Bridging nano-optics and condensed matter formalisms in a unified description of inelastic scattering of relativistic electron beams

In the last decades, the blossoming of experimental breakthroughs in the domain of electron energy loss spectroscopy (EELS) has triggered a variety of theoretical developments. Those have to deal with completely different situations, from atomically resolved phonon mapping to electron circular dichroism passing by surface plasmon mapping. All of them rely on very different physical approximations and have not yet been reconciled, despite early attempts to do so. As an effort in that direction, we report on the development of a scalar relativistic quantum electrodynamic (QED) approach of the inelastic scattering of fast electrons. This theory can be adapted to describe all modern EELS experiments, and under the relevant approximations, can be reduced to most of the last EELS theories. In that aim, we present in this paper the state of the art and the basics of scalar relativistic QED relevant to the electron inelastic scattering. We then give a clear relation between the two once antagonist descriptions of the EELS, the retarded dyadic Green function, usually applied to describe photonic excitations and the quasi-static mixed dynamic form factor (MDFF), more adapted to describe core electronic excitations of material. Using the photon propagator in a material, expressed in the relevant gauges, as a tool to understand the interaction between a fast electron and a material, we extend this relation to a newly defined quantity, the relativistic MDFF. The relation between the dyadic Green function and the relativistic MDFF does depend only on the photon propagator and not on the specifics of the particle (here, a fast electron) probing the target. Therefore, it can be adapted to any spectroscopy where a relation between the electromagnetic and electronic properties of a material is needed. We then use this theory to establish two important EELS-related equations. The first one relates the spatially resolved EELS to the imaginary part of the photon propagator and the incoming and outgoing electron beam wavefunction, synthesizing the most common theories developed for analyzing spatially resolved EELS experiments. The second one shows that the evolution of the electron beam density matrix is proportional to the mutual coherence tensor, proving that quite universally, the electromagnetic correlations in the target are imprinted in the coherence properties of the probing electron beam.

An Impurity Effect for the Rates of the Interparticle Coulombic Decay

The interparticle Coulombic decay is a synchronized decay and ionization phenomenon occurring on two separated and only Coulomb interaction coupled electron binding sites. This publication explores how drastically small environmental changes in between the two sites, basically impurities, can alter the ionization properties and process rate, although the involved electronic transitions remain unaltered. A comparison among the present electron dynamics calculations for the example of different types of quantum dots, accommodating a one- or a two-dimensional continuum for the outgoing electron, and the well-investigated atomic and molecular cases with three-dimensional continuum, reveals that the impurity effect is most pronounced the stronger that electron is confined. This necessarily leads to challenges and opportunities in a quantum dot experiment to prove the interparticle Coulombic decay.

Feshbach-Fano Approach for Calculation of Auger Decay Rates Using Equation-of-Motion Coupled-Cluster Wave Functions: Theory and Implementation

<p>We present a novel methodology to calculate Auger decay rates based on equation-of -motion coupled-cluster singles and doubles (EOM-CCSD) wave function, combined with a simplified continuum orbital describing the outgoing electron. In our approach the Auger process is considered as an autoionization of a resonant electronic state, which can be described with Feshbach-Fano projection technique in order to distill the resonance parameters. To this end, we employ core-valence separation (CVS) scheme as a method to extract the bound part of the decaying many-electronic state. Main advantages of our methodology include (1) flexible EOM-CCSD ansatz enabling to describe various electronic states, (2) simple, yet universal computational setup, (3) fast computations due to fully analytical evaluation of all mixed bound-continuum two-electron integrals, and (4) implementation in general-purpose software package for quantum-chemical calculations.</p>

Feshbach-Fano Approach for Calculation of Auger Decay Rates Using Equation-of-Motion Coupled-Cluster Wave Functions: Theory and Implementation

<p>We present a novel methodology to calculate Auger decay rates based on equation-of -motion coupled-cluster singles and doubles (EOM-CCSD) wave function, combined with a simplified continuum orbital describing the outgoing electron. In our approach the Auger process is considered as an autoionization of a resonant electronic state, which can be described with Feshbach-Fano projection technique in order to distill the resonance parameters. To this end, we employ core-valence separation (CVS) scheme as a method to extract the bound part of the decaying many-electronic state. Main advantages of our methodology include (1) flexible EOM-CCSD ansatz enabling to describe various electronic states, (2) simple, yet universal computational setup, (3) fast computations due to fully analytical evaluation of all mixed bound-continuum two-electron integrals, and (4) implementation in general-purpose software package for quantum-chemical calculations.</p>

Filtering spins by scattering from a lattice of point magnets

Nature creates electrons with two values of the spin projection quantum number. In certain applications, it is important to filter electrons with one spin projection from the rest. Such filtering is not trivial, since spin-dependent interactions are often weak, and cannot lead to any substantial effect. Here we propose an efficient spin filter based upon scattering from a two-dimensional crystal, which is made of aligned point magnets. The polarization of the outgoing electron flux is controlled by the crystal, and reaches maximum at specific values of the parameters. In our scheme, polarization increase is accompanied by higher reflectivity of the crystal. High transmission is feasible in scattering from a quantum cavity made of two crystals. Our findings can be used for studies of low-energy spin-dependent scattering from two-dimensional ordered structures made of magnetic atoms or aligned chiral molecules.

On the Accurate Description of Photoionization Dynamical Parameters

Calculation of dynamical parameters for photoionization requires an accurate description<br>of both initial and final states of the system, as well as of the outgoing electron.<br>We here show, that using a linear combination of atomic orbitals (LCAO) B-spline density<br>functional (DFT) method to describe the outgoing electron, in combination with<br>correlated equation-of-motion coupled cluster singles and double (EOM-CCSD) Dyson<br>orbitals, gives good agreement with experiment and outperforms other simpler approaches,<br>like plane and Coulomb waves, used to describe the photoelectron. Results<br>are presented for cross sections, angular distributions and dichroic parameters in chiral<br>molecules, as well as for photoionization from excited states. We also present a comparison<br>with the results obtained using Hartree-Fock (HF) and density-functional theory<br>molecular orbitals selected according to Koopmans’ theorem for the bound states.

On the Accurate Description of Photoionization Dynamical Parameters

Calculation of dynamical parameters for photoionization requires an accurate description<br>of both initial and final states of the system, as well as of the outgoing electron.<br>We here show, that using a linear combination of atomic orbitals (LCAO) B-spline density<br>functional (DFT) method to describe the outgoing electron, in combination with<br>correlated equation-of-motion coupled cluster singles and double (EOM-CCSD) Dyson<br>orbitals, gives good agreement with experiment and outperforms other simpler approaches,<br>like plane and Coulomb waves, used to describe the photoelectron. Results<br>are presented for cross sections, angular distributions and dichroic parameters in chiral<br>molecules, as well as for photoionization from excited states. We also present a comparison<br>with the results obtained using Hartree-Fock (HF) and density-functional theory<br>molecular orbitals selected according to Koopmans’ theorem for the bound states.

The collision of slow electrons with atoms. III.—The excitation and ionization of helium by electrons of moderate velocity

It has been shown that quantum mechanical methods are capable of providing a general explanation of the phenomena observed in the excitation of helium by the impact of low velocity electrons. Thus a well-known feature of the observations is that the probability of excitation of a triplet state attains a maximum for electrons of much lower velocities of impact than in the case of the singlet state and falls off very much more rapidly as the velocity increases. By using Born’s method of approximation and taking into account electron exchange the variation of excitation probability with velocity of impact has been calculated for various singlet and triplet levels of helium for energies between the resonance potential and 60 volts. When one compares the observed and calculated curves it is found that qualitative but not quantitative agreement is obtained. It is therefore necessary to improve the methods of calculation and an attempt was made to do this by taking into account the distortion of the incident and outgoing electron waves by the fields of the normal and excited atom respectively. As a result it was then found possible to explain the diffraction effects observed in the inelastic scattering of electrons at large angles but the calculated variation of cross-section with velocity is still not satisfactory. In order to improve the theory it is important to determine the range of validity of the simple method of approximation by extending the calculations to higher velocities of impact (up to 400 volts) where the method should be more accurate. This is of special interest in view of the recent experimental measurements of Lees and of Thiem who have measured the excitation functions of the various helium lines for electron energies up to, and in certain cases greater than 400 volts. In this paper we have extended the calculations in this way and have considered also ionizing collisions. Since the probability of ionization by electrons can be measured with considerable accuracy we can apply a very satisfactory test of the theory in this direction. In addition to the probabilities of ionization of hydrogen and helium the velocity and angular distributions of ejected and scattered electrons are also computed. The comparison of calculated and observed results is discussed in detail and it is found that Born’s approximation is valid for electrons with energies greater than 200 volts.