Theoretical Differential Cross Sections Research Articles

Theoretical triple differential cross sections for ionization of N 2 and CH 4 molecules by electron impact

We present the angular distribution of electron emission by calculating the triple differential cross sections for (e, 2e) process on N 2 and CH 4 by using the three-body formalism of molecular first Born approximation (MFBA), two-Coulomb wave (M2CW), and three-Coulomb wave (M3CW) models, respectively. In these models, a Coulomb distorted wave is considered for the motion of the incident electron. We have considered the continuum-continuum correlation effect by choosing the final state as the three-Coulomb and two-Coulomb wave functions in M3CW and M2CW models, whereas the ejected electron is affected by a single centre field of the target in the MFBA model. In the M2CW model, the interaction between scattered electron-residual target ion has been described as a plane wave. The distinguishing feature among the three models has been noted in the TDCS as a strong binary peak with and without a recoil peak for several electron emission energies at fixed scattering angle. In the case of N 2 molecule, the TDCS shows oscillatory behaviour with the variation of the electron emission angle. The positions of the binary peak obtained by our theoretical models are well established by the experimental findings, but a large deviation is found in the region of the recoil peak. The contributions of TDCS for different molecular orbitals of the molecules to the spectrum of angular distributions at different electron emission energies have also been analyzed. Finally, a comparison is made with the measurement in coplanar asymmetry geometry. Overall, good agreement was found between experiments and M3CW theory.

Measurement, evaluation and benchmarking of differential cross sections for proton elastic scattering on natO in the energy range E = 4–6 MeV, suitable for EBS

In this study we present the experimental differential cross sections of the natO(p,p0) elastic scattering, determined via the relative measurement technique, in the proton beam energy range Elab = 4–6 MeV with a varying step (from 5 to 15 keV), at six backscattering detector angles between 120° and 170° (every 10°). A thin, self-supporting target manufactured was used in this experiment and the determination of its stoichiometry was carried out according to the currently existing evaluation at lower energy, which has also been benchmarked recently. The measurements were performed using the Van de Graaff Tandem 5.5 MV Accelerator of N.C.S.R. “Demokritos” in Athens, Greece. Theoretical calculations leading to the extension of the existing evaluation up to Ep,lab ∼ 6 MeV have also been performed and the obtained results seem to reproduce well not only the differential cross-section datasets obtained in the present work, but also already existing ones in literature for this extended proton beam energy range. The observed peculiarities and discrepancies are discussed and analyzed, while the theoretical differential cross sections are validated via an accurate benchmarking experiment carried out at RUBION, Ruhr University Bochum, using a thick Bi2O3 target.

Cross sections for elastic electron scattering by benzene at low and intermediate energies

We present experimental and theoretical differential cross sections for elastic electron scattering from benzene. The present experimental results are obtained at incident electron energies ranging from 1 to 50 eV and for scattering angles from ${10}^{\ensuremath{\circ}}$ to ${130}^{\ensuremath{\circ}}$. The experimental measurements are compared to available results from 1 to 10 eV and to theoretical results from 10 to 50 eV, both based on the Schwinger multichannel (SMC) method. Different electron scattering calculations are carried out by employing varied basis sets and multichannel coupling schemes. This allows us to (i) obtain relatively converged cross sections with respect to the inclusion of Rydberg excited states, (ii) observe significant variations in the forward scattering as a function of the multichannel coupling scheme, and (iii) explore possible effects stemming from states lying above the ionization threshold. Overall, the agreement between experiments and models is found to be very good to excellent. The remaining discrepancies point out areas in which the SMC method should be improved.

Elastic and absorption electron collisions with acetaldehyde

We report a theoretical–experimental investigation on elastic electron scattering by acetaldehyde (CH $$_3$$ CHO) in the 0.5–800 eV energy range. Theoretically, the Pade approximation and the single-center partial-wave expansion method were applied to solve the Lippmann–Schwinger scattering equation, whereas a molecular complex optical potential was used to describe the electron–molecule interaction. Calculations in the independent-atom framework were also performed. Angular distributions of the elastically scattered electrons were measured in the 10 $$^{\circ }$$ –130 $$^{\circ }$$ and 30–800 eV ranges using a crossed beams geometry. Absolute values of differential cross sections were derived by the relative flow technique. In addition, integral and momentum transfer cross sections were obtained from the experimental and theoretical differential cross sections via a numerical integration procedure. Comparison between our results and previous experimental and theoretical calculations is made.

Nucleon-nucleus optical potential computed with the Gogny interaction

The ability of the Gogny forces of the D1 family to describe the nucleon-nucleus scattering is studied. To this end, we use an optical model (OM) potential built up using a semi-microscopic nuclear matter (NM) approach. The real and imaginary parts of the OM are provided by the first and second-order terms, respectively, of the Taylor expansion of the mass operator calculated within the Brueckner–Hartree–Fock (BHF) method using the reaction G-matrix built up with the effective Gogny force instead of a microscopic interaction. The optical potential in finite nuclei is obtained through the local density approximation (LDA) using the neutron and proton densities provided by a quasi-local Hartree–Fock (HF) calculation with the same Gogny force for the sake of consistency. A reasonable good agreement is found between the theoretical differential cross-sections and the analyzing powers (AP) of the elastic neutron and proton scattering along the periodic table from Ca to Pb calculated with the Gogny forces and the corresponding values predicted by the global phenomenological potential of Koning and Delaroche. To investigate the limits of the approximations used in this work, comparisons with the results of nucleon-nucleus elastic scattering in 40Ca and 48Ca obtained using the nuclear structure model (NSM) are also performed.

Theoretical and experimental study on scattering of low-energy electrons by dimethyl and diethyl ethers

We report a joint theoretical and experimental investigation on low-energy electron scattering by dimethyl and diethyl ethers. The experimental elastic differential cross sections were measured at impact energies from 1 eV up to 30 eV and scattering angle range of 10° to 130°. Theoretical elastic differential, integral and momentum-transfer cross sections are calculated at impact energies up to 30 eV, employing the Schwinger multichannel method implemented with norm-conserving pseudopotentials, in the static-exchange and static-exchange plus polarization approximations. Our experimental and theoretical results for dimethyl and diethyl ether are compared with previous data for their isomers, ethanol and butanol, respectively. These comparisons reveal that although the cross sections for the ether and its respective alcohol present similar magnitudes, the angular behavior of their differential cross sections shows some significant differences. From the analysis of the integral cross sections for electron scattering by dimethyl and diethyl ether, we observe a broad structure, at around 9.5 eV, which we assign as the overlap of several resonant structures.

Differential Production Cross Sections for Isotopes of Light Nuclei in the $$\boldsymbol{{}^{18}\textrm{O}+^{181}}$$Ta Reaction

The results of experiments performed at a high-resolution magnetic spectrometer (MAVR) are presented. The differential production cross sections for oxygen isotopes in the $${}^{18}\textrm{O}+^{181}$$ Ta reaction at the projectile energy of 10 MeV per nucleon were measured at the MAVR facility. The yield of reaction products is analyzed theoretically in the finite-range distorted-wave Born approximation (FR-DWBA method) by means of the FRESCO code. The theoretical differential cross sections are calculated for sequential neutron transfer. The contributions of the mechanisms of sequential neutron transfer and dineutron-cluster transfer to the production cross sections for the neutron-rich oxygen isotopes $${}^{20,22,24}$$ O are studied.

Theoretical and experimental cross sections for electron scattering from halothane

We report a joint theoretical and experimental study on elastic scattering of electrons from halothane (CF3CHBrCl). The theoretical differential, integral and momentum transfer cross sections were obtained with the Schwinger multichannel method implemented with pseudopotentials (SMCPP), and with the independent atom model with screening corrected additivity rule including interference effects (IAM-SCAR+I). The differential cross sections measurements were conducted for incident electron energies of 10, 20, 30 and 50 eV, while the scattered electron angular range varied from 7° to 100°. At these energies the present experimental differential cross sections are in reasonable agreement with both SMCPP and IAM-SCAR+I calculations. As expected, the two theoretical methodologies agree well with each other as the electron impact energy increases. We also discuss the presence of low-energy resonances and a bound anion state identified in our SMCPP calculations.

The physics of irradiation of biological matter by ion beams

In radiobiology, predicting the evolution of irradiated biological matter is nowadays an active field of research to identify DNA lesions or to adapt the radiotherapeutic protocols in radiation oncology. In this context, the numerical methods, based on Monte Carlo track-structure simulations, represent the most suitable and powerful tools for understanding the radiobiological damages induced by ionizing particles. In the present work, we report the theoretical differential and total cross sections, computed within the quantum mechanical continuum distorted wave-eikonal initial state (CDW-EIS) approach, for ion impact on water vapor and DNA nucleobases. These cross sections have been used to build up the input database for the homemade Monte Carlo track-structure TILDA-V. A comparison between the theoretical predictions and the available experimental data is presented. Micro-dosimetry results obtained with TILDA-V are also reported.

Communication: State-to-state inelastic scattering of interstellar O2 with H2.

Molecular oxygen (O2) is predicted to be a major reservoir of elemental oxygen in dense interstellar molecular clouds. However, the abundance of O2 derived from astronomical observations is much lower than expected. Solving the discrepancies between models and observations requires a review of the chemistry and collisional excitation of O2 in space. In particular, O2-H2 collisions are crucial to derive O2 abundance in space from the interstellar spectra. A crossed molecular beam experiment to probe the rotational excitation of O2 due to H2 collisions at energies of 650 cm-1 is reported. Velocity map imaging was combined with state-selective detection of O2( ) by (2 + 1) resonance-enhanced multiphoton ionization. The obtained raw images were corrected from density to flux and the differential cross sections (DCSs) were then extracted. Exact quantum mechanical calculations were also performed. Very good agreement between experimental and theoretical DCSs was found. The agreement demonstrates our ability to determine inelastic processes between O2 molecules and H2 both theoretically and experimentally and that the excitation of O2 in the interstellar medium can be correctly modeled. Consequences on the astrophysical modeling are briefly evaluated.

Elastic scattering and vibrational excitation for electron impact on para-benzoquinone.

We report on theoretical elastic and experimental vibrational-excitation differential cross sections (DCSs) for electron scattering from para-benzoquinone (C6H4O2), in the intermediate energy range 15-50 eV. The calculations were conducted with two different theoretical methodologies, the Schwinger multichannel method with pseudopotentials (SMCPP) and the independent atom method with screening corrected additivity rule (IAM-SCAR) that also now incorporates a further interference (I) term. The SMCPP with N energetically open electronic states (Nopen) at the static-exchange-plus-polarisation (Nopench-SEP) level was used to calculate the scattering amplitudes using a channel coupling scheme that ranges from 1ch-SE up to the 89ch-SEP level of approximation. We found that in going from the 38ch-SEP to the 89ch-SEP, at all energies considered here, the elastic DCSs did not change significantly in terms of both their shapes and magnitudes. This is a good indication that our SMCPP 89ch-SEP elastic DCSs are converged with respect to the multichannel coupling effect for the investigated intermediate energies. While agreement between our IAM-SCAR+I and SMCPP 89ch-SEP computations improves as the incident electron energy increases from 15 eV, overall the level of accord is only marginal. This is particularly true at middle scattering angles, suggesting that our SCAR and interference corrections are failing somewhat for this molecule below 50 eV. We also report experimental DCS results, using a crossed-beam apparatus, for excitation of some of the unresolved ("hybrid") vibrational quanta (bands I-III) of para-benzoquinone. Those data were derived from electron energy loss spectra that were measured over a scattered electron angular range of 10°-90° and put on an absolute scale using our elastic SMCPP 89ch-SEP DCS results. The energy resolution of our measurements was ∼80 meV, which is why, at least in part, the observed vibrational features were only partially resolved. To the best of our knowledge, there are no other experimental or theoretical vibrational excitation results against which we might compare the present measurements.

Differential cross sections for excitation of H2 by low-energy electron impact

Experimental and theoretical differential cross sections (DCS) for the electron-impact excitation of molecular hydrogen to the , , , , and the states are presented at incident energies near to threshold. The experimental DCSs were taken at incident energies of 14, 15, 16 and 17.5 eV and for scattering angles from 10° to 130°. The theoretical DCSs are from the convergent close-coupling method which has recently successfully modeled differential electron scattering from H2 when compared with available experiment at energies of 17.5 eV and above.

Triple differential cross sections for the ionization of formic acid by electron impact

Theoretical triple differential cross sections for the simple ionization of the two outermost valence orbitals of formic acid monomer are given in this work. The first Born approximation is used to describe the collision dynamics with one Coulomb wave function for the ejected electron. Single-center molecular wave functions are generated using the Gaussian 09 program. The cross sections are calculated for an average molecular orientation with the proper average method. The results show that the proposed framework provides better agreement with experimental data than the previously used orientation averaged molecular orbital approximation. Consequently, this work shows the importance of performing the orientation averaging on the cross sections and not on the molecular wave functions. It also provides a methodology that reduces the complexity of calculations while maintaining a good quality of the results.

Elastic Differential Cross Sections for Electron Scattering with Dichloromethane

SynopsisIn the present study joint experimental and theoretical elastic differential cross sections for electron scattering from dichloromethane in the incident electron energy region 7 to 50eV are discussed.

Experimental and theoretical triple differential cross sections for electron-impact ionization of Ar (3p) for equal energy final state electrons

There have been several studies of electron-impact ionization of inert gases for asymmetric final state energy sharing and normally one electron has an energy significantly higher than the other. However, there have been relatively few studies examining equal energy final state electrons. Here we report experimental and theoretical triple differential cross sections for electron impact ionization of Ar (3p) for equal energy sharing of the outgoing electrons. Previous experimental results combined with some new measurements are compared with distorted wave born approximation (DWBA) results, DWBA results using the Ward–Macek (WM) approximation for the post collision interaction (PCI), and three-body distorted wave (3DW) which includes PCI without approximation. The results show that it is crucially important to include PCI in the calculation particularly for lower energies and that the WM approximation is valid only for high energies. The 3DW, on the other hand, is in reasonably good agreement with data down to fairly low energies.

Theoretical and experimental study on electron interactions with chlorobenzene: Shape resonances and differential cross sections.

In this work, we report theoretical and experimental cross sections for elastic scattering of electrons by chlorobenzene (ClB). The theoretical integral and differential cross sections (DCSs) were obtained with the Schwinger multichannel method implemented with pseudopotentials (SMCPP) and the independent atom method with screening corrected additivity rule (IAM-SCAR). The calculations with the SMCPP method were done in the static-exchange (SE) approximation, for energies above 12 eV, and in the static-exchange plus polarization approximation, for energies up to 12 eV. The calculations with the IAM-SCAR method covered energies up to 500 eV. The experimental differential cross sections were obtained in the high resolution electron energy loss spectrometer VG-SEELS 400, in Lisbon, for electron energies from 8.0 eV to 50 eV and angular range from 7(∘) to 110(∘). From the present theoretical integral cross section (ICS) we discuss the low-energy shape-resonances present in chlorobenzene and compare our computed resonance spectra with available electron transmission spectroscopy data present in the literature. Since there is no other work in the literature reporting differential cross sections for this molecule, we compare our theoretical and experimental DCSs with experimental data available for the parent molecule benzene.

Comparison of experimental and theoretical triple differential cross sections for the single ionization ofCO2 (1πg)by electron impact

Experimental and theoretical triple differential cross sections for intermediate-energy (250 eV) electron-impact single ionization of the ${\mathrm{CO}}_{2}$ are presented for three fixed projectile scattering angles. Results are presented for ionization of the outermost $1{\ensuremath{\pi}}_{g}$ molecular orbital of $\mathrm{C}{\mathrm{O}}_{2}$ in a coplanar asymmetric geometry. The experimental data are compared to predictions from the three-center Coulomb continuum approximation for triatomic targets, and the molecular three-body distorted wave (M3DW) model. It is observed that while both theories are in reasonable qualitative agreement with experiment, the M3DW is in the best overall agreement with experiment.

Experimental and theoretical double differential cross sections for electron impact ionization of methane

Experimental and theoretical double differential cross sections (DDCSs) for electron-induced ionization of methane (CH4) are here reported for primary energies ranging from 50 eV to 350 eV and ejection angles between 25° and 130°. Experimental DDCSs are compared with theoretical predictions performed within the first Born approximation Coulomb wave. In this model, the initial molecular state is described by using single center wave functions, the incident (scattered) electron being described by a plane wave, while a Coulomb wave function is used for modeling the secondary ejected electron. A fairly good agreement may be observed between theory and experiment with nevertheless an expected systematic overestimation of the theory at low-ejection energies (<50 eV).

Theoretical and experimental differential cross sections for electron impact excitation of the electronic bands of furfural.

We report results from a joint experimental and theoretical investigation into electron scattering from the important industrial species furfural (C5H4O2). Specifically, differential cross sections (DCSs) have been measured and calculated for the electron-impact excitation of the electronic states of C5H4O2. The measurements were carried out at energies in the range 20-40 eV, and for scattered-electron angles between 10° and 90°. The energy resolution of those experiments was typically ∼80 meV. Corresponding Schwinger multichannel method with pseudo-potential calculations, for energies between 6-50 eV and with and without Born-closure, were also performed for a sub-set of the excited electronic-states that were accessed in the measurements. Those calculations were undertaken at the static exchange plus polarisation-level using a minimum orbital basis for single configuration interaction (MOB-SCI) approach. Agreement between the measured and calculated DCSs was qualitatively quite good, although to obtain quantitative accord, the theory would need to incorporate even more channels into the MOB-SCI. The role of multichannel coupling on the computed electronic-state DCSs is also explored in some detail.

State-to-State Inelastic Scattering of O2 with Helium.

Molecular oxygen (O2) is extremely important for a wide variety of processes on and outside Earth. Indeed, O2–He collisions are crucial to model O2 abundance in space or to create ultracold O2 molecules. A crossed molecular beam experiment to probe rotational excitation of O2 due to helium collisions at energies of 660 cm–1 is reported. Velocity map imaging was combined with state-selective detection of O2(X3Σg–) by (2+1) resonance-enhanced multiphoton ionization. The obtained raw O2+ images were corrected from density to flux and the differential cross sections (DCS) were then extracted for six O2 final states. Exact quantum mechanical calculations were also performed. A very good agreement between experimental and theoretical DCSs was found by using an initial O2 beam population ratio of 80% for the first rotational state and 20% for the first excited state. The agreement demonstrates our ability to model inelastic processes between O2 molecules and rare gas both theoretically and experimentally.