Coulomb Cross Section Research Articles

A machine-learning augmented mixed method for simulating α particle transport in inertial confinement fusion

The plasma heating by the α particle transport is a main self-heating source in inertial confinement fusion (ICF) that determines the capsule implosion performance. Due to the high energy of α particle and the high temperature in the ICF capsule hot spot, significant non-equilibrium effect exists and the continuum mechanics breaks down. For the numerical simulation of implosion and charged particle transport, the Boltzmann equation needs to be solved to capture the kinetic effects. However, the 7-dimensional Boltzmann equation, the highly frequent Coulomb collision, and the multi-folded integral stopping power formulation greatly limits the computational efficiency and challenges the computational power. To overcome the high computational cost of high-frequent Coulomb collisions, we propose a mixed collision model according to which the collisions are categorized into low-frequent large-angle collisions and high frequent small-angle grazing collisions. The large-angle collision process is precisely solved based on the Coulomb cross-section. For the highly frequent small-angle grazing, a statistic model is constructed with second-order accuracy in time. The mixed collision model reduces the computational cost of scattering calculation by two orders of magnitude. For the multi-folded integral stopping power formulation, a neural network is used to improve computational efficiency. Based on the proposed algorithm, we develop one-dimensional to three-dimensional module code to directly solve the α particle transport Boltzmann equation. The α transport module code is integrated into the multi-physics LARED-S program. The MC version ICF software is verified by a simulation study of the N210207 and N191110 experiment.

Investigations on Coulomb fission time scales and cross sections in inverse kinematics

In inverse kinematics, we explored Coulomb fission cross-sections and time scales. Heavier projectiles such as 238U, 132Xe, and 208Pb on lighter targets such as 16O 26Mg, 27Al, 32S, 35Cl, 40,48Ca, 45Sc, 48,50Ti, 56,58Fe, 64Ni, 89Y, 30Si and 65Zn were looked into. The photofission cross-sections and the number of equivalent photons impinge on the target nuclei are important parameters in cross-section assessment. The anticipated cross-sections increases with increase in atomic number of target nuclei. We also explored the time scale of projectile nuclei at various transition levels. The estimated time scales accord well with the available experimental value, which is in the order of picoseconds. In addition, we predicted time scales of 165Ho nuclei in the transition state from 19/2+→15/2+ to 29/2+→25/2+ for which experimental time scales are not available in literature. As a result, Coulomb fission is one of the causes that has severely hampered in the formation of compound nuclei. Prediction of time scales, in particular, would aid in understanding the structure of various energy levels.

Triaxiality and the nature of low-energy excitations in Ge76

The deformation properties of the low-lying states in Ge76 have been investigated following a safe-energy Coulomb excitation measurement with the GRETINA tracking array and CHICO2 heavy-ion counter at the ATLAS accelerator facility at Argonne National Laboratory. A comprehensive set of transition and static E2 matrix elements were extracted from the measured differential Coulomb cross sections and compared with results of configuration-interaction shell-model calculations and computations carried out within the framework of the generalized triaxial rotor model. The remarkable agreement between the calculated and experimental data supports a near-maximum triaxial deformation for the ground state of Ge76. In addition, the degree of softness of the asymmetry in Ge76 and Se76 was investigated using rotational invariants generated from configuration-interaction shell-model wave functions computed with the jj44b and JUN45 effective interactions. The resulting invariants are shown to be consistent with a stiff triaxial deformation in Ge76 and a predominantly soft triaxial potential for Se76, in agreement with the conclusions of recent works by this collaboration.5 MoreReceived 27 January 2023Accepted 3 April 2023DOI:https://doi.org/10.1103/PhysRevC.107.044314©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNuclear reactionsNuclear structure & decaysNucleon distributionProperties59 ≤ A ≤ 89TechniquesCollective modelsShell modelNuclear Physics

Plasmons in two-dimensional topological insulators

We analyze collective excitations in models of two-dimensional topological insulators using the random phase approximation. In a two-dimensional extension of the Su-Schrieffer-Heeger model, edge plasmonic excitations with induced charge-density distributions localized at the boundaries of the system are found in the topologically non-trivial phase, dispersing similarly as one-dimensional bulk plasmons in the conventional Su-Schrieffer-Heeger chain. For two-dimensional bulk collective modes, we reveal regimes of enhanced inter-band wave function correlations, leading to characteristic hardening and softening of inter- and intra-band bulk plasmonic branches, respectively. In the two-dimensional Haldane Chern insulator model, chiral, uni-directional edge plasmons in nano-ribbon architectures are observed, which can be characterized by an effective Coulomb interaction cross section. Bulk collective excitations in the two-dimensional Haldane model are shown to be originated by single-particle band structure details in different topological phases.

On the isospin effects in the geometry of vanishing flow in heavy-ion collisions

We study the behavior of the geometry of vanishing flow (GVF) and its system size dependence at different incident energies. We find that the geometry of vanishing flow is sensitive to the incident energy. We also study the role of isospin degree of freedom through Coulomb potential, symmetry energy and nucleon-nucleon cross sections. Our study reveals that isospin degree of freedom through nucleon-nucleon cross section plays a dominant role compared to Coulomb potential and symmetry energy.

The Effect of Non‐Coulomb Scattering of Relativistic Electrons on the Generation of Runaways in Multicomponent Plasma

AbstractHighly energetic runaway electrons are able to penetrate the electron shell of partly ionized heavy ions during collisions, for which reason they may be scattered by a positive charge effectively larger than that of a shielded nucleus. This effect increases the Coulomb cross section and can be treated via an effective ion charge Zeff (εkin) that depends on the energy of the incident electrons εkin. The increase of effective charge number with increasing electron energy in multi‐component plasmas renders qualitatively the same result as high Zeff Coulomb plasmas. Since the generation rate of runaways depends on Zeff, its production during the mitigation of disruptions by massive gas injection could in some cases decrease owing to a heavy impurity concentration in the boundary tokamak plasma. This may explain why it has been observed that the runaway's avalanche is suppressed at electron densities below the so‐called “Rosenbluth density” (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

J-matrix method for calculations of three-body Coulomb wave functions and cross sections of physical processes

The review is devoted to a widely known method of numerical solution to the three-body Coulomb problem, namely, the J-matrix method. Special attention is paid to ways of solving the Lippmann-Schwinger integral equation without attraction of pseudostates. Difficulties related to the formulation of the integral equation in spherical coordinates, leading to the divergence of its integral part if the wave function is calculated with two asymptotically free electrons, are demonstrated. In addition, the relation between exact and approximate solutions turns out to be unclear if the matrix of a residual potential is restricted to a finite number of basis functions, with the latter being increased. It is shown that, in principle, these problems can be avoided by reformulating a problem in parabolic coordinates.

Microscopic calculation of the magnetic field of neutron stars

Based on the Dirac equation describing an electron moving in a uniform and cylindrically symmetric magnetic field which may be the result of the self-consistent mean field of the electrons themselves in a neutron star, we have obtained the eigen solutions and the orbital magnetic moments of electrons in which each eigen orbital can be calculated. From the eigen energy spectrum we find that the lowest energy level is the highly degenerate orbitals with the quantum numbers pz = 0, n = 0, and m ≥ 0. At the ground state, the electrons fill the lowest eigen states to form many Landau magnetic cells and each cell is a circular disk with the radius λfree and the thickness λe, where λfree is the electron mean free path determined by Coulomb cross section and electron density and λe is the electron Compton wavelength. The magnetic moment of each cell and the number of cells in the neutron star are calculated, from which the total magnetic moment and magnetic field of the neutron star can be calculated. The results are compared with the observational data and the agreement is reasonable.

Coulomb and nuclear breakup effects in the single neutron removal reaction197Au(17C,16Cγ)X

We analyze the recently obtained new data on the partial cross sections and parallel momentum distributions for transitions to ground as well as excited states of the 16C core, in the one-neutron removal reaction 197Au(17C,16C gamma)X at the beam energy of 61 MeV/nucleon. The Coulomb and nuclear breakup components of the one-neutron removal cross sections have been calculated within a finite range distorted wave Born approximation theory and an eikonal model, respectively. The nuclear contributions dominate the partial cross sections for the core excited states. By adding the nuclear and Coulomb cross sections together, a reasonable agreement is obtained with the data for these states. The shapes of the experimental parallel momentum distributions of the core states are described well by the theory.

Temperatures in the upper ionosphere and plasmasphere

Modeling of the topside ionosphere requires a knowledge of the electron and ion temperatures (Te and Ti) as a function of height. Data in the International Reference Ionosphere (IRI) model are sometimes conflicting, and extend only up to 3000 km. An exact, analytic solution is found for the variation of Te along a magnetic field line, making full allowance for changes in the cross section and inclination of the tube of force. The downward heat flux is assumed to decrease smoothly with height, becoming zero at the top of the field line. Changes in the Coulomb cross section increase plasmaspheric temperatures by 6–8%. For a given field line, the temperature profile is defined by two parameters, taken as the temperature To and gradient Go at a reference height of 400 km. Results are fitted to satellite data, for mean day and night conditions, at intervals of 5° in latitude and heights from 400 to 8000 km. Diurnal changes are reproduced using sunrise and sunset transitions that are matched to observed values. Seasonal changes in Te are generally less than experimental errors. A solar activity variation of 30–40% is required, at low heights, to match the change in neutral temperature. Exospheric temperatures must also increase by 10–20%, near solar maximum. A first‐order correction is derived for high‐latitude heating during periods of magnetic activity. Values of Ti are calculated from the Te profile and the neutral temperature Tn, giving results that agree well with mean observations. The use of physically acceptable temperature profiles, fitted to the often conflicting satellite data, should give more consistent results for most purposes.

Excitation and neutron decay of xenon studied by forward-angle scattering of high-energy 17O ions

Excitation energy spectra and neutron decay of xenon have been measured in extreme forward angle scattering of 250 A and 400 A MeV 17O ions, using one quadrant of the CELSIUS storage ring as a magnetic spectrometer. The observed excitation energy spectrum, ranging from 12 to 36 MeV, has been compared with Coulomb cross section calculations. Neutron and missing energy spectra are compared with statistical decay calculations using the code CASCADE. In addition to statistical decay from giant resonances and other continuum excitations, a large fraction of forward peaked fast neutrons was observed throughout the entire excitation energy region. A possible reaction mechanism behind these fast neutrons is discussed.

Kinetic electrons in high‐speed solar wind streams: Formation of high‐energy tails

We study the evolution of the electron velocity distribution function in high‐speed solar wind streams from the collision‐dominated corona and into the collisionless interplanetary space. The model we employ solves the kinetic transport equation with the Fokker‐Planck collision operator to describe Coulomb collisions between electrons. We use a test particle approach, where test electrons are injected into a prescribed solar wind background. The density, temperature, and electric field associated with the background are computed from fluid models. The test electrons are in thermal equilibrium with the background at the base of the corona, and we study the evolution of the velocity distribution of the test electrons as a function of altitude. We find that velocity filtration, due to the energy dependence of the Coulomb cross section, is a small effect and is not capable of producing significant beams in the distribution or a temperature moment that increases with altitude. The distribution function is mainly determined by the electric field and the expanding geometry and consists of a population with an almost isotropic core which is bound in the electrostatic potential and a beam‐like high‐energy tail which escapes. The trapped electrons contribute significantly to the even moments of the distribution function but almost nothing to the odd moments; the drift speed and energy flux moments are carried solely by the tail. In order to describe the high‐speed solar wind observed near 0.3 AU by the Helios spacecraft, we use a multifluid model where ions are heated preferentially. The resulting test electron distribution at 0.3 AU, in this background, is in very good agreement with the velocity distributions observed by the Helios spacecraft.

Dreicer order ambipolar electric fields at Parker's steady state solar wind sonic critical point

The time‐independent ambipolar electric field E(r*) at Parker's solar wind sonic critical point r* is analytically shown to range between (0.6–2.0) ED(r*), where ED(r*) is the local Dreicer [1959, 1960] electric field. The ratio of ambipolar to Dreicer field strength scales as (〈T*〉/106° K)3/2 20/ln Λ, where 〈T*〉 is the average of electron and ion temperatures at the critical point. As a million degree corona is nearly certainly required for the wind as we observe it, E(r*) ≃ ED(r*). Since the steady state solar wind is characterized by no parallel currents, these large electric fields require generalizations of Dreicer's discussion of what are the results of such large electric fields. This is clear since even when E = 0.43ED in a homogeneous plasma, the electron fluid drifts at the electron thermal speed with respect to the ions in the absence of collective instabilities. Consequences of such a large current at the critical point are not found at 1 AU. The electric fields at the orbit of earth [Scudder, 1995b] and at the base of the fully ionized layer of the transition region [Scudder, 1995a] are nevertheless comparable to the local Dreicer electric field. From a theoretical point of view, the finding that such large electric fields are required in the plasma points to the need for basic modifications to the macroscopic description of a magnetized plasma that are outside of the Chapman‐Enskog‐Spitzer‐Braginskii closure schemes that assume perturbative corrections to homogeneous solutions as an expansion in the small parameter ε = E‖/ED. It is suggested that the possibility to form gradients, to allow heat to flow, and to allow the bulk plasma to move can short circuit the homogeneous expectations of bulk runaway implicit in the Dreicer discussion. However, the intrinsic bifurcation of the electron distribution reflects the physics of the Coulomb cross section in the presence of the very strong dc field and is suggested as the underlying reason for the omnipresent nonthermal distributions inside and out of the critical point. The ambipolar electric field at the solar wind critical point from two‐fluid theory and the electric field assumed in Spitzer‐Braginskii heat transport are shown to disagree at almost all the possible two‐fluid critical points. This same closure flaw also afflicts the fluid portion of any turbulence description that may be thought relevant for the wind.

Space distribution and energy straggling of charged particles via Fokker-Planck equation

The Fokker-Planck equation describing a beam of charged particles entering a homogeneous medium is solved here for a stationary case. Interactions are taken into account through Coulomb cross-section. Starting from the charged-particle distribution as a function of velocity and penetration depth, some important kinetic quantities are calculated, like mean velocity, range and the loss of energy per unit space. In such quantities the energy straggling is taken into account. This phenomenon is not considered in the continuous slowing-down approximation that is commonly used to obtain the range and the stopping power. Finally the well-known Bohr or Bethe formula is found as a first-order approximation of the Fokker-Planck equation.

Ion drag effects in inductively coupled plasmas for etching

Ion drag refers to Coulomb momentum transfer collisions between a directed flux of charged particles and a second charged species. It is an important force in determining the motion of negatively charged dust particles in plasma processing reactors. The same ion drag mechanism acts between the directed flux of positive ions moving towards the boundaries of a plasma etching reactor and negative ions being accelerated by electrostatic forces towards the center of the plasma. In this letter, we discuss the parameter space for inductively coupled plasma etching reactors in which ion drag forces on negative ions influence their transport using results from a two-dimensional plasma equipment model. We find that ion drag forces on negative ions are important at high plasma densities and low ion temperatures. Under these conditions, the large positive ion flux, coupled with a large Coulomb cross section, creates an ion drag force which may dominate the electrostatic forces on negative ions. The end result is that negative ions may accumulate near the sheath edge.

K-shell ionization cross sections of Al, Si, S, Ca, and Zn for oxygen ions in the energy range 1.1-8 MeV.

{ital K}-shell ionization cross sections induced by 1.1--8-MeV oxygen ions in Al, Si, S, Ca, and Zn were measured using different target thicknesses. The cross sections for vanishingly thin and for charge-equilibrium targets were obtained by extrapolation. The experimental results are compared to the perturbed stationary-state approximation with energy-loss, Coulomb, and relativistic corrections (ECPSSR) cross sections (Brandt and Lapicki, Phys. Rev. A 23, 1717 (1981)), to the modification of the ECPSSR theory (MECPSSR) (Benka, Geretschlaeger, and Paul, J. Phys. (Paris) Colloq. Suppl. 12, C9-251 (1987)), to the theory for direct Coulomb ionization of the 1{ital s}{sigma} molecular orbital (Montenegro and Sigaud, J. Phys. B 18, 299 (1985)), and to several semiclassical approximation codes using either the united atom binding procedure or the variational approach of Andersen {ital et} {ital al}. (Nucl. Instrum. Methods 192, 79 (1982)). The cross sections were also compared to the statistical molecular-orbital theory of inner-shell ionization for (nearly) symmetric atomic collisions (Mittelman and Wilets, Phys. Rev. 154, 12 (1967)). For fast collisions ({xi}{similar to}1), the ionization cross sections are well reproduced by theories for direct Coulomb ionization. For slower collisions ({xi}{lt}1), the experimental cross sections are systematically higher than the direct-ionization values, but they agree satisfactorilymore » with the summed cross sections for direct Coulomb ionization and for molecular-orbital ionization. Best agreement (within a factor of 2) was found for the sums of MECPSSR and statistical cross sections.« less

Oxidation studies of yttrium implanted copper, molybdenum and tantalum using high-energy resonant helium backscattering

The 16O(α,α) 16O resonance at 8.8 MeV was used to determine the oxidation rates of Y implanted Cu, Mo and Ta. At back angles this resonance has a uniform cross section of ≈ 25 times the Coulomb cross section over an energy range of ≈ 0.6 MeV, allowing the surface oxidation of metals to be easily determined without the necessity of weighing the samples. Oxidations were made at 200, 400 and 500° C for Cu, Mo and Ta, respectively and for times ranging from 10 min to 10 h. At short times the oxidation is enhanced in the Y implanted materials as compared to unimplanted materials. However, as the oxidation times increase the oxidation rate in the implanted materials falls, and in the case of Cu and Ta the total amount of oxygen in the implanted samples eventually becomes lower than that of the unimplanted samples. In all cases Y implantation strongly effects the oxidation process. For Ta and Cu retardation of grain boundary oxidation occurs. For Mo, implantation produces a discrete oxide layer which grows in a layer-by-layer manner. These data indicate that the YCu and the YTa oxides are more passivating than their unimplanted counterparts.

Method for including electron-electron collisions in Monte Carlo simulations of electron swarms in partially ionized gases.

A method whereby electron-electron collisions can be included in Monte Carlo simulations of electron swarms in low-temperature partially ionized plasmas is presented. In this method, electron-electron (e-e) collisions are treated as being functionally equivalent to electron--neutral-species collisions. In doing so, individual pseudoelectron particles in the simulation collide with an energy-resolved electron fluid. Energy is exchanged with this fluid using the Coulomb cross section. When e-e collisions dominate, the electron-energy distribution evolves to being Maxwellian. The method is made computationally tractable by using a modified null-cross-section technique that eliminates the need for recalculating collision probabilities as the electron-energy distribution evolves.

Soft giant dipole mode of 11Li.

The low-lying electric dipole distribution for {sup 11}Li is examined in detail in a large basis nonspurious shell model which includes up to 3{h bar}{omega} of excitation. A very strong enhancement of the {ital E}1 strength between 1 and 4 MeV of excitation is predicted when Woods-Saxon single-particle wave functions are used. The relativistic Coulomb excitation cross section is underestimated. However, an analysis of the contributions to the {ital E}1 matrix elements indicates that small changes in the structure of the low-lying states can lead to a significant increase in the predicted {ital E}1 strengths, so that excitations normally omitted from shell-model calculations are not necessarily needed to explain the anomalous Coulomb cross section.

Coulomb versus nuclear breakup in 11Li fragmentation.

The cross section for two-neutron removal from a beam of relativistic $^{11}\mathrm{Li}$ is calculated in an eikonal approximation. We find a larger nuclear cross section in reactions with heavy nuclei than estimated by Kobayashi et al. This lowers the inferred Coulomb cross section for reactions on $^{208}\mathrm{Pb}$ from 890 to a range of 560--740 mb, depending on the assumed single-particle binding energy of the valence neutron.