Electron Momentum Distribution Research Articles

Electron momentum spectroscopy investigation on electronic structure of iso-dichloroethylene valence shell

Here an electron momentum spectroscopy study on the electronic structure of valence shell of iso-dichloroethylene molecule is reported. The experiment is carried out with a binary (e, 2e) spectrometer at incident electron energy of 1200 eV, employing noncoplanar symmetric arrangement. The binding energy spectra and electron momentum distributions (EMDs) of iso-dichloroethylene valence shell have been obtained. Theoretical EMDs are predicted with both Hartree-Fock and density functional theory methods, generally indicating good agreements with the measurement results. The interference effect is observed to significantly influence the EMDs of 2a2 and 5b2 Cl lone-pair orbitals.

Modelling a Transition-Edge Sensor X-Ray Microcalorimeter Linear Array for Compton Profile Measurements and Energy Dispersive Diffraction

Transition-edge sensors are a type of superconducting detector that offers high energy resolution based on their sharp resistance-temperature feature in the superconducting-to-normal transition. TES X-ray microcalorimeters have typically been designed and used for spectroscopic applications. In this work, we present a design optimization for a TES X-ray microcalorimeter array for high-energy scattering and diffraction measurements. In particular, Compton scattering provides information about the electron momentum distribution, while energy dispersive diffraction provides structural information about dense engineering materials. Compton scattering and energy dispersive diffraction experiments must be conducted in the very hard X-ray regime (~ 100 keV), demanding a high X-ray stopping power in the detector; therefore, an absorber with a large heat capacity is needed in conjunction with the TES. In addition, both applications would benefit from an array composed of parallel strips. We present a design for a TES X-ray microcalorimeter optimized for such applications. In particular, we model the longitudinal position dependence due to the finite thermal diffusion time in the absorber.

Electron Polarimetry with Nonlinear Compton Scattering

Impacts of spin-polarization of an ultrarelativistic electron beam head-on colliding with a strong laser pulse on emitted photon spectra and electron dynamics have been investigated in the quantum radiation regime. We simulate photon emissions quantum mechanically and electron dynamics semiclassically via taking spin-resolved radiation probabilities in the local constant field approximation. A small ellipticity of the laser field brings about an asymmetry in angle-resolved photon spectrum, which sensitively relies on the polarization of the electron beam. The asymmetry is particularly significant in high-energy photon spectra, and is employed for the polarization detection of a high-energy electron beam with extraordinary precision, e.g., better than 0.3\% for a few-GeV electron beam at a density of the scale of $10^{16}$ cm$^{-3}$ with currently available strong laser fields. This method demonstrates for the first time a way of single-shot determination of polarization for ultrarelativistic electron beams via nonlinear Compton scattering. A similar method based on the asymmetry in the electron momentum distribution after the interaction due to spin-dependent radiation reaction is proposed as well.

Magnetic reconnection and impulsive instabilities in tokamak plasmas: Some analogies with astrophysical flares

Four kinds of tokamak plasma dynamical processes are described, which could be of interest for a comparative study with events such as solar and astrophysical flares. The first two processes are related to instabilities with different mechanism and different spatial location (violation of the Kruskal–Shafranov limit around the plasma center in one case and violation of a pressure gradient limit at the plasma edge in the other case); nevertheless, both result in similar cycles of slow accumulation and rapid release of energy. The third process is related to a kinetic instability of the electron momentum distribution: beamed electrons can destabilize plasma waves, which in turn transfer energy to electron motion perpendicular to the magnetic field, resulting in enhanced synchrotron emission. Cycles with slow accumulation and rapid release are observed here too. The fourth kind of event consists in the disruption of a current channel, during which a substantial fraction of the stored magnetic energy is transferred to a population of relativistic electrons.

Angular distribution of multiple Compton scattered gamma rays of 662 keV in tin

In multiple Compton scattering, the incident gamma photon is scattered more than once due to finite dimensions of the sample. It serves as a noise for the exact evaluation of electron momentum distribution in Compton profile, Compton cross section and non-destructive testing of in-assessable large samples. To overcome these difficulties, there is a need to characterise the contribution of multiple scattering as a function of atomic number, scattering angle and incident gamma photon energy. In the present work, measurements are carried out to investigate the multiple scattering of 662 keV photons with tin sample of different thickness in the forward and backward hemispheres. The scattered photon flux is recorded by a NaI(Tl) scintillation detector and with an HPGe solid-state detector to check for the trend of saturation thickness as a function of resolution of the detector. The number of multiply scattered photons is found to be increasing with the sample thickness up to a particular thickness value called saturation thickness beyond which it remains constant with increase in target thickness. The effect of detector collimator size on multiply scattered photons is also studied. Both the detectors show the same trend of saturation thickness as a function of thickness. Angular distribution of multiply scattered photons shows symmetry around 90° scattering angle. The low energy side of multiple scattered photon spectrums is also characterised as a function of sample thickness and order of scattering. Monte Carlo calculations support the present experimental results.

Controlling non-sequential double ionization with chirped laser pulse

The non-sequential double ionization (NSDI) of He in a chirped few-cycle laser pulse is studied using a full-dimensional semi-classical model. The NSDI probability is found to be very sensitive to the rate of wavelength change. An abrupt jump is found in the probability distribution during the crossover from up- to down-chirped pulse, followed with a further increase of the probability when keep increasing the rate of wavelength change. In the meantime, the correlated electron momentum distribution transfers from anti-correlated to a correlated pattern. Further analysis reveals the underlying mechanism to be the increase of the kinetic energy of returned electron acquired from the chirped pulse in the re-collision process. The dominant NSDI mechanism transfers from recollision-induced excitation with subsequent field ionization (RESI) to electron-impact ionization (EI). Therefore, the chirped laser pulse could be a useful tool for controlling the electron dynamics in NSDI and beyond.

Anisotropic ultrafast optical response of terahertz pumped graphene

We have measured the ultrafast anisotropic optical response of highly doped graphene to an intense single cycle terahertz pulse. The time profile of the terahertz-induced anisotropy signal at 800 nm has minima and maxima repeating those of the pump terahertz electric field modulus. It grows with increasing carrier density and demonstrates a specific nonlinear dependence on the electric field strength. To describe the signal, we have developed a theoretical model that is based on the energy and momentum balance equations and takes into account optical phonons of graphene and the substrate. According to the theory, the anisotropic response is caused by the displacement of the electronic momentum distribution from zero momentum induced by the pump electric field in combination with polarization dependence of the matrix elements of interband optical transitions.

Development of a 3-D energy-momentum analyzer for meV-scale energy electrons

In this article, we report on the development of a time-of-flight based electron energy analyzer capable of measuring the 3-D momentum and energy distributions of very low energy (millielectronvolt-scale) photoemitted electrons. This analyzer is capable for measuring energy and 3-D momentum distributions of electrons with energies down to 1 meV with a sub-millielectronvolt energy resolution. This analyzer is an ideal tool for studying photoemission processes very close to the photoemission threshold and also for studying the physics of photoemission based electron sources.

Nonsequential double ionization by co-rotating two-color circularly polarized laser fields.

Nonsequential double ionization (NSDI) of Ar in co-rotating two-color circularly polarized (TCCP) laser fields is investigated with a three-dimensional classical ensemble model. Our numerical results indicate that co-rotating TCCP fields can induce NSDI by recollision process, while the yield is an order of magnitude lower than counter-rotating case. NSDI yield in co-rotating TCCP fields strongly depends on field ratio of the two colors and achieves its maximum at a ratio of 2.4. In co-rotating TCCP fields, the short recollision trajectory with traveling time smaller than one cycle is dominant. Moreover, the recollision time in co-rotating TCCP laser fields depends on the field ratio, which is mapped to the electron momentum distribution. This provides anavenue to obtain information about recollision time and access the subcycle dynamics of the recollision process.

Compton profile of VO2 across the metal-insulator transition: Evidence of a non-Fermi liquid metal

Many-body diffusion Monte Carlo is used to obtain the first-principles momentum distribution and Compton profile of vanadium dioxide. Our results for the Compton profile are in good agreement with the experimental values, and we show that good qualitative agreement in the scaled Compton profile difference across the monoclinic to rutile phase transition depends on an accurate description of electron correlation. The electron momentum distribution enables new insights into the metal-insulator phase transition. For example, the probability for electron scattering in the proximity of the Fermi surface (forward scattering) is suppressed in the vanadium chain direction (rutile $c$ axis) but enhanced in perpendicular directions. However, along the $c$ axis we observe an increase at $\ensuremath{\sim}2{k}_{\mathrm{F}}$ in the momentum distribution, which is characteristic for Friedel oscillations (backscattering). Our analysis of the momentum distribution supports experimentally observed anisotropies and provides an explanation for the anomalously low electronic thermal conductivity observed recently in the metallic phase [S. Lee et al., Science 355, 371 (2017)]. Moreover, our results indicate non-Fermi liquid behavior as well as quasi-one-dimensional Friedel oscillations in the metallic rutile phase, which is reminiscent of a Tomanaga-Luttinger liquid with impurities.

Third-order S-matrix study of electron-electron correlation in nonsequential double ionization

Correlated electron momentum distribution of nonsequential double ionization of a Ne atom in intense laser fields is calculated using a third-order S-matrix formalism which takes into account the interaction between the Coulomb potential of the parent ion and the photoelectrons. Compared to the second-order S-matrix calculation, the correlation distributions of the two processes which take into account the effect of the ionic Coulomb potential on either of the two ionized electrons after their collision tend to be concentrated off the diagonal of the first and third quadrants, which are closer to the experimental observations. Our further analysis shows that this modification to the second-order calculation is due to the fact that, scattering of the emitted electron upon the parent ion will alter the photoelectron angular distribution from concentration in the laser direction to focus in a direction deviating from the laser field. And this will significantly reduce the momentum of the electron in the direction of the laser field. Our results are in accord with previous studies which reveal that electron-nuclear Coulomb interaction, electron-electron collision and the final-state electron repulsion all play significant roles in the formation of the fingerlike structure.

Identification of tunneling and multiphoton ionization in intermediate Keldysh parameter regime.

Quantitative identification of tunneling ionization (TI) and multiphoton ionization (MPI) with Keldysh parameter γ in intermediate regime is of great importance to better understand various ionization-triggered strong-field phenomena. We theoretically demonstrate that the numerical observable ionization delay time is a more reliable indicator for characterizing the transition from TI to MPI under different laser parameters. Using non-linear iterative curve fitting algorithm (NICFA), the detected time-dependent probability current of ionized electrons can be decoupled into weighted TI and MPI portions. This enables us to confirm that the observed plateau-like structure in ionization delay time picture at the intermediate γ originates from the competition between TI and MPI processes. A hybrid quantum and classical approach (HQCA) is developed to evaluate the weights of TI and MPI electrons in good agreement with NICFA result. Moreover, the well separated TI and MPI electrons using HQCA are further propagated classically for mapping their final momentum, which well reproduces the experimental or ab-initio numerical calculated signatures of ionized electron momentum distribution in a rather broad γ regime.

Determining the carrier-envelope phase of relativistic laser pulses via electron-momentum distribution

The impacts of the carrier-envelope phase (CEP) of a long relativistic tightly-focused laser pulse on the dynamics of a counter-propagating electron beam have been investigated in the, so-called, electron reflection regime, requiring the Lorentz factor of the electron $\gamma$ to be approximately two orders of magnitudes lower than the dimensionless laser field parameter $\xi$. The electrons are reflected at the rising edge of the laser pulse due to the ponderomotive force of the focused laser beam, and an asymmetric electron angular distribution emerges along the laser polarization direction, which sensitively depends on the CEP of the driving laser pulse for weak radiative stochastic effects. The CEP siganatures are observable at laser intensities of the order or larger than $10^{19}$ W/cm$^2$ and the pulse duration up to 10 cycles. The CEP detection resolution is proportional to the electron beam density and can achieve approximately $0.1^{\circ}$ at an electron density of about $10^{15}$ cm$^{-3}$. The method is applicable for currently available ultraintense laser facilities with the laser peak power from tens of terawatt to multi-petawatt region.

On the magnetization and the radiative efficiency of BL Lac jets

Theoretical modelling and observations of AGN jets suggest that the non-thermal electrons emitting the observed radiation should (i) carry an amount of energy comparable to the magnetic fields ($U_e\sim U_B$), which is likely the case if the magnetic fields play a dynamically important role in the jet's acceleration process; (ii) cool efficiently in a dynamical time ($t_{\rm cool}\lesssim t_{\rm dyn}$), which is suggested by the fact that a large fraction of the jet's kinetic energy is promptly converted into radiation. These expectations are at odds with the results of the simplest one-zone Self-Synchro-Compton (SSC) model for the Spectral Energy Distribution (SED) of BL Lacs. Indeed, the model predicts $U_e\gg U_B$ and $t_{\rm cool}\gg t_{\rm dyn}$ for most of the objects. Here we closely investigate one of the key assumptions of this model, namely that the momentum distribution of the non-thermal electrons is isotropic. We find that this assumption may be an oversimplification. If the magnetic energy is dissipated via a turbulent MHD cascade, the highest energy electrons may instead retain a small pitch angle. Since the synchrotron emissivity is suppressed when the pitch angle is small, this effect may importantly affect the modelling of the SED. As an illustrative example, we present an anisotropic model for the electron momentum distribution such that $U_e\sim U_B$ and $t_{\rm cool}\lesssim t_{\rm dyn}$ at the same time. Our model manages to simultaneously solve the two problems with one only more free parameter with respect to the usual isotropic one-zone SSC model.

Vibrational effects on electron momentum distributions of outer valence orbitals of benzene**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300).

The outer valence electron momentum distributions of benzene are reinvestigated with theoretical calculations involving the vibrational effects. The results are compared with recent experimental measurements [Phys. Rev. A 98 042705 (2018)]. The significant discrepancies between theories and experiments in previous works have now been interpreted quantitatively, indicating that the vibrational motion in benzene molecule has noticeable influence on its electron momentum distributions.

Longitudinal momentum of the electron at the tunneling exit

The longitudinal momentum of the electron at the tunneling exit is a useful quantity to make sense of the tunneling ionization process. It was usually assumed to be zero from a classical argument, but recent experiments show that it must be nonzero in order to explain the measured electron momentum distributions. In this article we show that the flow momentum of the probability fluid is a sensible quantum mechanical definition for tunneling-exit momentum, and it can be (and in general is) nonzero at the tunneling exit point where the kinetic energy is zero by definition. We show that this longitudinal momentum is nonzero even in the static or adiabatic limit, and this nonzero momentum is a purely quantum mechanical effect determined by the shape of the wave function in the vicinity of the tunneling exit point. Nonadiabaticity or finite wavelength may increase this momentum substantially, and the detailed value depends on both the atomic and the laser parameters.

A co-axial velocity map imaging spectrometer for electrons

We present the design of an electron velocity map imaging (VMI) spectrometer where the ionizing laser source propagates along the symmetry axis of the spectrometer. The co-axial geometry is useful in a variety of experiments, because it provides a unique 2-dimensional projection of the 3-dimensional electron momentum distribution. Initial simulations show that this co-axial VMI can work with both high energy (more than 100 eV) and low energy (tens of eV) electrons. We demonstrate the performance of this co-axial VMI spectrometer at the Linac Coherent Light Source X-ray Free Electron Laser facility.

Gamma and neutron radiation effect on Compton profile of the multi-walled carbon nanotubes

In this study it has been investigated the effect of gamma and neutron radiation on the electron momentum distribution (Compton profile) of the Multiwall Carbon Nanotube (MWCNT) using a Compton spectrometer with an annular 241Am radioactive source. The samples were irradiated with 10 kGy (kGy) gamma rays, thermal and fast neutrons. The photons emitted from the 241Am source were incident on the irradiated samples and the scattered photons from the samples were recorded using HPGe detector. Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM) results are also given to show the changes at the atomic structure of the MWCNT. The results clearly show that the Compton profile of multi-walled carbon nanotubes has changed with gamma and neutron irradiation. These changes are attributed to the delocalization of the electrons in the sample (in real space) which is clearly seen in the increased height of Compton profile of MWCNT at low momentum range (localization in momentum space) during sample’s irradiation.

Direct Experimental Access to the Nonadiabatic Initial Momentum Offset upon Tunnel Ionization

We report on the nonadiabatic offset of the initial electron momentum distribution in the plane of polarization upon single ionization of argon by strong field tunneling and show how to experimentally control the degree of nonadiabaticity. Two-color counter- and corotating fields (390 and 780nm) are compared to show that the nonadiabatic offset strongly depends on the temporal evolution of the laser electric field. We introduce a simple method for the direct access to the nonadiabatic offset using two-color counter- and corotating fields. Further, for a single-color circularly polarized field at 780nm, we show that the radius of the experimentally observed donutlike distribution increases for increasing momentum in the light propagation direction. Our observed initial momentum offsets are well reproduced by the strong-field approximation. A mechanistic picture is introduced that links the measured nonadiabatic offset to the magnetic quantum number of virtually populated intermediate states.

Electron momentum spectroscopy study of outer valence electronic structure of pyrrole

The binding energy spectrum and electron momentum distributions (EMDs) for the outer valence shells of pyrrole molecule are measured by a high-sensitivity (e, 2e) spectrometer at incident energy of 1200 eV plus the binding energy employing non-coplanar symmetric kinematic geometry. The obtained EMDs are compared with the theoretical calculations at equilibrium molecular geometry as well as considering vibrational effect by density functional theory method. The result shows that the molecular vibrational motion has obvious influence on EMDs for some of the outer valence orbitals. The controversy over the assignment of the ionization bands, especially the positions of satellite states concerning the ionization of 1b1 orbital, in the binding energy range of 11–16.5 eV has been clarified.