Calculations Of Differential Cross Sections Research Articles

Theoretical estimate of fivefold differential cross sections and spin asymmetry forK-shell(e,3e)processes with transversely-spin-polarized relativistic electrons

Ab initio first-order Born calculations of the fivefold differential cross section (FDCS) and transverse spin asymmetry in FDCS for the $K$-shell double ionization of atoms by transversely polarized incident electron are reported. The FDCS and transverse spin asymmetry in FDCS are found to be sensitive to atomic number $Z$, ejection angle, and energy-sharing ratio of the ejected electrons. FDCS is decomposed into longitudinal and transverse contributions and their effects on the angular profile of FDCS such as shifting in the binary peak are reported. Hitherto, all $(e,3e)$ experiments have been performed in the nonrelativistic energy regime without consideration of spin polarization. We hope that the present calculation of FDCS and spin asymmetry in FDCS may induce quantum mechanically complete $(e,3e)$ experiments in the relativistic energy regime wherein spin-dependent interaction becomes prominent.

Ab Initio studies of the interaction potential for the Xe–NO(X 2Π) van der Waals complex: Bound states and fully quantum and quasi-classical scattering

Adiabatic potential energy surfaces for the ground electronic state of the Xe⋅⋅⋅NO(X(2)Π) van der Waals complex have been calculated using the spin-restricted coupled cluster method with single, double, and non-iterative triple excitations (RCCSD(T)). The scalar relativistic effects present in the Xe atom were included by an effective core potential and we extended the basis with bond functions to improve the description of the dispersion interaction. It has been found that the global minimum on the A(') adiabatic surface occurs at a T-shaped geometry with γ(e) = 94° and R(e) = 7.46 a(0), and with well depth of D(e) = 148.68 cm(-1). There is also an additional local minimum for the collinear geometry Xe-NO with a well depth of 104.5 cm(-1). The adiabat of A('') symmetry exhibits a single minimum at a distance R(e) = 7.68 a(0) and has a skewed geometry with γ(e) = 64° and a well depth of 148.23 cm(-1). Several C(nl) van der Waals dispersion coefficients are also estimated, of which C(6, 0) and C(6, 2) are in a reasonable agreement with previous theoretical results obtained by Nielson et al. [J. Chem. Phys. 64, 2055 (1976)]. The new potential energy surfaces were used to calculate bound states of the complex for total angular momentum quantum numbers up to J = 7/2. The ground state energy of Xe⋅⋅⋅NO(X(2)Π) is D(0) = 117 cm(-1), which matches the experimental value very accurately (within 3.3%). Scattering calculations of integral and differential cross sections have also been performed using fully quantum close coupling calculations and quasi-classical trajectory method at a collision energy of 63 meV. These calculations reveal the important role played by L-type rainbows in the scattering dynamics of the heavier Rg-NO(X) systems.

Strong dynamical screening of the (e, 2e) processes for electron impact ionization of helium in the perpendicular plane symmetric geometry

We apply BBK, DS3C model and the new modified Sommerfeld parameters of the present DS3C model to calculation of the triple differential cross sections (TDCS) for electron impact ionization of helium in the perpendicular plane symmetric geometry. The results of the present are compared with the measurements and those of other theoretical models. It was found that the present results give a better description for the experimental data and the dynamical screening effects are strong in this geometry. The influence of the Sommerfeld parameters on the triple differential cross sections is also analyzed and discussed in the perpendicular plane geometry.

The theoretical calculation of (e,2e) triple differential cross sections of Ag+ (4p,4d) in coplanar asymmetric geometry

The three-body distorted-wave Born approximation is used to calculate the (e,2e) triple differential cross sections (TDCSs) of Ag+(4p10) and Ag+(4d10) in different kinematical variables in coplanar asymmetric geometry. The angles 4, 10 and 20 are selected as the scattering electron angles. We find that the position of binary peak or the dip between split peaks are not in the direction of momentum transfer, which is probably ascribed to one kind of double-binary collision. We also find that the binary peaks show abnormal splits for Ag+(4p10). Such abnormal splits indicate that an (e,2e) process for inner valence orbital of ionic target becomes more complicated than for outer valence orbital. Furthermore, beside the binary peak and the recoil peak, some pronounced peaks appear at certain ejected angles in the (e,2e) TDCSs of Ag+(4p10) and Ag+(4d10). We consider that these pronounced peaks are probably related to one kind of double-binary collision.

Triple differential cross sections for the ionization of water by electron and positron impact

Triple differential cross section calculations for the ionization of several valence orbitals of the water molecule by electron and positron impact are reported. We found a very good agreement with the experimental data in case of the almost spherical 2A1 orbital. By changing the projectile’s charge, significant differences were observed between the electron and positron TDCSs.

Indistinguishability in electron-impact excitation-ionization of helium

We present fully differential cross section (FDCS) calculations for electron-impact excitation-ionization of helium using the four-body distorted wave-exchange (4DWE) model. This model includes both the direct and exchange amplitudes, which account for the indistinguishability of the free electrons in the final state. The results of the 4DWE model are compared with absolute experimental results, and we find that the exchange amplitude has a minimal impact in determining the shape and magnitude of the FDCS.

Study of the structure of light, unstable nuclei and the mechanism of elastic proton scattering

The review presents calculations of elastic p 6He-, p 8Li-, p 9Li- and p 9C scattering in the framework of the Glauber theory of multiple diffraction scattering at intermediate energies of 70 and 700 MeV/nucleon. The most significant result of the calculations is that we have utilized realistic three-body wave functions obtained within modern nuclear models. The relation is found between differential cross sections and intercluster potentials, where the nuclear wave functions are calculated. Conclusions are made concerning the types of potentials which describe most realistically the available experimental data. The method for calculation of three-body wave functions in α-n-n-, α-t-n-, 7Be-p-p-, α-t-2n-, and 7Li-n-n models is described with discussion of inter-cluster potentials and the quantum-number configurations taken into consideration. It is revealed how the wave functions and the nuclear electromagnetic characteristics calculated using these wave functions depend on the choice of intercluster potentials. The derivation of matrix elements (amplitudes) of pA scattering in the framework of the Glauber approach with three-body wave functions is presented by an example of 6He nucleus. Discussing the results of calculation of differential cross sections and the analyzing power (A y ), we established how the calculated characteristics depend on a wave-function structure and dynamics of the process determined by a Glauber operator of multiple scattering. The calculated differential cross sections and analyzing powers are compared with available experimental data and calculations by other authors performed for different formalisms, which allows us to make justified conclusions.

Triple differential cross section for the ionization of helium by electronic impact

We report results of analytical triple differential cross sections ( tdcs) for the single ionization of the helium iso-electronic ions by the electron impact. A two variational parameters wave function is used to evaluate the tdcs. This study shows the accuracy of the tdcs for helium atom and helium like ions in the first Born approximation ( fba) at high incident energy domain. The theory is quite acceptable as a fast calculation of the triple differential cross section, particularly at high energies where other theories and methods are cumbersome. A comparison is made of our calculations with previous results of the other theoretical methods and experiment. The fba results obtained here with the two variational parameters wave function are in good agreement with the experiment data at high incident energy. The results show that the electron correlation effects are important around the maxima and influence only the extrema magnitude but not their positions. The calculations presented here are extanded to the cases where the energies of the outgoing electrons are more equal.

Semiempirical potentials for positron scattering by atoms

We report calculations of differential and integral cross sections for positron scattering by noble gas and alkaline-earth atoms within the same methodology. The scattering potentials are constructed by scaling adiabatic potentials so that their minima coincide with the covalent radii of the target atoms. Elastic differential and integral cross sections are calculated for Ne, Ar, Be, and Mg, and the results are very close to experimental and best theoretical data. Particularly, elastic differential cross sections for Be and Mg at low energies are reported.

Electron-impact excitation of the(2p2)1Dand(2s2p)1Poautoionizing states of helium

An experimental study of the excitation of the ($2{p}^{2}$) ${}^{1}D$ and ($2s2p$) ${}^{1}{P}^{o}$ autoionizing states of helium by 250-eV electron impact is presented. The ejected-electron angular distributions and energy spectra are measured in coincidence with the corresponding scattered electrons for a scattering angle of $\ensuremath{-}{13}^{\ensuremath{\circ}}$ and for a range of ejected-electron angles in both the forward and backward directions. Resonance profiles are analyzed in terms of the Shore-Balashov parametrization to obtain the resonance asymmetry ${A}_{\ensuremath{\mu}}$ and yield ${B}_{\ensuremath{\mu}}$ parameters and the direct ionization cross section $f$. The spectra and their parameters are compared to the previous measurements of Lower and Weigold [J. Phys. B. 23, 2819 (1990)] and McDonald and Crowe [J. Phys. B 26, 2887 (1993)]. Comparison is also made with the recent theoretical triply differential cross-section calculations based on the first and second Born approximations. In general, good qualitative agreement is found between the experimental results. Some differences are found at the forward and backward directions. These differences in the shape and magnitude of the cross sections are attributed to the different incoming electron energies used in the experiments. The second Born approximation with inclusion of the three-body Coulomb interaction in the final state agrees reasonably well with experiments in the binary region. However, the ${}^{1}{P}^{o}$ resonance yield parameter ${B}_{\ensuremath{\mu}}$ is significantly overestimated at the recoil region, giving a relatively large recoil peak, in contradiction to the experiment. There is also a discrepancy between the two theories available for the ${}^{1}D$ resonance yield parameter ${B}_{\ensuremath{\mu}}$ in this region. Remaining discrepancies between theories and experiments are also discussed.

Low-energy neutral-current neutrino scattering onTe128,130isotopes

Differential, total, and cumulative cross section calculations for neutral current neutrino scattering on $^{128,130}\mathrm{Te}$ isotopes are performed in the context of the quasiparticle random phase approximation by utilizing realistic two-nucleon forces. These isotopes are the main contents of detectors of ongoing experiments with multiple neutrino physics goals (COBRA and CUORE at Gran Sasso), including potential low-energy astrophysical neutrino (solar, supernova, geoneutrinos) detection. The incoming neutrino energy range adopted in our calculations (${\ensuremath{\varepsilon}}_{\ensuremath{\nu}}\ensuremath{\leqslant}100$ MeV) covers the low-energy $\ensuremath{\beta}$-beam neutrinos and the pion-muon stopped neutrino beams existing or planned to be conducted at future neutron spallation sources. The aim of these facilities is to measure neutrino-nucleus cross sections at low and intermediate neutrino energies with the hope of shedding light on open problems in neutrino-induced reactions on nuclei and neutrino astrophysics. Such probes motivate theoretical studies on weak responses of various nuclear systems; thus the evaluated cross sections may be useful in this direction.

Elastic electron scattering from the DNA bases: cytosine and thymine

Relative elastic differential cross sections for elastic scattering from cytosine and thymine have been measured using the crossed-beam method. The measurements have been performed at two electron energies of 500 and 100 eV, and cover the angular range of 10°-130°. Calculations of elastic differential cross sections have been performed via the screen corrected additivity rule method, and agreement is quite good with the present experimental results. The results obtained are important for the modelling of energy deposition in living tissue.

Calculation of (e, 2e) triple differential cross sections of Mg in coplanar geometry

We report the results of triple differential cross section of coplanar (e, 2e) processes on Mg (3s) atom in modified distorted wave Born approximation (DWBA). The standard DWBA formalism has been modified by including the correlation-polarization potential (which is function of electron density) and post collision interaction. We compare our computed results with the available experimental data and observe that the inclusion of polarization potential in the standard DWBA is able to improve the agreement with experimental results.

Calculation of the multifold differential cross section of the electron-impact ionization of molecular hydrogen by prolate spheroidal external complex scaling method with second Born corrections

We introduce the second Born dipole corrections in our recently developed ab initio procedure based on the driven Schr\odinger equation formalism and the external scaling method for the determination of the multifold differential cross sections of the single and double ionization of molecular hydrogen by electron impact. To test our procedure, we first apply it to the excitation-ionization process of a He atom and compare the results to those of equivalent theoretical results, which are available. We then show that the introduction of the second Born correction including only dipole terms improves the agreement with the experimental results only in the case of the simple ionization. We think that the introduction of nondipole contributions in the second Born term which are not taken into account in the present work is necessary in the case of the double ionization process.

Microscopic K +-nucleus optical potential and calculations of differential elastic-scattering cross sections and total reaction cross sections

The differential elastic-scattering cross sections and the total reaction cross sections for the interaction of K+ mesons with 12C and 40Ca nuclei at beam momenta of 0.635, 0.715, and 0.8 GeV/c are calculated. The microscopic optical potential derived in the high-energy approximation is used in these calculations. It is determined by the amplitude for kaon-nucleon scattering and the density distribution of pointlike nucleons of the target nucleus. In the high-energy approximation, the Klein-Gordon-Fock equation reduces to the form of the Schrodinger equation. It is shown that small distinctions between the reduction methods do not lead to significant changes in differential elastic-scattering cross sections, but the effects of relativization as such are quite large. Good agreement with experimental data on elastic K+A scattering is attained. The total reaction cross sections can be described upon adding, to the volume potential, a term that takes the form of its derivative and which has a maximum at the periphery, its contribution being fitted to experimental data.

Multiple ionization processes involving fast charged particles

This review is devoted to certain aspects of the theory of multiple ionization of a quantum target by a fast charged particle. Atoms and molecules, and their ions as well, are considered as targets, while electrons and protons are considered as projectiles. Special attention is paid to the effective charge approximation while constructing continuum wave functions for several charged fragments in the exit channel of the reaction. Theoretical calculations of differential and total cross sections of various multiple ionization processes are presented and, where possible, comparison of the results of these calculations with experimental data is carried out.

Triple differential cross section of potassium for doubly symmetric ionization

We report the results of our modified distorted wave Born approximation calculation of triple differential cross section in the coplanar symmetric single ionization of potassium atom. We have included correlation–polarization potential as a function of electron density parameter and also studied the effect of post-collision interaction. The present attempt significantly improves the agreement between theoretical and experimental results.

Born series in the theory of electron impact ionization of an atom

In this review, a generalization of few-body quantum scattering theory is given for the case of Coulomb interaction. Since in this specific case the scattering amplitude, which is a solution to a resolvent-type equation, possesses a singularity when the complex parameter z tends to the energy shell, a definition of the physical amplitude is provided. A recipe for regularizing integrals (eliminating divergences), which describe the terms of a perturbation theory series for different perturbing potentials, is formulated. As an example, the general theory is applied to the calculations of differential cross sections for a quasi-elastic electron impact ionization reaction on atomic hydrogen.

Substitution effects in elastic electron collisions with CH3X (X=F, Cl, Br, I) molecules

We report absolute elastic differential, integral, and momentum transfer cross sections for electron interactions with the series of molecules CH(3)X (X=F, Cl, Br, I). The incident electron energy range is 50-200 eV, while the scattered electron angular range for the differential measurements is 15 degrees-150 degrees. In all cases the absolute scale of the differential cross sections was set using the relative flow method with helium as the reference species. Substitution effects on these cross sections, as we progress along the halomethane series CH(3)F, CH(3)Cl, CH(3)Br, and CH(3)I, are investigated as a part of this study. In addition, atomic-like behavior in these scattering systems is also considered by comparing these halomethane elastic cross sections to results from other workers for the corresponding noble gases Ne, Ar, Kr, and Xe, respectively. Finally we report results for calculations of elastic differential and integral cross sections for electrons scattering from each of the CH(3)X species, within an optical potential method and assuming a screened corrected independent atom representation. The level of agreement between these calculations and our measurements was found to be quite remarkable in each case.

Time-dependent close-coupling calculations of the double photoionization of He@C60

The double photoionization of a He atom enclosed in a ${\mathrm{C}}_{60}$ molecule, He@C${}_{60}$ was investigated using the time-dependent close-coupling method with the ${\mathrm{C}}_{60}$ molecule represented by a spherical shell potential and the He atom treated nonperturbatively. Comparisons are made with the double photoionization of a bare He atom. The ratio of the total double photoionization cross section of He@C${}_{60}$ to that of a bare He atom is found to exhibit oscillations due to reflection of a slow electron. This is confirmed by calculations of the single energy differential cross section that peaks at unequal energy sharing when one of the ejected electrons has an energy comparable to the ${\mathrm{C}}_{60}$ well depth. Triple differential cross sections are found to be shifted in magnitude, but unchanged in shape from the bare He atom.