Born Approximation Results Research Articles

Analysis of electron induced single ionisation differential cross-section of CO2 molecules in different kinematics

Theoretical investigations of electron-impact ionisation for carbon dioxide (CO2) in low to intermediate energy ranges are presented. In addition to the energy range, we have estimated triple differential cross-section (TDCS) in coplanar and perpendicular plane geometry. We have calculated the TDCS for electron impact using the modified distorted wave formalism up to the second order. Post-collision interaction effects have also been introduced to describe the collision dynamics accurately. There is a good correlation between the distorted-wave Born approximation results and the experimental results in terms of forward and backward scattering regions.

Universal Minimum Conductivity in Disordered Double-Weyl Semimetal* *Supported by the the National Natural Science Foundation of China (Grant No. 11874337).

We report an exact numerical study on disorder effect in double-Weyl semimetals, and compare exact numerical solutions for the quasiparticle behavior with the Born approximation and renormalization group results. It is revealed that the low-energy quasiparticle properties are renormalized by multiple-impurity scattering processes, leading to apparent power-law behavior of the self-energy. Therefore, the quasiparticle residue surrounding nodal points is considerably reduced and vanishes as Z E ∞ Er with nonuniversal exponent r. We show that such unusual behavior of the quasiparticle leads to strong temperature dependence of diffusive conductivity. Remarkably, we also find a universal minimum conductivity along the direction of linear dispersion at the nodal point, which can be directly observed by experimentalist.

Low-energy electron-impact laser-assisted ionization of atomic hydrogen

We have studied the influence of a linearly polarized laser field on the dynamics of low $(e,2e)$ collisions in atomic hydrogen. The influence of the laser on the target states is treated using a first-order perturbation approach. The continuum states of the scattered and ejected electrons are described respectively by Volkov and Coulomb-Volkov wave functions. The second Born approximation is used to calculate triple differential cross sections for laser-assisted ionization by low-energy electron impact. The required scattering amplitudes are evaluated by using the Sturmian basis expansion. The influence of the laser parameters (photon energy, intensity, and direction of polarization) on the triple differential cross sections is analyzed, and several illustrative examples are discussed. Our second Born approximation results agree very well with those obtained in the first-order Born approximation at larger incident energies. The margins between the second and first Born approximation results are large at low incident energies in the vicinity of the recoil peaks.

Full t-matrix approach to quasiparticle interference in non-centrosymmetric superconductors

We develop the full t-matrix theory of quasiparticle interference (QPI) for non-centrosymmetric (NCS) superconductors with Rashba spin-orbit coupling. We give a closed solution for the QPI spectrum for arbitrary combination and strength of nonmagnetic (V c ) and magnetic (V m ) impurity scattering potentials in terms of integrated normal and anomalous Green’s functions. The theory is applied to a realistic 2D model of the Ce-based 131-type heavy fermion superconductors. We discuss the QPI dependence on frequency, composition and strength of scattering and compare with Born approximation results. We show that the QPI pattern is remarkably stable against changes in the scattering model and can therefore give reliable information on the properties of Rashba-split Fermi surface sheets and in particular on the accidental nodal position of the mixed singlet-triplet gap function in NCS superconductors.

SOLUTION OF THE ELECTROMAGNETIC SCATTERING PROBLEM FROM AN ELECTRICALLY LARGE RANDOM DIELECTRIC MEDIUM

The time-harmonic electromagnetic scattering problem from a random inhomogeneous dielectric medium (here a turbulent plasma wake created by the atmospheric reentry of a vehicle) is considered. The electronic density of the plasma, that gives rise to its dielectric permittivity, has a ∞uctuating part †f(r), the variance and correlation function of which are known a priori. Because the electrical dimensions of the wake can be very large, the numerical solution of Maxwell's equations via a full-wave calculation performed with a boundary element and flnite element method is prohibitive when statistical quantities such as the mean Radar Cross Section (RCS) and its variance are required, that necessitate a large number of random realizations. To remedy this di-culty, two approximations are considered and illustrated for a 2D scattering problem. First, a Mie series approach is adopted where the medium is discretized with small disks, thus reducing considerably the number of unknowns for a given random realization of †f(r), and a domain decomposition method is proposed to further reduce the complexity of the numerical solution of the corresponding system. Second, the statistical mean and the variance of the RCS are derived in closed-form from the Born approximation and yield accurate results when, as expected, the statistical mean of the relative dielectric permittivity is close to unity and j†f(r)j is small. Conversely, it is shown how these expressions can be used to validate the results obtained with the Mie series approximation. Numerical examples are presented that illustrate the potentialities of these techniques.

Electron-impact ionization of atomic hydrogen: dynamical variational treatment

A simple and straightforward calculating scheme is proposed for electron-impact single and multiple ionization of atoms. The method is based on the application of the Hulthen-Kohn dynamical variational principle. An effective charge seen by the scattered electron is determined for a certain type of trial wave functions mathematically in a rigorous way excluding any empirical assumptions. Validity of the elaborated approach is assessed by calculating triply differential cross section (TDCS) for electron-impact ionization of hydrogen. It is shown that, inclusion of the effective charge into the calculation reduces height of a “binary peak” in comparison with the first Born approximation result. The height of a “recoil peak” depends on the sign of the effective charge. The calculated TDCS are compared with the available experimental data and with the results of sophisticated theories and agreement is found.

Differential cross section calculations of positron and electron impact ionization of Ar (3p)

We report the distorted wave Born approximation results of triple differential cross section of Ar (3p) by positron and electron impact. We compare the results of our calculations with the recent available experimental and theoretical results. We also provide a comparison of our positron impact ionization results with the electron impact ionization results to understand the effect of projectile charge on the projectile-target interaction.

CDW-EIS calculations for multiple ionization of Ne, Ar, Kr and Xe by the impact of H+ and He+, including post-collisional electron emission

We present theoretical single to quintuple ionization cross sections for Ne, Ar, Kr and Xe bombarded by H+ and He+. Post-collisional contributions due to Auger-like processes are taken into account using recent photoionization data. The present continuum distorted wave-eikonal initial state (CDW-EIS) and first Born approximation results are compared with the experimental data available in the energy range of 50–10 000 keV amu−1 for H+ on Ne and Ar, and 50–1000 keV amu−1 for the other cases. In general, the combination of the CDW-EIS with the post-collisional branching ratios describes well the multiple ionization data above 300 keV amu−1, showing a clear tendency to coalesce with the first Born approximation at high energies. The surprising result of this work is the good performance of the first Born approximation which describes rather well the experimental data of double and triple ionization, even in the intermediate energy range (50–300 keV amu−1), where direct ionization is the dominant contribution.

Perturbative theory of grazing-incidence diffuse nuclear resonant scattering of synchrotron radiation

Theoretical description of off-specular grazing-incidence nuclear resonant scattering of synchrotron radiation (Synchrotron M\"{o}ssbauer Reflectometry, SMR) is presented. The recently developed SMR, similarly to polarized neutron reflectometry (PNR), is an analytical tool for the determination of isotopic and magnetic structure of thin films and multilayers. It combines the sensitivity of M\"{o}ssbauer spectroscopy to hyperfine interactions and the depth selectivity of x-ray reflectometry. Specular reflection provides information on the depth profile, while off-specular scattering on the lateral structure of scattering layers. Off-specular SMR and PNR intensity formulae of a rather general multilayer with different domains, based on a Distorted Incident-Wave Approximation (DIWA) are presented. The Distorted-Wave Born Approximation (DWBA) results are given in an Appendix. Physical and numerical implications, why using DIWA, are explained. The temporal character of SMR imposes specific differences between SMR and PNR. In order to reveal the limits of DIWA and to compare the two analytical methods, two-dimensional diffuse SMR and PNR maps of an antiferromagnetic multilayer are calculated and critically compared. Experimental '$\omega-2\theta$' SMR map of a periodic $[ \mathrm{Fe}/\mathrm{Cr}]_{20}$ multilayer is presented and compared with simulations by the present theory.

Scaling relation in the collision of hydrogenlike ions with antiprotons

The impact excitation and ionization of hydrogen (H)-like ions by antiprotons are studied by solving the time-dependent Schr\"odinger equation with a time-dependent generalized pseudospectral method in a wide scaled impact energy region (1 to 1000 keV). The validity region of the scaling relation is investigated by comparing the time-dependent calculations with the first Born approximation results. The numerical error and the validity region of the time-dependent generalized pseudospectral method have been explored. Based on the present study, we conclude that (i) the scaling relation of the ionization and excitation cross sections is valid for high-Z H-like ions or in the high-impact-energy regime for low-Z H-like ions; (ii) for given H-like ions, the scaling relation works better for the impact excitation to the dipole allowed transition than for the impact excitation to the dipole forbidden transition; and (iii) the time-dependent generalized pseudospectral method is not valid in a very weak perturbation system, which can be fairly studied by the time-independent methods. We also discuss the physical originations of the numerical observations.

Signatures of Two-Pair Correlations after Simultaneous Excitation of Excitons and Free Electron-Hole Pairs in a Quantum Wire

The impact of all kinds of two-pair correlations (biexcitons, exciton–exciton scattering states, two free electron–hole pairs) on four-wave-mixing (FWM) signals generated by ultra-short optical pulses that simultaneously excite excitons and free electron–hole pairs is analyzed. Calculations accounting non-perturbatively for the Coulomb interaction are compared with the Born approximation (BA) and mean-field (MF) results. Thereby signatures of two-pair correlations are identified as well as qualitative differences between microscopic scattering theories and phenomenological treatments of pair relaxations.

Inner-shell ionization of a neon atom by electron impact

A model is proposed to study the inner-shell (K- shell) ionization of the inert gas atoms (e.g., Ne, Ar, etc.) by fast electron impact in coplanar geometry in the framework of a distorted wave approximation. An independent particle model is employed with a one-electron orbital for the multielectron target atom. Triple differential cross sections (TDCS) are presented for both symmetric and asymmetric kinematics of neon atom. The most salient feature noted in the TDCS structure is the presence of intense recoil peak that for certain dynamics (particularly when the ejected energy is much lower than the K-shell binding energy) is even larger than the binary peak, an unusual feature for the outer-shell ionization process. Results are compared with the relative measurements [P. Bickert and W. Hink, in 2nd European Conference on $(e,2e)$ Collisions and Related Problems (Kaiserslautern, 1989), edited by H. Ehrhardt] and the theoretical distorted-wave Born approximation results, available only for asymmetric kinematics. The qualitative agreement of the present results with the experiment by Bickert and Hink is quite good, particularly in respect to the binary/recoil intensity ratio, the latter being greater than unity in both cases for the particular dynamics at which the measurements by Bickert and Hink were performed. Additional results are also presented for symmetric as well as some other asymmetric kinematics.

Contribution of bound-electron pair production to the dispersion relation for Delbrück scattering

In photon-atom scattering the customary partitioning of the elastic scattering amplitude into Rayleigh and Delbr\"uck amplitudes (as well as nuclear amplitudes) in the single-electron formalism involves summations over complete sets of intermediate electron states in the atomic potential. This leads to the Rayleigh amplitude which is usually compared with experiment. However, another consequence of the partition is that the total cross section for bound-electron pair-production into all bound states, regardless of occupation, is included in the optical theorem for the imaginary part of the forward Delbr\"uck amplitude. The corresponding real part of the forward Delbr\"uck amplitude can be obtained through the use of a dispersion relation. We show that for $Z=92$ the inclusion of the bound-electron pair-production cross section leads to a contribution to the real part of forward Delbr\"uck amplitude, which can be as much as $\ensuremath{\approx}12%$ of the Born approximation result, for photon energies near the pair-production threshold. This bound-electron pair-production contribution is therefore comparable in magnitude to the corrections due to Coulomb and screening effects in the ordinary pair-production cross section (electron in continuum). The net correction to Born approximation is small well below threshold, significant well above threshold.

3D thermal wave scattering on buried inhomogeneities in ac thermal microscopy

The scattering of the thermal waves on buried small thermal resistances is theoretically studied in the framework of conductive thermal modelling of the coupling between a SThM probe and a sample. Lateral resolutions for the amplitude and phase of the probe's ac thermal response are obtained. The modelling, using an iterative method, goes beyond the usual first Born approximation results. Technically, the ac temperature field in the entire geometry is expressed in terms of two-dimensional plane wave spectra which permit direct use of fast Fourier transform algorithms. The various analytical results are easily obtained via a multilayer treatment of the probe and of the sample.

One-particle spectral weight of the three-dimensional single-band Hubbard model.

Dynamic properties of the three-dimensional single-band Hubbard model are studied using Quantum Monte Carlo combined with the maximum entropy technique. At half-filling, there is a clear gap in the density of states and well-defined quasiparticle peaks at the top (bottom) of the lower (upper) Hubbard band. We find an antiferromagnetically induced weight above the naive Fermi momentum. Upon hole doping, the chemical potential moves to the top of the lower band where a robust peak is observed. Results are compared with spin-density-wave (SDW) mean-field and self consistent Born approximation results, and also with the infinite dimensional Hubbard model, and experimental photoemission (PES) for three dimensional transition-metal oxides.

Retardation effects in nonrelativistic two-photon electron bremsstrahlung in the Coulomb field.

We investigate the deviations from the dipole approximation for the two-photon bremsstrahlung cross section ${\mathrm{\ensuremath{\sigma}}}_{4}$, corresponding to the observation of the emitted photons (but not the scattered electron) in coincidence, which has been the subject of recent experiments. Our analysis is for the Coulomb field, and it is done in the Born approximation. We find that retardation effects are important, even in the lower energy range (8--12 keV) of the Hippler experiments, but not in the particular configuration for which experiments were performed. Using the simple analytic expression that we derive, including retardation, in the nonrelativistic Born approximation, we show that, in the incident electron energy range 10--50 keV, the differences between the relativistic Born (Smirnov's approach) and nonrelativistic dipole approximation results are mainly retardation effects. \textcopyright{} 1996 The American Physical Society.

On-shell and off-shell low-frequency approximations for potential scattering in a strong laser field-optical theorem and sum rule

We present analytical and numerical results for the T matrix and cross sections (differential and total) for scattering in a strong low-frequency laser field. Presented results, based on recently derived expressions for the off- and on-shell low-frequency T matrices are beyond the first Born approximation results of Daniele et al. (1986) for scattering on the Yukawa potential in a laser field. An analytical expression for the total cross section is obtained using the (1,1) Pade approximant to the off-shell low-frequency T matrix. This result explicitly shows departure from the sum rule and it is analysed as function of the laser field intensity and polarization angle. If the laser field is so strong that the laser field induced scattering particle impulse eA0 is comparable with the initial impulse pi this departure has a maximum. For an ultra-strong laser field (eA0>>pi) the total cross section is small in comparison with the field-free section, i.e. the influence of the scattering potential is weak. The results for different values of the screening radius are also presented and it is observed that the departure from the sum rule is larger for long-range potentials (when the interplay between the potential and the intense radiation field is important). The departure is strong for small values of the polarization angle ( Theta i<20 degrees ) and weak for 45 degrees < Theta i<135.

Multiple scattering calculation of double and single differential cross sections for ionization of hydrogen atoms by electrons at intermediate energies

The multiple scattering approach of Das and Seal, which was applied earlier to calculate the triple differential cross section for the ionization of atomic hydrogen by electrons is now used to calculate the double and the single differential cross sections for the same system. The range of the incident electron energy is taken to be 100–250 eV. The present results are compared with the measured results of Shyn and with the available distorted wave Born approximation results.

Positronium formation in positron-lithium collisions

Differential and total cross sections have been studied for ground-state positronium (Ps) formation using the Glauber-eikonal approximation in positron-lithium atom collisions. The valence electron of the alkali-metal target and the effect of the core have been treated in the framework of a pseudopotential formalism. Results are reported for intermediate and high energies along with the first-order Born-approximation results. Even at very high energies the eikonal cross sections are found to be different from the corresponding first-order Born approximation showing the importance of higher-order effects.

Solvent influenced nonadiabatic transitions: A classical kinetic theory

We derive an Enskog level kinetic equation for a time correlation function appropriate to the description of weak quantum transitions induced by collisions in a classical equilibrium fluid. This time correlation function involves propagation on two potential surfaces, reflecting the dependence of the elastic potentials on the quantum state. The dynamical variable of the correlation function is the phase space density of a tagged pair of molecules; one member of the pair undergoes the transition and the other induces it. The original motivation for this work was the calculation of vibrational relaxation rates in fluids [P. S. Dardi and R. I. Cukier, J. Chem. Phys. 86, 2264, 6893 (1987)], but the results derived here should also be applicable to other weak nonadiabatic processes, e.g., electronic transitions. The kinetic equation includes the interactions between the tagged pair exactly. In its low density limit, the rate constant based on the kinetic equation corresponds to the thermally averaged, semiclassical distorted wave Born approximation result. The solvent-tagged particle interactions are described at the Enskog level, which includes the effects of all uncorrelated collisions. The tagged particle–solvent collision operators depend on the quantum state of the molecule undergoing the transition. This new effect is not incorporated in more phenomenological descriptions of solvent influenced nonadiabatic transitions. Our derivation is based on a binary collision expansion. We also derive Enskog level kinetic equations, using the binary collision expansion, for standard one potential surface, tagged single particle and tagged pair time correlation functions. We compare our results for the standard time correlation functions with results from renormalized kinetic theory to show that the correct Enskog kinetic theory for both hard and soft forces is obtained.