient numerical codes that allow obtaining relevant information on the role of atomic structure in the dynamics of ionization. Part II: Using Sturmian expansions of the Dirac-Coulomb Green's functions derived by R. Szmytkowski (J. Phys. B: At. Mol. Opt. Phys. 30, 825 (1997), fully relativistic treatment) and us (quasirelativistic approach), we have derived in a rigorous way the explicit expressions of the two-photon absorption, Rayleigh and Raman scattering probability amplitudes that take into account both relativistic and retardation effects. A distinctive feature of our tensor treatment is that the expressions derived are quite general and could be applied to any multipole of the two-photon bound-bound transitions. An illustration of our method is undertaken by computing the two-photon absorption transition rates from the ground state towards the excited states of L and M shells for the lighter elements to the heavier ones. A comparison is made also with, (PHYS 3) -- UCL, 2010

In the last few years, the development of high order harmonic generation sources and free electron lasers delivering ultra-intense and ultra-short VUV-XUV pulses has made it possible to study nonlinear processes in atoms and molecules on the electronic time scale. The theoretical support required by the ongoing experiments comes notably in the form of numerical tools intended to solve the time-dependent Schrodinger equation. The wavepacket produced in these approaches has a multichannel character and its analysis in terms of the observed physical channels is a problem in itself. Various solutions have been proposed so far, which all suffer from one or another inconvenience, ranging from very heavy computational costs to the inability to characterize differential cross sections. The purpose of this paper is to propose a new, low-cost and complete method of analysis. It consists in propagating the Fourier components of the wavepacket with respect to the hyper-radius all the way to the genuine asymptotic region where the various channels disentangle from each other based on their kinematics. We demonstrate the feasibility and versatility of this proposal by applying it to two different time-propagation codes in the case of one-photon double ionization of helium using short pulses.

We present a theoretical study of strong-low-frequency-field ionization of atoms in the intermediate regime where the Keldysh parameter is close to one. For that purpose we have developed a novel method based on an explicit algorithm for the propagation of the time-dependent Schrödinger equation which is known to be very stiff. This method overcomes the stiffness by taking into account the eigenfrequencies of the interacting system. With the help of this approach we are able in particular to investigate the ionization of the hydrogen atom by ultra-short (25 fs) 790 nm laser pulses at intensities 0.5−6 × 1014 W/cm2.

The asymptotic behaviour of a dynamical system is described by probability measures that are invariant under the dynamic. For a chaotic dynamical system, there are many invariant measures but some of them have a stronger physical meaning, especially the SRB measures, which are invariant measures with some regularity properties as the absolute continuity with respect to the Lebesgue measure. Under very general assumptions, it can be proven that finite dimensional chaotic dynamical systems have only one SRB measure. In the case of infinite dimensional systems, the picture is radically different: weakly coupled systems tends to have only one SRB measure, and strongly coupled systems may have several. This phenomenon is known as a phase transition. This thesis will be devoted to the study of phase transitions for some infinite dimensional chaotic dynamical systems called coupled map lattices. We will define a coupled map lattice inspired by Stavskaya's probabilistic cellular automata for which it is possible to prove a phase transition at the level of SRB measures. We will also prove that a wide class of measures converge exponentially fast toward the invariant measure that appears at strong coupling. This will imply that this SRB measure has the exponential decay of correlations property both in space and time., Le comportement asymptotique d'un système dynamique est décrit par des mesures de probabilité invariantes sous l'évolution temporelle associée au système dynamique. Dans le cas d'une dynamique chaotique, s'il existe en général un très grand nombre de mesures invariantes, toutes n'ont cependant pas la même pertinence physique, et en particulier, il convient de distinguer les mesures SRB, qui sont des mesures invariantes possédant des propriétés de régularité supplémentaires comme l'absolue continuité par rapport à la mesure de Lebesgue. Si les systèmes dynamiques chaotiques en dimension finie possèdent en général une unique mesure SRB, le comportement des systèmes chaotiques en dimension infinie est beaucoup plus riche: les systèmes faiblement couplés possèdent une unique mesure SRB, tandis que les systèmes fortement couplés peuvent en avoir plusieurs. Par analogie avec la mécanique statistique, ce phénomène est connu sous le nom de transition de phase. Cette thèse se propose d'étudier les transitions de phase pour une classe particulière de systèmes dynamiques chaotiques en dimension infinie: les réseaux d'applications couplées. Il sera défini un réseau d'applications couplées s'inspirant de l'automate cellulaire probabiliste de Stavskaya, pour lequel il est possible de démontrer l'existence d'une transition de phase au niveau des mesures SRB, et la convergence exponentiellement rapide pour une vaste classe de mesures vers la mesure SRB qui apparaît à fort couplage. Cela impliquera entre autre que cette mesure SRB possède la propriété de décroissance exponentielle des corrélations dans le temps et dans l'espace., (PHYS 3) -- UCL, 2009

We present a spectral method of configuration-interaction type for three-dimensional helium which combines the complex rotation method with an appropriate expansion of the atom wave function in a basis of products of Coulomb-Sturmian functions of the electron radial coordinates with independent dilation parameters for the two electrons and bipolar spherical harmonics of the angular coordinates. The matrix elements of the kinetic energy and of the electron-nucleus interaction term are calculated using Gauss-Laguerre integration techniques. A combination of Gauss-Laguerre integration techniques with the generalized Wigner-Eckart theorem and recurrence relations allows an efficient and stable calculation of the matrix elements of the electron-electron interaction. The freedom of the choice of the dilation parameters permits us to access highly excited states with rather small sizes of the basis. Highly doubly excited states up to the tenth ionization threshold of singlet and triplet S states of helium are presented.

We consider two-photon double ionization of helium and analyse the electron dynamics in the region where the process is direct (39.49 eV < <(h)over bar>omega < 54.42 eV). The fundamental process of two-photon double ionization (TPDI) is far from being well understood. In order to gain physical insight into the dynamics involved in TPDI, we investigate the electron energy distributions for <(h)over bar>omega = 46 eV and (h) over bar omega = 50 eV, angular distributions are also analysed. The theoretical approach is based on the resolution of the time-dependent Schrodinger equation (TDSE), using a spectral approach. At the end of the pulse the TPDI probability is extracted from the total wavefunction using two different approaches. The first one neglects the electron interaction in the double continuum while the second one includes electron correlation effects. At (h) over bar omega approximate to 45 eV the electrons are preferably emitted back-to-back with equal energy. At (h) over bar omega = 50 eV the excess energy is likely to be transfered to one of the electron, while the electrons are emitted in opposite or same directions.

Ce travail porte sur l'étude théorique de la double ionisation à deux photons de l'atome d’hélium avec comme objectif de comprendre le rôle des corrélations électroniques dans le mécanisme de double éjection. En analysant les distributions en énergie et les distributions angulaires des électrons émis, nous montrons que lors du processus direct, le système initialement dans son état fondamental évolue vers un état hautement corrélé. Les corrélations angulaires forcent les deux électrons à être éjectés dans des directions opposées, le long de l'axe de polarisation. Sous l'effet de "l'écrantage dynamique" c'est-à-dire des corrélations radiales, les deux électrons ont tendance à partager équitablement l'énergie disponible au dessus du seuil de double ionisation. Pour valider ou invalider ce mécanisme, nous proposons de mesurer la distribution des impulsions des ions doublement chargés He++. Tous ces résultats s'obtiennent en résolvant l'équation de Schrödinger dépendante du temps à l’aide d'une méthode spectrale combinée à celle de la matrice de Jacobi. En parallèle, et toujours dans le cas de l'ionisation double à deux photons de l'hélium, nous analysons les effets des corrélations électroniques à l'échelle attoseconde., (PHYS 3) -- UCL, 2008

We consider the two-photon double ionization (DI) of helium and analyze electron dynamics on the attosecond timescale. We first re-examine the interaction of helium with an ultrashort XUV pulse and study how the electronic correlations affect the electron angular and energy distributions in the direct, sequential and transient regimes of frequency and time duration. We then consider pump-probe processes with the aim of extracting indirect information on the pump pulse. In addition, our calculations show clear evidence for the existence under certain conditions of direct two-color DI processes.

Experiments using new sources of XUV pulses now tackle the difficult problem of few- photon direct double ionization of atoms. Despite its apparent simplicity, the fundamental process of two- photon direct double ionization of helium is far from being understood. Here, we use a time- dependent approach to study the process. Our results for the electron angular and energy distributions demonstrate that the dominant mechanism for double- electron escape involves a highly correlated electron motion. Angular correlations strongly favour back- to- back electron emission along the polarization axis, while dynamical screening leads to an equipartition of the electron energy for a broad range of field frequencies. These features are reflected in the recoil- ion- momentum distributions that are presently accessible to experiments.

As a highly correlated process, direct two-photon double onization of helium represents a very challenging theoretical problem. A wide rande of computational methods have been used to evaluate generalized cross sections. However, despite considerable efforts, a quantitative agreement between all calculations has not been reached. In this contribution, we address several issues regarding the origin of the discrepancies in the total cross section and the behaviour of this cross section close to the sequential regime. Our ab initio calculations are based on the numerical solution of the time-dependent Schrödinger equation by means of a spectral method combined with Jacobi-matrix calculations. This method which, in principle, takes fully into account electron correlations, provides also a consistent physical picture of the double escape mechanism.

In this paper, we present a model aimed at exploring the role of the Coulomb potential in the mechanism of ionization of atomic hydrogen exposed to a strong low frequency pulsed laser field. Our approach is based on the solution of the time-dependent Schrodinger equation in momentum space. Although we are in a frequency and intensity regime where tunnelling is expected to dominate, our results indicate that the atomic structure associated to the Coulomb potential plays a significant role for low energy ejected electrons. (c) 2006 Elsevier B.V. All rights reserved.

We give a detailed account of an ab initio computational treatment of multiphoton single ionization (with or without excitation) as well as double ionization of two-electron atoms exposed to short-wavelength electric fields. This treatment is time dependent and based on a spectral method of configuration interaction type combined with Jacobi or J-matrix calculations. It involves a complete treatment of electron-electron correlation in the initial and final states as well as during the time propagation. The atom eigenvalue problem is first solved by means of the spectral method. It consists of expanding the atom wave function in a basis of products of complex Coulomb-Sturmian functions of the electron radial coordinates and bipolar harmonics of the angular coordinates. This method allows a high-resolution study of many atomic states, in particular high-lying singly excited states as well as many doubly excited states. Results for He are presented and discussed in detail. The time-dependent Schrodinger equation is then solved by means of an explicit scheme of Runge-Kutta type. An accurate calculation of the probability of single and double ionization is carried out by projecting the ionizing wave packet on fully correlated multichannel scattering wave functions generated by means of the J-matrix method. After a detailed analysis of the accuracy of this method, we show that our results for the total cross section of one-photon single and double ionization of He and H- are in very good agreement with those obtained by the most sophisticated approaches. Two-photon double ionization of He is then considered, and results are presented in a frequency regime where substantial discrepancies subsist between all existing calculations. Our results demonstrate that electron correlations in the final state play a significant role.

We question the conclusions reached by De Castro [Phys. Rev. A 72, 023410 (2005)] regarding the theoretical analysis of experimental results by Laarman [Phys. Rev. A 72, 023409 (2005)] on photoionization of He in the presence of a strong free-electron laser radiation pulse.

We study two-photon double ionization of helium. We demonstrate that attosecond pulses can be used to probe in the time-domain the electron dynamics within the atom. The interaction of helium with attosecond pulses whose duration is close to the correlation time provides information about the relaxation of the residual ion after the first electron ejection. Here, we show that such interaction of attosecond pulses with helium also modifies the double ionization probability in a non-trivial way. We examine the situations where sequential double ionization is permitted (omega >= 2 au) and where only the direct two-photon double ionization is allowed (omega < 2 au). All the calculations rely on both a model and the numerical solution of the time-dependent Schrodinger equation in its full dimensionality.

We study two-photon double ionization of helium in its ground state at sufficiently low laser intensities so that three and more photon absorptions are negligible. In the regime where sequential ionization dominates, the two-photon double ionization one-electron energy spectrum exhibits a well defined double peak structure directly related to the electron-electron correlation in the ground state. We demonstrate that when helium is exposed to subfemtosecond or attosecond pulses, both peaks move and their displacement is a signature of the time needed by the He+ orbital to relax after the ejection of the first electron. This result rests on the numerical solution of the corresponding non-relativistic time-dependent Schrodinger equation.

We develop further a new method for employing a set of real basis functions to represent the Green function at energies in the continuum, without regard for the asymptotic boundary conditions. The method is based on the analyticity of the Green function with respect to its underlying time scale. The diagonalization of large matrices is unnecessary. Although a large complex symmetric linear system of equations must be solved, this can be done with high stability and efficiency by using a generalization of the Cholesky decomposition of real positive definite symmetric matrices. We present results of test applications to S-1-wave electron scattering from a hydrogen atom and photodetachment of the negative hydrogen ion. The extension from two- to three-body collisions entails the use of projection operators to distinguish different groups of asymptotic channels.

Angular distributions of the two ejected electrons resulting from the double ionization of helium by electron impact have been measured by means of a multicoincidence multiangle (e,3e) spectrometer at an incident energy of about 0.6 keV and equal outgoing energies E-b=E-c=11 eV. We identify various regimes of kinematical parameters where substantial differences are found with respect to the first-Born convergent close-coupling calculations: an angular shift of the position of the main lobe and the presence of additional lobes. These differences are attributed to high-order contributions in the projectile-target interaction. This conclusion is supported by recent (e,3e) calculations performed within the second-Born approximation.