Total Momentum Transfer Research Articles

Electron scattering cross sections from NH3: a comprehensive study based on R-matrix method

In this study, a comprehensive cross-sectional computation on the electron scattering from NH3 was performed using the frame of the R-matrix method. Cross section sets for total elastic, differential, momentum transfer, total ionization, and electronic excitation are presented. The electron-impact dissociation of NH3 to NHH and NH+H2 was considered by summing up the cross sections for the molecular dissociative excitations to the correlated dissociation channels. The reported cross sections for vibrational excitation of NH3 remain controversial and are unable to distinguish the N–H symmetric and asymmetric stretching modes of close frequencies. Here, the excitation cross section for each vibrational mode of NH3 was computed by applying the theoretical approach combining the fixed-nuclei R-matrix method, normal mode approximation and the vibrational frame transformation. The uncertainties of the cross section sets computed in this study were estimated for convenience of use in the plasma modeling.

Convergent close-coupling calculations of positron scattering from atomic carbon

We report on the extension of the single-center convergent close-coupling method to positron scattering on multielectron atoms, along with the development of a technique for separating the direct ionization and positronium-formation channels in single-center calculations. We have performed calculations of positron scattering on carbon and present total elastic, momentum transfer, excitation, direct ionization, total ionization, total inelastic, positronium-formation, stopping power, and total cross sections from threshold to 5000 eV. We also present oscillator strengths, the scattering length, the hidden Ramsauer-Townsend minimum, the energy of the positron-carbon virtual state, and the mean excitation energy. Agreement with electron-scattering experiment and positron-scattering theory for several cross sections has been demonstrated for high energies. However, discrepancies exist between different theoretical methods at lower energies and for the ionization and positronium-formation processes.

Neural network model of neutral beam injection in the EAST tokamak to enable fast transport simulations

The neutral beam injection (NBI) system in EAST produces energetic neutral particles, which collide with electrons and ions in tokamak plasmas and heat the plasmas through Coulomb collisions. Moreover, it drives a non-inductive source of current, due to the charge-exchange collision between neutral particles and ions, and injects toroidal torque, which generates a toroidal rotation of the plasma. The effect caused by the NBI system, such as plasma heating, current drive, total neutron rate, momentum transfer, and shine-through, are modeled by a comprehensive module called NUBEAM. However, NUBEAM is computationally intensive since it relies on Monte Carlo methods. In this work, a neural network model has been developed as a surrogate model for NUBEAM in EAST. The database for neural-network model training, validation and testing is generated by running TRANSP for experimental discharges from recent EAST campaigns (after the latest NBI upgrade) while using the NUBEAM module. Simulation results illustrate that the trained neural network has the capability of replicating the predictions made by NUBEAM while demanding a significantly shorter execution time. These results indicate that surrogate models like the one proposed in this work could enable fast transport simulations for EAST after integrating them into a control-oriented predictive code such as COTSIM.

Elastic and inelastic low-energy electron scattering from pyridine.

A comprehensive investigation of elastic and inelastic electron scattering from molecular pyridine is reported using the ab initio R-matrix method with the static exchange plus polarization and close-coupling approximations for incident energies up to 10eV. The two well-known low-lying 1 2B1 and 1 2A2 shape resonances as well as a 2 2B1 mixed-character resonance compare well with the theoretical and experimental results. We also detect five core-excited resonances (1 2A1, 1 2B2, 3 2B1, 2 2A2, and 4 2B1), which lie above the first electronic excitation threshold. The total elastic cross sections and momentum transfer cross sections agree reasonably with previous reference data. Comparisons of the differential elastic cross sections of pyridine with those measured for benzene, pyrazine, and pyrimidine show remarkable agreement at scattering angles above 40° but behave differently for forward scattering below 40° below 6eV, due to the dominant effect of the permanent dipole moment on the differential cross section in the low energy region with narrow scattering angles. Inelastic electronic excitation cross sections are presented, showing the influence of core-excited resonances below the ionization threshold for the first time.

Elastic Scattering of Electron and Positron by Radium and Radon Atoms

The Differential Cross Sections (DCS's), Total Cross Sections (TCS's) and Momentum Transfer Cross Sections (MTCS's) of electron and positron scattering by radium and radon atoms were calculated in the range of energy (5–500) eV using a total potential consisting of combining the static, exchange and polarization potentials at long distances. In addition, the correlation potential of Perdew–Zunger at short distances for electrons was used, as well as the correlation potential of Jain for positrons. The exchange potential for positrons was neglected. In this study, a good agreement with other experimental values and theoretical values of many investigators was found.

Time-dependent forces between a swift electron and a small nanoparticle within the dipole approximation

In this paper we calculate the time-dependent forces between a swift electron traveling at constant velocity and a metallic nanoparticle made of either aluminum or gold. We consider that the nanoparticle responds as an electric point dipole and we use classical electrodynamics to calculate the force on both the nanoparticle and the electron. The values for the velocity of the electron and the radius of the nanoparticle were chosen in accordance with electron microscopy observations, and the impact parameter was selected to fulfill the constraints imposed by the dipole approximation. We found that there are times when the force on the nanoparticle is attractive and others when it is repulsive, and show that this is due to the delayed electromagnetic response of the nanoparticle. To establish the limits of validity of our approach, we calculate the total linear momentum transfer to the nanoparticle, and compare it with results obtained, in frequency space, using the full multipole expansion of the fields induced on the nanoparticle, considering the effects of electromagnetic radiation.

Revisiting the limits of photon momentum based optical power measurement method, employing the case of multi-reflected laser beam

In this work, we review the viability and precision of the photon-momentum-based optical power measurement method that employs an amplification effect caused by a multi-reflected laser beam trapped in an optical cavity. Measuring the total momentum transfer of the absorbed and re-emitted photons from a highly reflective surface (reflection of the laser beam from an optical mirror) as a force provides the possibility of measuring the optical power with direct traceability to SI units. Trial measurements were performed at two different metrology laboratories: the laboratory for mass/force at the Technical University of Ilmenau, and the clean room laser radiometry laboratory at PTB, with a portable force measurement setup consisting of two electromagnetic force compensation balances. We compared the results of the optical power measurements performed with the force measurement setup, via the photon-momentum-based method, with those performed using a calibrated reference standard detector traceable to PTB’s primary standard for optical power, the cryogenic radiometer. The comparison was carried out for an optical power range between 1 W and 10 W at a wavelength of 532 nm, which corresponds to a force of approximately 2000 nN at the upper limit, yielding approximately 2.3% relative standard uncertainty in the case of 33 reflections. Thus, conflating the high-precision force metrology technique at μN to nN levels with the optical setup required to achieve specular multi-reflection configuration of the laser beam, where a macroscopic optical cavity with ultra-high reflective mirrors (>99.995%) can adjustably be suspended from the force sensors, depending on required geometry of reflections, we show that the uncertainty of the optical power measurements upon further increase of the nominally applied optical power, the number of laser beam reflections, or the reflectivity coefficient of the mirrors can be markedly reduced.

Study of kaon structure using the light-cone quark model

We investigate the various distributions explaining multi-dimensional structure of kaon at the level of its constituents ($u$ and $\bar{s}$) using the light-cone quark model. The overlap form of wavefunctions associated with the light-cone quark model is adopted for the calculations. The generalized parton distributions(GPDs)of $u$ and $\bar{s}$ quarks are presented for the case when the momentum transfer in the longitudinal direction is non-zero. The dependence of kaon GPDs is studied in terms of variation of quark longitudinal momentum fraction, momentum transfer in longitudinal direction and total momentum transfer to the final state of hadron. The transverse impact-parameter dependent GPDs are also studied by taking the Fourier transformation of general GPDs. Further, the quantum phase-space distributions; Wigner distributions are studied for the case of unpolarized, longitudinally-polarized and transversely-polarized parton in an unpolarized kaon. The Wigner distributions are analysed in the transverse impact-parameter plane, the transverse momentum plane and the mixed plane. Further, to get a complete picture of kaon in terms of its valence quarks, the variation of longitudinal momentum fraction carried by quark and antiquark in the generalized transverse momentum-dependent parton distributions (GTMDs) is studied for different values of transverse quark and antiquark momentum $({\bf k}_\perp)$ as well as for different values of momentum transferred to the kaon in transverse direction $({\bf \Delta}_\perp)$. This has been done for zero as well as non-zero skewedness representing respectively the absence and presence of momentum transfer to the final state of kaon in longitudinal direction. Furthermore, the possible spin-orbit correlation for $u$ and $\bar{s}$ in kaon is elaborated in context of Wigner distributions and GTMDs.

Multiquark matrix elements in the proton and three gluon exchange for exclusive ηc production in photon-proton diffractive scattering

Exclusive production of a $\eta_c$ pseudo-scalar meson in $\gamma^{(*)} + p \to \eta_c + p$ scattering at high energies involves a ${\cal C}$-odd exchange in the $t$-channel. We formulate the description of this process within the high-energy framework of eikonal dipole scattering. We obtain expressions for the light-cone wave function of the $\eta_c$ required in this framework as well as for the ${\cal C}$-odd amplitudes due to exchange of a single photon, of a photon plus two gluons, and of three gluons. We relate these amplitudes to correlators of the $+$ component of the quark current in the light-cone wave function of the proton. For high transverse momenta these correlators correspond to Generalized Parton Distributions (GPDs) given by diagrams where all exchanged gauge bosons attach to a single quark in the proton. Diagrams involving multi-quark matrix elements potentially sensitive to correlations, screen infrared singularities. Moreover, they are numerically important for configurations where the exchanged bosons nearly share the total momentum transfer. Using two simple models for the three quark Fock state of the proton at $x\simeq0.1$, we find that single photon exchange dominates for $|t|<1.5$~GeV$^2$. Here, the quark GPD could be measured cleanly in $\gamma^{(*)} + p \to \eta_c + p$ via single photon exchange. For higher momentum transfer three gluon (`Odderon') exchange is dominant.

Analytical approach to Coulomb focusing in strong-field ionization. I. Nondipole effects

The role of the Coulomb potential of the atomic core for creation of caustics in the photoelectron momentum distribution for tunneling ionization in a linearly polarized strong laser field, usually termed as Coulomb focusing, is investigated within classical theory beyond the dipole approximation. Coulomb focusing is addressed by analytical calculation of Coulomb momentum transfer to the tunneled electron due to rescatterings, while applying perturbation theory and classifying the recollisions either as fast or as slow. The accuracy of the obtained analytical formulas for the Coulomb momentum transfer is investigated by analytical derivation of asymptotic photoelectron momentum distribution and its comparison to exact numerical calculations. With the help of the applied analytical treatment, we analyze the origin of the counterintuitive energy-dependent bend of the Coulomb focusing cusp in the photoelectron momentum distribution in a linearly polarized laser field in the non-dipole regime, and its scaling with the field parameters. The importance of high-order recollisions is also investigated and they are shown to be responsible for a decrease of the bend of the cusp at very low energies in this regime. In general, the momentum transfer caused by high-order rescattering events, while being a perturbation with respect to the instantaneous electron momentum at the rescattering, is shown to induce a significant non-perturbative contribution to the total momentum transfer.

Analytical approach to Coulomb focusing in strong-field ionization. II. Multiple recollisions

An analytical method for treating Coulomb focusing in strong-field ionization in a linearly polarized laser field has been proposed in the first paper of this series, where analytical formulas have been derived for the Coulomb momentum transfer to the tunneled electron at the tunnel exit and due to rescatterings. In this paper, we analytically investigate a buildup of the Coulomb momentum transfer during multiple laser driven recollisions of the tunneled electron on the parent ion. We find that the momentum transfer at rescattering events, while being a perturbation with respect to the instantaneous electron momentum at the rescattering, induces a significant nonperturbative contribution to the total momentum transfer. Moreover, we show that the higher-order recollisions contribute considerably to the total momentum transfer and cannot be omitted for the proper description of the Coulomb focusing. We also show that our analytical approach to Coulomb focusing is well suitable for proper description of the Coulomb focusing cusps of the photoelectron momentum distribution at energies larger than 50 meV.

Total momentum transfer produced by the photons of a multi-pass laser beam as an evident avenue for optical and mass metrology.

The use of the radiation pressure of a laser field, as an effect of the momentum transfer of the absorbed and re-emitted photons, suggests rather a complementary than an alternative possibility for metrology to generate calibration forces or to calibrate the optical power directly traceable to the International System of Units (SI). This paper reports a method and experimentally measured evidence on options to extend the effective use of radiation pressure for generating optical forces in the sub-microNewton (μN) range. Among other features and results presented, we emphasize the variability in controlling the accuracy of these forces through the proper utilization of the power of a multi-pass laser beam (semi- or completely) locked within confined systems. The direct measurements of these forces, augmented due to the partial or total momentum transfer of the photons of a multi-pass laser beam extended from several hundreds of picoNewton (pN) up to sub-μN range for the same power of laser source, are done by a precision force measurement system and compared with basic theoretical computations. We also discuss the opportunities to probe the fundamental physical limits associated with this method and to the considerable extent other competing contributing effects that might be regarded as sources of errors in metrological tasks.

Rotational Doppler shift induced by spin-orbit coupling of light at spinning metasurfaces

The interaction of light with spinning objects can lead to a frequency shift as a result of the transferred angular momentum. Subwavelength plasmonic nanostructures on an optical surface provide an efficient platform for local light manipulation and thus can be utilized for such momentum exchanges. Here we demonstrate reflective-type plasmonic metasurface q-plates based on the geometric Pancharatnam-Berry phase that are capable of changing the spin and orbital angular momentum of light. When these metasurfaces rotate at a constant angular speed, we observe a rotational Doppler frequency shift of the reflected light, which depends on the total angular momentum transfer. The flexibility in the design of the metasurfaces even enables complex reflective phase masks that can transfer different orbital angular momenta, at the same time, to the beam. Our experiments show that such complex metasurface phase masks can be used to obtain spatially variant Doppler shift in the reflected beam profile.

Spin-orbit optomechanics of optically levitated chiral Bragg microspheres

We explore the spin-orbit nature of the optical torque exerted on chiral liquid-crystal microspheres exhibiting circular Bragg reflection. Experimental investigation relies on the direct optomechanical observation of spinning liquid-crystal droplets immersed in water and held in a circularly polarized laser levitator. More generally, we anticipate that the total angular momentum transfer per photon may depart from the commonly assumed spin-only $\ifmmode\pm\else\textpm\fi{}2\ensuremath{\hbar}$ contribution, when the topological features of the illuminated microsphere are taken into account.

Cross sections for electron collision with difluoroacetylene

We report a detailed calculation of total elastic, differential elastic, momentum transfer and electronic excitation for electron impact on difluoroacetylene (C2F2) molecules using the R-matrix method at low energies. After testing many target models, the final results are reported for the target model that gave the best target properties and predicted the lowest value of the shape resonance. The shape resonance is detected at 5.86 eV and 6.49 eV with the close-coupling and static exchange models due to 2Πg (2B2g, 2B3g) states. We observed that the effect of polarization becomes prominent at low energies below 4 eV, decreasing the magnitude of the elastic cross section systematically as it increases for C2F2. We have also computed elastic cross sections for C2H2, C2F4 and C2H4 with a similar model and compared with the experimental data for these molecules along with C2F2. General agreement is found in terms of the shape and nature of the cross section. Such a comparison shows the reliability of the present method for obtaining the cross section for C2F2. The calculation of elastic scattering cross section is extended to higher energies up to 5 keV using the spherical complex optical potential method. The two methods are found to be consistent, merging at around 12 eV for the elastic scattering cross section. Finally we report the total ionization cross section using the binary encounter Bethe method for C2F2. The perfluorination effect in the shape and magnitude of the elastic, momentum transfer and ionization cross sections when compared with C2H2 showed a similar trend to that in the C2H4–C2F4 and C6H6–C6F6 systems. The cross-section data reported in this article could be an important input for the development of a C2F2 plasma model for selective etching of Si/SiO2 in the semiconductor industry.

Direct estimates of friction factors for a mobile rippled bed

AbstractNew friction factor estimates are computed from the total momentum transfer applied to a rippled sediment bed. The total time‐dependent momentum flux is achieved by implementing the double‐averaged horizontal momentum equation on the nearbed flow field collected with PIV. Time‐independent friction factors are obtained by regressing the total momentum flux to the common quadratic stress law given by. The resulting friction factors compare favorably with available analysis techniques including energy dissipation, vertical turbulence intensity, and maximum shear stress, but can be 2‐6 times smaller than estimates determined with the model byMadsen (1994)and the formula ofSwart (1974)using the ripple roughness.

Coherent Momentum Exchange above and within a Scots Pine Forest

Biorthogonal decomposition (BOD) is used to detect and study synchronous coherent structures occurring at multiple levels in the vertical momentum flux (u′w′) within and above a planted Scots pine forest during a 12-week continuous measurement period. In this study, the presented method allowed for the simultaneous detection and quantification of the number of coherent structures (N), their duration (D) and separation (S) at five measurement heights (z1–z5) covering the range z1/h = 0.11 to z5/h = 1.67, with h being the mean stand height at the measurement site. Results presented for five different exchange regimes (C1–C5) and for four different atmospheric stability conditions (stable, transition to stable, near-neutral, forced convection) demonstrate that during the measurement period, above-canopy momentum flux was only to a limited extent involved in the evolution of spatiotemporal momentum flux patterns found within the below-canopy space. Fully-coupled turbulent momentum exchange over the investigated height range occurred during 19% of all analyzed half-hourly datasets. Across the analyzed exchange regimes, the median contribution of strong sweeps and ejections to total momentum transfer above the canopy varied between 30% and 39% while covering 28%–32% of the time. In the below-canopy space, the contribution of coherent structures varied between 19% and 21% while covering the same amount of time. This suggests that momentum transfer through synchronous coherent structures is very efficient above the forest canopy, but attenuated in the below-canopy space. Since the majority of the presented results agrees well with the results from previous studies that analyzed coherent structures at single levels, the BOD is a promising tool for the consistent investigation of synchronous coherent structures at multiple measurement heights.

Elastic scattering polarimeter for a polarized antiproton beam at U-70 accelerator of IHEP

The absolute polarimeter based on the elastic p̄p-scattering in the diffraction kinematic regions with the total momentum transfer squared coverage of 0.1 < − t < 0.3 (GeV/c)2 is proposed for the polarized antiproton beam at the U-70 proton synchrotron of IHEP. It is shown that it would take ∼200-400 hours for measuring the beam polarization at the statistical errors of ΔPB/PB ≃10–15%. These time estimates include also the time which is necessary for the measurements of an analyzing power AN, using a polarized target. Besides the measurements of beam polarizations, the proposed polarimeter provides an opportunity for carrying out the experimental studies of the small momentum transfers physics which would be a valuable enrichment of the SPASCHARM experiment capabilities and its physics program.

Density functional theory study of the influence of segregation of S or Fe impurities on electromigration in nano-grained copper interconnects

The reliability of the circuits in the modern microelectronic devices remains, during last decades, one of the key topics in research and gains an attention for improving the promising candidates for conductors. Improvement of materials for such applications can be obtained by both electronic and compositional optimization. Ab initio calculations using full potential linearized augmented plane wave method in density functional theory are applied to explain the reduction in electromigration effect in the vicinity of grain boundaries (GB) in nano-structured Cu due to the segregation of some additives to the GB. Several possible mechanisms are considered. It is demonstrated that S atoms segregated to GB of nano-structured Cu lead to the growth of effective mass of the electrons. This decreases the mobility of electrons in external electric field, and, correspondingly, the momentum that they may transfer to atoms in collisions. Fe atoms segregated to GB of Cu create new empty states at the top of the valance band. These non-occupied states may stimulate the current of holes when external electric field is applied to the system, creating the “hole wind” in the direction opposite to the current of electrons. Such “hole wind” will compensate the forces generated by the electron current and therefore will reduce the total momentum transfer between charge carriers and atoms. The calculated electron density maps show that S and Fe segregating to Cu GB increases the strength of covalent bonds reducing the diffusion of Cu atoms in the vicinity of GB.

Viscosity cross sections for the heavy noble gases

We have calculated viscosity cross sections for argon, krypton and xenon from zero to 1 keV using the phase shifts from our previous publication [R.P. McEachran, A.D. Stauffer, Eur. Phys. J. D 68, 153 (2014)] which presented total elastic and momentum transfer cross sections for these gases. As previously, we present simple analytic fits to our results to aid in modelling plasmas containing these atoms. By using the current results and those in reference [R.P. McEachran, A.D. Stauffer, Eur. Phys. J. D 68, 153 (2014)] the first two ‘partial cross sections’ used in the general moment method of solving the Boltzmann equation can be obtained. The agreement of our viscosity cross sections with experimentally derived results indicates the overall reliability of our calculations.