Total Inelastic Scattering Cross Sections Research Articles

Electron scattering cross sections for the ground and excited states of tin

A comprehensive set of cross sections for electron scattering from the ground and first four excited states of tin has been calculated using the Relativistic Convergent Close-Coupling method. Elastic scattering, momentum transfer, total scattering, and total-inelastic scattering cross sections have been produced for the 5p23P0,1,2, 1D2 and 1S0 states of atomic tin over a projectile energy range of 0.1 eV to 1000 eV. Over the same projectile energy range, state-resolved cross sections for excitations to the 5p2, 5p6s, 5p5d and 5p6p manifolds from the ground and first four excited states of tin are presented. Total single-ionisation cross sections have been calculated which account for the direct ionisation of electrons in the valence 5p and closed 5s shells, as well as indirect contributions from excitation auto-ionisation. These ionisation cross sections are presented for projectile energies up to 1000 eV. Maxwellian rate coefficients have been calculated for all studied transitions over electron temperatures ranging from 0.5 eV to 200 eV and fitted with simple formulas. The fit coefficients are tabulated for use in modelling applications.

What can we learn from (n,xnγ) cross sections about reaction mechanism and nuclear structure?

Inelastic (n,n') cross section is a key quantity to accurately simulate reactor cores, and its precision was shown to need significant improvements. To bypass the experimental difficulties to detect neutrons from (n,xn) reaction and to discriminate inelastically scattered neutrons from those following the fission process in case of fissile targets, an indirect but yet powerful method is used: the prompt γ-ray spectroscopy. Along this line, our collaboration has developed the GRAPhEME setup, optimized for actinides, at the GELINA facility to measure partial (n,xn γ) cross sections, from which the total (n,xn) cross section can be inferred. (n,xn γ) experiments with actinides are still particularly challenging, as their structure presents a high level density at low energy, and the competing neutron-induced fission reaction contaminates the γ-energy distribution. New precise measurements of the partial (n,xn γ) cross sections provide a stringent test to theoretical model and offer a way to improve them. This is a path to a better determination of the total inelastic scattering cross sections. In this contribution we discuss modeling aspects of the 238U and 182W (n,n' γ) reactions, also measured with GRAPhEME, using the three codes TALYS, EMPIRE and CoH. We will highlight the needed/expected improvements on reaction modeling and nuclear structure input.

Giant Cross Section for Molecular Ion Formation in Ultracold Rydberg Gases.

We have studied the associative ionization of a Rydberg atom and a ground-state atom in an ultracold Rydberg gas. The measured scattering cross section is 3 orders of magnitude larger than the geometrical size of the produced molecule. This giant enhancement of the reaction kinetics is due to an efficient directed mass transport which is accelerated by the Rydberg electron. We also find that the total inelastic scattering cross section is given by the geometrical size of the Rydberg electron's wave function.

Simple model of bulk and surface excitation effects to inelastic scattering in low-energy electron beam irradiation of multi-walled carbon nanotubes

The effect of bulk and surface excitations to inelastic scattering in low-energy electron beam irradiation of multi-walled carbon nanotubes (MWNTs) is studied using the dielectric formalism. Calculations are based on a semiempirical dielectric response function for MWCNTs determined by means of a many-pole plasmon model with parameters adjusted to available experimental spectroscopic data under theoretical sum-rule constrains. Finite-size effects are considered in the context of electron gas theory via a boundary correction term in the plasmon dispersion relations, thus, allowing a more realistic extrapolation of the electronic excitation spectrum over the whole energy-momentum plane. Energy-loss differential and total inelastic scattering cross sections as a function of electron energy and distance from the surface, valid over the energy range ∼50–30,000 eV, are calculated with the individual contribution of bulk and surface excitations separated and analyzed for the case of normally incident and escaping electrons. The sensitivity of the results to the various approximations for the spatial dispersion of the electronic excitations is quantified. Surface excitations are shown to have a strong influence upon the shape and intensity of the energy-loss differential cross section in the near surface region whereas the general notion of a spatially invariant inelastic mean free path inside the material is found to be of good approximation.

The interaction potential of Ne-HF system and close coupling calculations of the scattering cross sections

An analytic expression of the intermolecular interaction potential of the ground state of the Ne-HF system is obtained by nonlinear least square method to fit the intermolecular interaction energies，which have been calculated for the coupled cluster singles and doubles including connected triple excitations level andwith the augmented correlation consistent polarized quadruple zeta basis set CCSD (T)/aug-cc-pVQZ. Differential and partial cross sections for the Ne-HF scattering are obtained by means of converging close coupling calculations from the fitted ab initio CCSD (T) potential. The calculation is performed separately at the incident energies 60，75，100 and 150meV. The tendency of the scattering cross sections varying with incident energy and the influence of the state-to-state excitation cross sections on the total inelastic scattering cross section are discussed in detail.

Monte Carlo simulations of positrons transmission and backscattering probabilities in nickel

Monte Carlo simulations for positron backscattering from the semi-infinite nickel with normal angle of incidence and the transmission through nickel foils of isotropically implanted positrons from a 22Na β + source is reported. The elastic scattering cross section, have been obtained from Rutherford differential cross section where the numerical coefficient in the atomic screening parameter and spin-relativistic correction factor is taken to be variable. Inelastic scattering model was employed to simulate the energy loss using Gryzinski’s semi-empirical expression and Liljequist and Gryzinski models to calculate the total inelastic scattering cross section. The simulated results and the available experimental data are found to be in reasonable agreement.

PLASMON EXCITATIONS IN METAL CLUSTERS AND FULLERENES

This paper gives a survey of physical phenomena manifesting themselves in electron and photon collisions with atomic clusters. The emphasis is made on electron scattering, photoabsorption and photoionization of fullerenes and metal clusters, however some results are applicable to other types of clusters as well. It is demonstrated that the diffraction and interference phenomena play an important role in the processes of clusters interaction with photons and electrons. The essential role of the multipole surface and volume plasmon excitations is elucidated in the formation of electron energy loss spectra on clusters as well as in the total inelastic scattering cross sections and in multiphoton absorption regime. Attention is paid to the elucidation of the role of the polarization interaction in low energy electron-cluster collisions. This problem is considered for the electron attachment to metallic clusters and the plasmon enhanced photon emission. The mechanisms of electron excitation widths formation and the relaxation of electron excitations in metal clusters and fullerenes are discussed.

Differential cross sections for elastic scattering of electrons by atoms and solids

Differential cross sections (DCSs) for elastic scattering of electrons by neutral atoms are extensively used in studies of electron transport in solids and liquids. A new NIST database has recently been released with DCSs calculated from a relativistic Dirac partial-wave analysis in which the potentials were obtained from Dirac–Hartree–Fock electron densities computed self-consistently for free atoms. We have compared calculated DCSs with measured DCSs for argon for electron energies between 50 eV and 3 keV, and found good agreement for electron energies above about 1 keV but with increasing deviations as the energy is reduced. These deviations are due to the neglect of absorption and polarizability effects in the calculations. Nevertheless, DCSs for neutral atoms have been successfully used in simulations of elastic backscattering of electrons by solid surfaces with energies down to 300 eV as well as for many other applications. It is suggested that this success might be due at least partially to the smaller absorption correction for the DCSs in solids on account of the smaller total inelastic scattering cross sections than for the corresponding free atoms.

Approximate inelastic scattering cross sections of electrons

The approximate expressions for the differential inelastic scattering cross sections of electrons in a medium are proposed from distant and close interactions using generalized oscillator strength. The approximate total inelastic scattering cross section of electrons in a medium is calculated by using the presented expressions for distant and close interactions. For several media, the calculated K- and L-shell electron-impact ionization cross sections, total electron-impact ionization cross sections and inelastic mean free paths and collision stopping powers of electrons are compared to other theoretical and experimental values available from the literature.

Semiclassical inelastic electron-ion collisional excitations in nonideal plasmas

Semiclassical electron-hydrogenic ion collisional excitation cross sections for 1s→2s and 1s→2p0 in nonideal plasmas are obtained. An effective pseudopotential model taking into account the plasma screening and collective effects is applied to describe the electron-ion interaction potential in a classical nonideal plasma. The semiclassical straight-line trajectory approximation is applied to the motion of the projectile electron in order to investigate the variation of the total inelastic scattering cross section as a function of the projectile energy, nonideal plasma parameter, and Debye length. It is found that the transition probabilities in ideal plasmas described by the Debye–Hückel potential model are greater than those in nonideal plasmas described by the pseudopotential model. The maximum position of the transition probability gets closer to the target core as the projectile energy increases. It is also found that the scaled cross section decreases when the nonideal plasma parameter (γ) is increased, i.e., the nonideality of plasmas reduces the electron-ion collision cross section.

Monte-Carlo calculations of positron implantation profiles in silver and gold

To investigate the implantation profiles of positrons in silver and gold, the Monte-Carlo programs developed previously by Özmutlu and Aydın (1997) to simulate the transport of positrons in metals was used. The simulation technique is mainly based on the screened Rutherford differential cross section with a spin-relativistic correction factor for the elastic scattering at high energies supplemented by total cross sections at low energies, Gryzinski’s semi-empirical expression to simulate the energy loss due to inelastic scattering, and Liljequist’s model to calculate the total inelastic scattering cross section. Backscattering probabilities and mean penetration depths were calculated from the implantation profiles of positrons at energies between 1 and 50 keV, entering normally to semi-infinite silver and gold targets. The calculated backscattering probabilities and mean penetration depths are compared with comparable Monte-Carlo data and experimental results for semi-infinite silver and gold targets. The agreement is quite satisfactory, at least, in parts.

Many-body treatment of electron inelastic scattering on metal clusters

In this paper we suggest the many-body treatment for the inelastic scattering of fast electrons on metal clusters. The accurate many-body theory for this process is necessary because electrons in the cluster experience collective excitations during the collision. We perform our calculation in the random phase approximation with exchange using the wavefunctions of the Hartree - Fock jellium model and also in the plasmon resonance approximation. The latter approach is appropriate to treat collective excitations in clusters. We analyse the differential and total inelastic scattering cross sections and elucidate the relative importance of collective electron excitations and single-electron transitions in the formation of the inelastic scattering cross section on metal clusters. We perform this calculation for the magic sodium clusters and . Theoretical results are also compared with the experimental data available for electron collisions with the and clusters. We report some discrepancy between theoretical and experimental results.

Complex scattering lengths in multi-channel atom–molecule collisions

It is shown that in the presence of inelastic scattering, zero energy elastic and inelastic scattering can be characterized by a complex scattering length, the imaginary part of which is related directly to the total inelastic scattering cross section. Collisions between H atoms and vibrationally excited H 2 molecules are investigated. Zero energy cross sections for all vibrational states of H 2 and the corresponding complex scattering lengths are reported using accurate quantum mechanical calculations. We obtain large values of the elastic cross sections which we attribute to s-wave bound and quasi-bound states of H⋯H 2( v). The energies and lifetimes of the quasi-bound states are extracted from the complex scattering lengths.

Monte-Carlo calculations of low energy positrons in copper

An analogue Monte-Carlo code has been used to simulate the transport of positrons in copper with an incoming energy range of 60 eV-30 keV. The simulation technique is based mainly on the screened Rutherford differential cross section with a spin relativistic correction factor for elastic scattering including some extra total cross section information for low energies, Gryzinski's semi-empirical expression was used to simulate energy loss due to inelastic scattering and the Liljequist and Gryzinski models to calculate the total inelastic scattering cross section. The calculated results are compared with experimental data and those from other calculations. Good agreement is observed except in cases of backscattering.

Inelastic Neutron Scattering by235U and238U Nuclei

Inelastic scattered neutron spectra and fission neutron spectra for 235 U and 238 U at incident neutron energies of 1.17, 1.79, and 2.19 MeV were measured by the neutron time-of-flight spectrometer at the Institute of Physics and Power Engineering. A solid tritium target was used as the neutron source. The experimental data were simulated by a Monte Carlo code. The interaction of beam protons inside the target, the reaction kinematics, and multiple scattering in the samples were taken into account. The data were normalized with respect to the C(n,n) and 235 U(n,f) standard reaction cross sections. The experimental results were verified against absolute fission spectrum measurements by using well-known fission cross-section and v values. The Maxwell distribution parameters for the fission spectra, the total inelastic scattering cross sections, and the inelastic scattered neutron spectra were derived. The results of this work confirm the ENDF/B-VI evaluations for 238 U are very close to those of ENDF/B-VI. however, substantial discrepancies exist between our experimental data for 238 U and the ENDF/B-VI and JENDL-3 evaluations concerning the excitation functions for levels between 0.5 and 1.2 MeV and continuum spectra

Monte Carlo calculations of 50 eV-1 MeV positrons in aluminum

An analog Monte Carlo code has been developed to simulate the transport of positrons in aluminum with the incoming energy range 50 eV-1 MeV. The simulation technique is based mainly on the screened Rutherford differential cross section with the spin-relativistic correction factor for the elastic scattering with some extra total cross section information for low energies, Gryzinski's semi-empirical expression to simulate the energy loss due to inelastic scattering and Liljequist's model to calculate the total inelastic scattering cross section. The calculated results are compared with experimental data and those of other calculations and usually good agreement is observed. Our results are consistent with other calculations, but are not in agreement with experiment in backscattering cases.

The many-phonon coupled-channel approach and the analysis of low-energy neutron scattering by spherical nuclei

A way to solve the system of equations of the traditional coupled-channel approach (CCA) by means of the Green-function method is proposed. A many-phonon CCA version is formulated within the harmonic (for the phonons) approximation. Within this version the A-dependence of the s- and p-neutron strength functions and scattering radii, the anisotropy parameters of the angular distribution and the polarization for the elastic scattering, the total inelastic-scattering cross section (to the first 2 + level) are calculated. It is shown that for many nuclei it is necessary to take into account the coupling of single-particle states to many-phonon ones and for these nuclei the mentioned characteristics are slightly dependent on the strength of the imaginary part of the optical potential.

Proton-90Zr interaction at sub-Coulomb proton energies.

The proton-/sup 90/Zr interaction at sub-Coulomb energies has been investigated in the context of the Lane model, with isospin coupling included, and with alternate decay modes represented with the Hauser-Feshbach model. Scattering and reaction cross sections were accurately measured in order to obtain enough information to constrain the real and absorptive parts of the proton potential. Differential elastic scattering excitation functions were measured at back angles of 135/sup 0/ and 165/sup 0/ from 2 to 7 MeV, with cross section accuracies of 3%. The energy range was sufficient to go from a region where the backscattering was predominantly Coulomb, enabling additional checks on the cross section accuracies, to a region where the gross structure of the cross sections deviated significantly from Rutherford scattering. Radiative capture cross sections were measured from 1.9 to 5.7 MeV proton energies. The capture cross sections were obtained by summing the measured cross sections for the first two primary gamma rays in addition to some 34 other transitions which terminated on the ground and first excited state. The total inelastic scattering cross section to all /sup 90/Zr excited states (except the first excited state which has been previously measured) was measured at several energies between 3.9more » and 5.7 MeV by observing the radiative decay of the residual, excited /sup 90/Zr nuclei. The analysis yielded several model parameters suggestive of large nuclear structure effects. The depth of the absorptive potential was found to vary as W/sub D/ = 2.73+0.70 E/sub p/ in the 2 to 7 MeV proton energy range studied. A real diffuseness of 0.54 fm, significantly smaller than that obtained in neighboring nuclei, was obtained.« less

High-resolution structural material (n,xy) production cross sections for 0.2 <En≤ 40 MeV

Abstract An experimental program has been initiated at the Oak Ridge Electron Linear Accelerator (ORELA) to measure yields of individual gamma rays resulting from interactions of 0.2- to 40-MeV neutrons with elements of structural materials of interest both for applied needs and basic research. In this paper we outline this program and present some cross-section results for ″natCr(n,xγ), 56Fe(n,xγ) and 58Ni(n,xγ). A good estimate of the total inelastic scattering cross section is obtained from the production cross section of the gamma ray corresponding to de-excitation of the first 2+ level in the even-even nuclides studied. In addition, cross sections for production of gamma rays resulting from tertiary reactions are measured, thus obtaining scarce cross-section information about these reactions.

Inclusive pion scattering in theΔ(1232)region

A systematic study of inclusive pion scattering from targets of $^{4}\mathrm{He}$, $^{12}\mathrm{C}$, $^{58}\mathrm{Ni}$, and $^{208}\mathrm{Pb}$ has been performed at incident ${\ensuremath{\pi}}^{+}$ kinetic energies of ${T}_{{\ensuremath{\pi}}^{+}}=100, 160, 220, \mathrm{and} 300$ MeV. Particular attention was paid to the kinematic region where energy losses were greater than typical single-particle binding energies. The spectra of scattered pions were integrated to yield angular distributions and total inelastic-scattering cross sections. The spectra for all targets are similar, showing a peak near that expected for a single-step quasifree scattering process.NUCLEAR REACTIONS $^{4}\mathrm{He}$, $^{12}\mathrm{C}$, $^{58}\mathrm{Ni}$, $^{208}\mathrm{Pb}$, (${\ensuremath{\pi}}^{+}, {{\ensuremath{\pi}}^{+}}^{\ensuremath{'}}$), ${T}_{{\ensuremath{\pi}}^{+}}=100, 160, 220, 300$ MeV; measured $\frac{{d}^{2}\ensuremath{\sigma}}{d{\ensuremath{\Omega}}_{{{\ensuremath{\pi}}^{+}}^{\ensuremath{'}}}d{E}_{{{\ensuremath{\pi}}^{+}}^{\ensuremath{'}}}}$.