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We consider the process of high-order harmonics generation (HHG) in the xenon atom enhanced by the intershell correlation between the valence $5p$ and inner $4d$ shells. We derive the HHG spectrum from a numerical solution of the one-electron time-dependent Schr\"odinger equation multiplied by the enhancement factor taken as the photoionization cross-sections ratio calculated with and without the intershell correlation. Such a simplified approach is adequate to describe the experimental HHG spectrum reported by Shiner et al. [Nat. Phys. 7, 464 (2011)] generated by a single color IR laser. Similarly, we find good agreement when applied to the two-color driven HHG spectra reported by Faccial\'a et al. [Phys. Rev. Lett. 117, 093902 (2016)].

Numerical attoclock is a theoretical model of attosecond angular streaking driven by a very short, nearly a single oscillation, circularly polarized laser pulse. The reading of such an attoclock is readily obtained from a numerical solution of the time-dependent Schr\"odinger equation as well as a semi-classical trajectory simulation. By making comparison of the two approaches, we highlight the essential physics behind the attoclock measurements. In addition, we analyze the predictions of the Keldysh-Rutherford model of the attoclock [Phys. Rev. Lett. 121, 123201 (2018)]. In molecular hydrogen, we highlight a strong dependence of the width of the attoclock angular peak on the molecular orientation and attribute it to the two-center electron interference. This effect is further exemplified in the weakly bound neon dimer., Comment: 8 pages, 7 figures

We solve the time-dependent Schr\"odinger equation for a noble gas atom (He and Ne) driven by an ionizing XUV and dressing IR fields. From this solution we deduce an angular dependence of the photoemission time delay as measured by the RABBITT (reconstruction of attosecond beating by interference of two-photon transitions) technique. We use a recent angle-resolved RABBITT measurement on helium [S. Heuser et al., Phys. Rev. A 94, 063409 (2016)] to test and calibrate our theoretical model. Based on this calibration, we find no significant difference between the time delay in He measured in the angle-integrated RABBITT experiments [C. Palatchi et al., J. Phys. B 47, 245003 (2014) and D. Gu\'enot et al., J. Phys. B 47, 245602 (2014)] and measured or calculated in the polarization axis direction. The angular dependence of the photoemission time delay of Ne is shown to be qualitatively different from He because of the different orbital character of the valence $2p$ orbital. The angular momentum projection dependence of the time delay in Ne is also investigated.

We report on three-dimensional (3D) electron momentum distributions from single ionization of helium by a laser pulse consisting of two counterrotating circularly polarized fields (390 nm and 780 nm). A pronounced 3D low energy structure and sub-cycle interferences are observed experimentally and reproduced numerically using a trajectory based semi-classical simulation. The orientation of the low energy structure in the polarization plane is verified by numerical simulations solving the time dependent Schr\"odinger equation., Comment: 5 pages, 4 figures, PRA Rapid Communications accepted

Single photon laser enabled Auger decay (spLEAD) has been redicted theoretically [Phys. Rev. Lett. 111, 083004 (2013)] and here we report its first experimental observation in neon. Using coherent, bichromatic free-electron laser pulses, we have detected the process and coherently controlled the angular distribution of the emitted electrons by varying the phase difference between the two laser fields. Since spLEAD is highly sensitive to electron correlation, this is a promising method for probing both correlation and ultrafast hole migration in more complex systems., Comment: 5 pages, 3 figures

Physical Review A, 95 (1), ISSN:1094-1622, ISSN:0556-2791, ISSN:1050-2947

Double ionization following the absorption of a single photon is one of the most fundamental processes requiring interaction between electrons(1-3). Information about this interaction is usually obtained by detecting emitted particles without access to real-time dynamics. Here, attosecond light pulses(4,5), electron wave packet interferometry(6) and coincidence techniques(7) are combined to measure electron emission times in double ionization of xenon using single ionization as a clock, providing unique insight into the two-electron ejection mechanism. Access to many-particle dynamics in real time is of fundamental importance for understanding processes induced by electron correlation in atomic, molecular and more complex systems.

In this Letter, the statement 'I.I. and A.B. performed computations at the NCI Australia' was missing from the Acknowledgements section. This has been corrected online.

This work describes the first observations of the ionisation of neon in a metastable atomic state utilising a strong-field, few-cycle light pulse. We compare the observations to theoretical predictions based on the Ammosov-Delone-Krainov (ADK) theory and a solution to the time-dependent Schrödinger equation (TDSE). The TDSE provides better agreement with the experimental data than the ADK theory. We optically pump the target atomic species and measure the ionisation rate as the a function of different steady-state populations in the fine structure of the target state which shows significant ionisation rate dependence on populations of spin-polarised states. The physical mechanism for this effect is unknown.

We present accurate measurements of carrier-envelope phase effects on ionisation of the noble gases with few-cycle laser pulses. The experimental apparatus is calibrated by using atomic hydrogen data to remove any systematic offsets and thereby obtain accurate CEP data on other generally used noble gases such as Ar, Kr and Xe. Experimental results for H are well supported by exact TDSE theoretical simulations however significant differences are observed in case of noble gases., Comment: 4 pages, 5 figures, submitted to PRL (manuscript number LH15031)

The past decade has seen extraordinary theoretical progress in the field of fully kinematically resolved atomic electron-impact ionisation, and its closely related field of double photoionisation. These processes were challenging to calculate due to formal and computational difficulties associated with break-up problems involving the long-range Coulomb potential. Presently, however, these processes can be calculated accurately for simple targets such as atomic hydrogen and helium, irrespective of the kinematics considered or the geometry of detectors. We report on the computational progress, and how it has resulted in a deeper understanding of the formalism of Coulomb few-body problems.

Attosecond photoemission delays for all the valence (5p3/2, 5p1/2, 5s, 4d5/2, 4d3/2) subshells of xenon have been accessed using the interferometric RABBITT technique. The 4d subshell delays in Xe have been accessed for the first time, to the best of our knowledge, due to the high photon energy used. A novel technique of single-shot referencing in the collinear back-focusing geometry has been introduced. This enables us to distinguish the signal from principal photoelectron peaks due to ionization by extreme ultraviolet radiation only and infrared-induced sideband contributions, especially in the regions of spectral overlap.

We present an angle resolved study of photoelectrons emitted from ions of the noble gases neon, argon and krypton by means of time-of-flight spectroscopy. The ionic targets are generated in a sequential two-photon process induced by the free-electron laser FLASH. Values of the anisotropy parameters β2 and β4 are derived from electron angular distribution measurements in the photon energy range from 38 to 91 eV and compared with recent theoretical calculations.

Using orthogonally polarized two-color laser fields on neon and coincidence momentum imaging we gain access to the Coulomb influence in single ionization on sub-cycle times, and demonstrate a strong electron-electron anti-correlation in double ionization.

The interpretation of electron spectroscopy data is often complicated by the presence of satellites. These satellites are either due to different final states reached after the excitation (intrinsic satellites) or due to energy loss experienced by the escaping electron on its way out the target (extrinsic satellites). Unravelling these two contributions in an unambiguous way is difficult. In this paper we compare the intrinsic satellite structures obtained for germanium by two different high-energy spectroscopies: Auger spectroscopy of deep core levels and valence band electron momentum spectroscopy. Despite the different nature of the two probes we find a similar shape of the intrinsic satellites and comparable intensity.

We investigate the effect of a static electric field on photoionization of the He atom in the ground 1S and low-lying 2S and 2P excited states. The field-affected ionization potential and photoionization cross-section are determined from the complex eigenvalues of the time-dependent Schrodinger equation solved by the complex rotation method in the Floquet ansatz. Accuracy of the method is enhanced by the use of the Hylleraas basis set. For the ground state of helium, we find that the total photoionization cross-section remains constant or decreases as a function of the DC field strength until this field reaches a certain critical value. For the low-lying excited states, effect of the static field is similar to the ordinary DC Stark effect.

We apply a non-perturbative procedure for the calculation of the total photoionization cross-section of two-electron atomic systems. The procedure is based on the Floquet-Fourier representation of the time-dependent Schrodinger equation. With the use of the Hylleraas-type basis functions, the total photoionization cross-sections obtained are within the accuracy of a fraction of a percent, which, we believe, is the most accurate estimate for the cross-sections available. The total photoionization cross-sections for neutral helium deviate notably from the benchmark experimental data [J.A.R. Samson et al., J. Phys. B 27, 887 (1994)].

Convergent close-coupling results for the triply differential cross section for double photoionization of He that include dipole-quadrupole terms are shown to have improved agreement (as compared to dipole approximation results) with recent experiments using linearly polarized light (Knapp A et al 2005 J. Phys. B: At. Mol. Opt. Phys. 38 615) for a number of kinematical configurations.

The spectral momentum density of vanadium and V2O3 is measured by electron momentum spectroscopy. Results are compared with band structure calculations based on density functional theory. Qualitatively the agreement between theory and experiment is good. The calculated total band width of vanadium metal seems somewhat smaller (’ 0.5 eV) than the observed one. The splitting between the outer and inner valence band in V2O3 is 2 eV larger in the experiment than in the density functional theory calculation. The observed momentum distributions agree reasonable well with the calculated distribution. The momentum density near the Fermi level in V metal resembles that of atomic V3d orbitals. However momentum proles of the V3d orbitals in V2O3 are much sharper peaked than the atomic 3d orbital in both the theory and experiment. Correlation eects are identied and theoretical problems in describing EMS data from narrow band systems are identied.

We present a joint experimental and theoretical study of the gerade and ungerade amplitudes of the photo double ionization of helium at excess energies of 100 eV and 450 eV above the threshold. We describe a method of extracting the amplitudes from a COLTRIMS data set. The experimental results are well reproduced by convergent close-coupling (CCC) calculations. The fully differential cross section data underlying this study can be found in our companion papers immediately preceding this one.

We present a joint experimental and theoretical study for the fully differential cross section of the photo double ionization (PDI) of helium with linearly polarized light at the excess energies Eexc = 100 eV and 450 eV above the threshold. The fully differential cross section is obtained by measuring the three-dimensional momentum vectors of one electron and the He 2+ ion in coincidence using the COLTRIMS method. We give an overview of the momentum distribution of the three-body continuum 100 eV above the threshold. We show angular distributions for both electrons for various energy sharings at Eexc = 100 eV and 450 eV. The experimental results are well reproduced by a set of convergent close-coupling (CCC) calculations.

Electron momentum spectroscopy is a coincidence technique that measures the spectral momentum density of matter. In this paper we outline the theoretical framework underlying these measurements, give a description of the spectrometer, and show in detail the information this technique can provide for the prototypical material silicon. We present results for single crystals as well as amorphous samples, describe the influence that diffraction and inelastic multiple scattering have on these measurements. The results are compared with full-potential linear-muffin-tin-orbital (FP-LMTO) calculations (for dispersion), and many-body calculations (for line shapes).

Electron momentum spectroscopy is often used to determine the spectral function of materials. It relies on the determination of the scattering angle of electrons with extremely high precision. In practice, it is important to calibrate these angles, and hence the momentum scales. Here we describe a method to do so and show how minor misalignments affect the measured momentum densities of Li2O. Using the same procedure we further calibrated the momentum scale by measuring the spectral momentum density along a Brillouin zone boundary of a Si single crystal.

We employed electron momentum spectroscopy (EMS) to measure the bulk electronic structure of calcium oxide. We extracted the electron momentum density (EMD), density of occupied states (DOS), band dispersions, bandwidths and intervalence bandgaps from the data. The results are compared with calculations based on the full potential linear muffin-tin orbital (FP-LMTO) approximation. While the bandwidths of 0.6 ± 0.2 and 1.2 ± 0.1 eV for the s- and p-bands, respectively, and their dispersions agree well with the LMTO calculation, the relative intensity of the two bands is at odds with the theory. The measured intervalence bandgap at the Γ-point of 16.5 ± 0.2 eV is larger by 2.1 eV than that from the LMTO calculation. The experimental bandwidth of the Ca 3p semi-core level of 0.7 ± 0.1 eV agrees with the LMTO prediction. The measured bandgap between this level and the s-band is 3.6 ± 0.2 eV. The Ca 3s–3p level splitting is in excellent agreement with the literature.

The spectral function A(q,omega) of silicon has been measured along a number of symmetry directions using high-energy high-resolution electron momentum spectroscopy. It is compared with first-principles calculations based on the interacting one-electron Green's function which is evaluated in the GW and the cumulant expansion approximations. Positions of the quasiparticle peaks (dispersion), their widths (lifetimes), and the extensive satellite structures are measured over a broad range of energies and momenta. The band dispersions are well described by both calculations, but the satellite predicted by the GW calculation is not observed. Unlike the GW calculation, the cumulant expansion calculation gives a significantly better description of the shape and momentum dependence of the satellite structure, presenting a promising approach for studying high-energy excitations.The spectral function A(q,omega) of silicon has been measured along a number of symmetry directions using high-energy high-resolution electron momentum spectroscopy. It is compared with first-principles calculations based on the interacting one-electron Green's function which is evaluated in the GW and the cumulant expansion approximations. Positions of the quasiparticle peaks (dispersion), their widths (lifetimes), and the extensive satellite structures are measured over a broad range of energies and momentum dependence of the satellite structure, presenting a promising approach for studying high-energy excitations.

In electron momentum spectroscopy (EMS), an incoming energetic electron (50 keV in this work) ionizes the target and the scattered and ejected electrons are detected in coincidence (at energies near 25 keV). From the energy and momentum of the detected particles, the energy \omega and momentum {\bf q} transferred to the target can be inferred. The observed intensity distribution I(\omega, {\bf q}) is proportional to the spectral momentum density of the target and hence provides a direct challenge to many-body theoretical descriptions of condensed matter. This is illustrated by comparing some many-body calculations with EMS measurements on graphite and polycrystalline aluminium.

Electron momentum spectroscopy is used to determine the spectral function of silicon single crystals. In these experiments 50 keV electrons impinge on a self-supporting thin silicon film and scattered and ejected electrons emerging from this sample with energies near 25 keV are detected in coincidence. Diffraction effects are present that give rise to additional structures in the measured spectral momentum densities. Spectra for a specific momentum value can be obtained at different orientations of the crystal relative to the analysers. By comparing these spectra for which the measured momentum density is the same, but the diffraction conditions of the incoming and outgoing electron trajectories differ, one can distinguish between features due to diffraction of the incoming and/or outgoing electrons, and those due to the electronic structure of the target itself.

Atomic and Molecular Physics Laboratories, Research School of Physical Sciences and Engineering, The Australian National University, Canberra ACT 0200, Australia. The energy-momentum resolved valence band structure of beryllium oxide has been measured by electron momentum spectroscopy (EMS). Band dispersions, bandwidths and intervalence bandgap, electron momentum density (EMD) and density of occupied states have been extracted from the EMS data. The experimental results are compared with band structure calculations performed within the full potential linear muffin-tin orbital approximation. Our experimental bandwidths of 2.1 ± 0.2 and 4.8 ± 0.3 eV for the oxygen s and p bands, respectively, are in accord with theoretical predictions, as is the s-band EMD after background subtraction. Contrary to the calculations, however, the measured p-band EMD shows large intensity at the Γ point. The measured full valence bandwidth of 19.4 ± 0.3 eV is at least 1.4 eV larger than the theory. The experiment also finds a significantly higher value for the p-to-s-band EMD ratio in a broad momentum range compared to the theory.

We present the results of attosecond angular streaking of atomic Hydrogen using elliptically polarized, 5.5 fs pulses that are centered around 770 nm, within the intensity range of 1.65 to 4 × 1014 W/cm2. We measure angular offsets in the photo-electron momentum distribution relative to the peak of the electric field of light in the polarization plane. We find a strong agreement in these results with the solutions of complete 3D-TDSE simulations. Further, we compute the contribution of coulomb effects (between the ionized electron-parent ion) to the measured angular offsets using Yukawa potential, subtracting which yields the real 'tunneling delays'.

The two-dimensional sub-cycle-time to electron momentum mapping provided by orthogonal two-color laser fields is applied to photoelectron spectroscopy. Using neon as the example we gain experimental access to the dynamics of emitted electron wave packets in electron momenta spectra measured by coincidence momentum imaging. We demonstrate the opportunities provided by this time-to-momentum mapping by investigating the influence of the parent ion on the emitted electrons on laser-sub-cycle times. It is found that depending on their sub-cycle birth time the trajectories of photoelectrons are affected differently by the ion's Coulomb field.

Using ab-initio simulations and fully quantum analytical theory for hydrogen atom, we show that atto-clock delays are induced entirely by interaction of the outgoing electron with the core and do not result from tunneling delays.

Electron momentum spectroscopy is a tool ideally suited for the study of energy-resolved momentum densities. Here we present new data from a high-energy EMS experiment using 50 keV incoming and 25 keV outgoing electrons. Both the measured energy distributions and the measured momentum distributions are affected by multiple scattering. However, after correcting for these effects, neither distribution can be fully understood using electronic structure calculations that take electron–electron correlation into account only on a mean-field level.

γ, 2e) triple differential cross sections (TDCS) are presented for helium at 60 eV above the photodouble ionisation threshold with energy sharing ratios ( R = E2/E1) for the two ejected electrons of R = 1, 5 and 11. The measurements were taken using a toroidal spectrometer and linearly polarised light from an undulator beamline (SU6) at the Super-ACO synchrotron. Good agreement is found with TDCSs obtained by the CCC method and by the length gauge of 3C theory.

The dynamics of He double ionization by 2 keV electron impact is studied experimentally for a momentum transfer of 0.6 a.u. at excess energies of 10 and 40 eV. Complete sets of fivefold differential cross sections are presented for all electron emission angles in coplanar geometry. Contributions beyond the first Born approximation are identified comparing experimental data with first order convergent close-coupling calculations which are in considerably better agreement with the present experiment than with the earlier measurement of Kheifets et al. [J. Phys. B 32, 5047 (1999)].

Electron momentum spectroscopy is a tool ideally suited for the study of the energy-resolved momentum densities. Here we present new data from a high-energy EMS experiment using 50 keV incoming and 25 keV outgoing electrons. Momentum profiles have been measured from a thin aluminum film for the 2 core level and the valence band near E. The resolution of f these momentum profiles, as well as the effects of multiple scattering are discussed. It is found that the high-energy EMS experiment measures momentum densities with superior resolution and very little background. © 2001 Elsevier Science B.V. All rights reserved.

We have measured the bulk energy-momentum resolved conduction band structure of metallic calcium using electron momentum spectroscopy (EMS). From the EMS data we have extracted the band dispersion, occupied bandwidth and density of states. The experimental results are compared with band structure calculations performed within the linear muffin-tin orbital (LMTO) approximation. The free-electron parabola expected for the dispersion relation in a metallic solid is clearly reproduced in the experimental data and is in good agreement with our calculation. A background produced by multiple-scattering events within the target is also evident in the EMS results. In order to make a quantitative comparison, we have included the effects of multiple scattering in the calculation using a Monte Carlo (MC) simulation. The results of this procedure reproduce the measured conduction band features and background intensity very well. The occupied bandwidth is measured to be 3.3±0.2 eV, and agrees with previous measurements and the value predicted by our LMTO calculation when the MC simulation is included. However, the experiment indicates that the band dispersion curve is narrower in momentum by as much as 0.1 au compared with the theory. We have also made measurements of the energies of the 3s and 3p core levels in metallic calcium, and obtained values of 45.0±0.4 eV and 25.6±0.2 eV respectively. These results are in good agreement with previous experiments.

We have measured the energy- and momentum-resolved band structure, and ground state of occupation of the bands, for a crystalline silicon sample along the 100 and 110 directions. Band structures were determined directly by the technique of electron momentum spectroscopy (EMS) for a self-supporting Si membrane with a thickness of approximately 7 nm. We compare our experimental results with ab initio calculations for bulk crystalline silicon performed within the linear muffin tin orbital approximation. Qualitative agreement is seen between experiment and theory for the main valence band peak. Additional intensity is observed in the measurement on either side of the main peak and is attributed mainly to multiple-scattering events. Satellite structure could also be present in these additional features, although there is no direct evidence for this.

Electron momentum spectroscopy (EMS) has been used to measure the valence band electronic structure of thin magnesium and magnesium oxide films. The band structures have also been calculated within the linear muffin-tin orbital (LMTO) approximation. The free-electron-like parabola characteristic of metallic solids was observed for magnesium with a bandwidth of approximately 6 eV, in agreement with previous measurements. The inclusion of energy broadening due to finite hole-lifetime effects and a Monte Carlo simulation of multiple scattering events gives good agreement between calculated and measured band structures. However, we measure a much higher intensity due to plasmon excitation compared with the simulated intensity. Upon oxidation the valence structure splits into two distinct, less dispersive bands typical of an ionic solid. Intensity due to plasmon excitation was almost completely absent in the experimental spectra for magnesium oxide. The LMTO calculation reproduces the overall structure and dispersion range of the oxide. The measured and calculated energy gap between upper and lower valence bands and their relative intensities do not agree quantitatively. This discrepancy may be due to a contribution of magnesium s states to the predominantly oxygen p states in the upper band.

We calculate electron momentum densities of various crystalline solids by employing the linear-muffin-tin-orbital (LMTO) method. We use three levels of approximation to the LMTO: the simplest atomic sphere approximation (ASA), the ASA with overlap correction, and the full-potential (FP) LMTO. Although the band energies calculated using the ASA and the FP-LMTO are practically the same, there is a noticeable difference in the electron momentum densities which is not cured by making a simple overlap correction to the ASA-LMTO method.

The electronic excitation spectra at arbitrary momentum values can be determined in principle by (e,2e) spectroscopy. These experiments are performed using high energy electrons (1 keV up to 20 keV) meaning that refraction of electrons at the surfaces, a complicating factor for low energy photoemission measurements, can be avoided. However at such high energies the geometry of the experiment has to be known very accurately. Here we describe a procedure to check the actual geometry of the experiment, and how to adjust for misalignments, if they are present. Spectral momentum densities obtained in this way for graphite along low symmetry directions are compared with full potential linear muffin tin orbital calculations. The measured intensities agree quite well with the calculations, however the observed dispersion of the graphite σ band exceeds the calculated one by 1.5-2 eV, and the separation between s and p band is somewhat smaller in the calculation compared to the experiment.

We report on the three-dimensional electron momentum densities (EMD) of graphite and fullerene obtained by a so-called (,e) experiment, i.e. the coincident detection of an inelastically scattered hard x-ray photon with its recoil electron. A monochromatized flux of 1012 photons s-1 at 150 keV from the high-energy x-ray wiggler beamline of the ESRF was directed onto thin graphite or fullerene targets. Comparison with a pseudopotential and a full-potential linear muffin-tin orbital calculation in the case of graphite is made. Inclusion of electron correlation via the Lam-Platzman correction is discussed. The experimental EMD of C60 shows stronger electron delocalization in the `buckyball' compared to graphite, which is supported by theory.

We have measured absolute triple differential cross sections for photo-double ionization of helium at 20 eV excess. The measurement covers the full ranges of energy sharing and emission angles of the two photoelectrons. We compare our data for selected geometries with the convergent close-coupling (CCC) calculations as well as 2SC calculations by Pont and Shakeshaft and 3C calculations by Maulbetsch and Briggs. In terms of the absolute magnitude and the trend in the shapes of the triple differential cross section for different geometries we find good agreement of the CCC and published 2SC calculations with our measurement, though differences with respect to the observed shape of individual patterns still exist.

We have measured the energy-momentum density of amorphous silicon dioxide using an $(e,2e)$ spectrometer with 20.8 keV incident, 19.6 keV scattered, and 1.2-keV ejected electron energies. The amorphous ${\mathrm{SiO}}_{2}$ sample was prepared by oxidizing a thin silicon membrane. The experimental data show a valence electronic structure characteristic of upper $p$-like and lower $s$-like bands. The width of the upper valence band is 10 eV. This is separated by 9 eV from the lower valence band, which exhibits 2-eV dispersion. We have calculated the energy-momentum density of \ensuremath{\alpha}-quartz using the ab initio linear muffin-tin orbital method and the result is spherically averaged over all crystal directions to enable comparison with the experiment. The calculated electron momentum densities show very good agreement with experiment for both the upper and lower valence bands. The theoretical prediction of the energy separation between the upper and lower valence bands is about 2 eV smaller than that measured and this discrepancy is discussed. The agreement between theory and experiment suggests that the short-range order in silicon dioxide plays an important role in determining the electronic structure of this material.

The purpose of this paper is to first give an overview of the information obtained by electron momentum spectroscopy (EMS) on the electronic structure of different forms of solid carbon (single crystal graphite, polycrystalline carbon, different forms of amorphous carbon, and fullerenes). We show for sp2 bonded carbon that, with decreasing order, the structures observed change but certain basic features remain. sp3-bonded carbon films and fullerene films both have electronic structures different from these graphitic films. The results of EMS are compared with the results of other spectroscopic and scattering techniques. It is argued that the combination of energy and momentum resolution is crucial in order to get a clear picture of the changes in the electronic structure due to the changes in atomic arangements. Only EMS resolves both energy and momentum for all these solids.

Laser light intensities, currently obtained in the laboratories, make it possible to observe many multi-photon phenomena in the interaction of light and matter (such as multi-photon ionisation or MPI process). Theoretical description of such phenomena necessitates the use of essentially non-perturbative framework. We present such an approach based on the recasting of the Schrodinger equation for the system atom+field into a set of coupled integral equations of the Lippmann–Schwinger type.

Electron momentum spectroscopy has been used to measure the electronic structure of aluminium after exposure to increasing amounts of oxygen. The experimental valence band results showed the structural features of aluminium oxide beginning to dominate the free electron contribution of metallic aluminium as the exposure increased. The interpretation of this is that the aluminium oxide layer increases in thickness as the exposure increases, eventually saturating at a thickness of about 15 A. After subtracting the intensity of the underlying Al metal contribution from the oxidised states the valence band features of aluminium oxide were resolved even after exposure to only 600 L of oxygen. It is estimated that only about 5 A of aluminium oxide is formed at this stage. A quantitative comparison was made to a linear muffin-tin orbital (LMTO) calculation for spherically averaged α-Al2O3. Best agreement was obtained for the results of the lowest oxygen exposure (600 L). The chemical shifts of the Al 2p core level were also measured in separate experiments for two intermediate oxygen exposures between the aluminium and aluminium oxide cases for further characterisation. These measurements show that electron momentum spectroscopy is able to obtain the electron bands and the momentum densities of very thin disordered surface layers.

The energy-resolved momentum densities of the valence band of a thin polycrystalline aluminium film have been measured using electron momentum spectroscopy (EMS). The spectrometer used for these measurements has estimated energy and momentum resolutions of 0.9 eV and 0.10 atomic units respectively. The valence band of aluminium was clearly resolved, resembling very closely that of a free-electron parabola. The measurement has been compared to linear muffin-tin orbital (LMTO) calculations for spherically averaged crystalline aluminium. A comparison has also been made between the experiment and Monte Carlo simulations which take into account additional elastic and inelastic scattering events not considered in the LMTO calculations. The final agreement obtained between the measurement and theory for the dispersion and relative intensities of the aluminium valence band is excellent when lifetime broadening of the band is allowed for.

Accurate knowledge of the intensity of focused ultrashort laser pulses is crucial to the correct interpretation of experimental results in strong-field physics. We have developed a technique to measure laser intensities approaching ${10}^{15}\phantom{\rule{0.28em}{0ex}}\text{W}/{\text{cm}}^{2}$ with an accuracy of 1$%$. This accuracy is achieved by comparing experimental photoelectron yields from atomic hydrogen with predictions from exact numerical solutions of the three-dimensional time-dependent Schr\"odinger equation. Our method can be extended to relativistic intensities and to the use of other atomic species.

The microwave absorption in a weak magnetic field H ⪡ H c ( T ) is reported in pure polycrystalline tin in the superconducting state near T c . A novel experimental technique is used which employs an ESR apparatus with the perpendicular configuration of the static and microwave magnetic fields and the radio-frequency modulation of the static field. This measurement is related to the true superconducting state of the bulk material. The characteristic decrease of the microwave absorption in a static magnetic field is detected at 0.8 T / T c ω / T c = 0.12 which is predicted by the microscopic theory of the surface impedance of type-I superconductors.