Intermediate Impact Energies Research Articles

Effect of boundary conditions on the low‐velocity impact damage mechanism of fiber metal laminate

AbstractThe boundary condition is a very important factor when characterizing the impact performance of a material or a structure. However, its effect on fiber metal laminate (FML) has been rarely mentioned. In the present investigation, three levels of low‐velocity impact tests were conducted on the glass fiber reinforced aluminum laminate (Glare) under two different boundary conditions, one was that defined in ASTM D7136 and another one was self‐designed that has the same constraint area but different constraint degree. One basis of the experiments, finite element analyses were performed to gain a deeper understanding of the different damage mechanisms. With which another three boundary conditions were investigated for further considering the effect of constraint areas on both the impact and non‐impact sides, including that defined in another commonly used standard ASTM D5628 and two self‐designed cases. It was indicated that the boundary conditions influenced less the force and energy responses of Glare laminate, regardless of the impact damage levels, and hardly on the damage behavior as well when perforation was encountered. However, influences were obtained under lower and intermediate damage levels, and it was the constraint area on the rear side and constraint degree that played the dominant roles, respectively. The results achieved can provide suggestions for reasonably evaluating the low‐velocity impact performance of FML.Highlights Comparisons were made between the low‐velocity impact behavior of Glare laminates under five different boundary conditions. Boundary conditions influenced hardly on maximum impact force and energy absorbed ratio, but evidently on damage behavior. Constraint area and constraint degree governed damage mechanism under lower and intermediate impact energies, respectively. Influence of boundary conditions on damage behavior disappeared when the impact energy was enough to perforate Glare laminate.

Quantum-mechanical four-body versus semi-classical three-body theories for double charge exchange in collisions of fast alpha particles with helium targets

AbstractWithin the two-channel distorted wave second-order perturbative theoretical formalism, we study capture of both electrons from helium-like targets by heavy nuclei as projectiles at intermediate and high impact energies. The emphasis is on the four-body single-double scattering (SDS-4B) method and the three-body continuum distorted wave impact parameter method (CDW-3B-IPM). The SDS-4B method deals with the full quantum-mechanical correlative dynamics of all the four interactively participating particles (two electrons, two nuclei). The CDW-3B-IPM is a semi-classical three-body independent particle model (one electron, two nuclei), using a combinatorial calculus to describe double capture by a product of two uncorrelated probabilities, integrated over impact parameters. Both theories share a common feature in having altogether two electronic full Coulomb continuum wave functions. One such function is centered on the projectile nucleus in the entrance channel, whereas the other is centered on the target nucleus in the exit channel. These two methods satisfy the correct initial and final Coulomb boundary conditions in the asymptotic region of scattering, at infinitely large inter-particle separations. Yet, it is presently demonstrated that most of the available experimental data on total cross sections for the double capture from helium by alpha particles distinctly favor the SDS-4B method. This is especially true at intermediate energies. Such energies are critically important in versatile applications under the general umbrella of ion transport in matter, including thermonuclear fusion (plasma physics) and ion therapy (medicine).

The BCIS-4B method for state-selective and state-summed total cross sections: Proton–helium​ charge exchange at 10–4000 keV

This work is on single electron capture by protons from helium targets at intermediate and high impact energies (10–4000 keV). Assessed is the overall performance of the second-order four-body boundary-corrected continuum intermediate state (BCIS-4B) method by detailed comparisons with all the available measurements. The state-selective Qnl,Qn and state-summed QΣ total cross sections are computed for n≤4, including all the sub-levels. Cross sections Qn are the sum of Qnl for 0≤l≤n−1. The state-summed cross sections QΣ are obtained by using Qn exactly for 1≤n≤3 and approximately for n≥4 through the Oppenheimer n−3 scaling rule. Overall, the measured cross sections are extremely favorably represented by the BCIS-4B method for Qnl,Qn and QΣ, even toward the lowest part of the considered intermediate energy region. Most notably, at all the energies above 10 or 20 keV, e.g. cross sections Q2p,Q3p and Q3d from the BCIS-4B method are in excellent agreement with the corresponding experimental data. This is very important since it is precisely for the non-spherically symmetric states (l≠0) of the captured electron that the existing discrepancies between measurements and other theories are the largest or even enormous.

Hyperfine-induced effects on the Kα1 angular distribution following electron-impact excitation of heliumlike spin- 1/2 Tl79+ ions

Angular distribution of the $K{\ensuremath{\alpha}}_{1}$ $(1s2p\phantom{\rule{0.16em}{0ex}}^{1,3}P_{1,2}\ensuremath{\rightarrow}1{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0})$ emission line following electron-impact excitation of heliumlike spin-1/2 ${\mathrm{Tl}}^{79+}$ ions is studied within the framework of the density-matrix theory and the relativistic distorted-wave theory. In particular, we aim to explore how a (nonzero) nuclear magnetic dipole moment ${\ensuremath{\mu}}_{I}$ affects the $K{\ensuremath{\alpha}}_{1}$ angular distribution due to the hyperfine interactions. To this end, detailed calculations are performed for selected spin-1/2 $_{81}^{A}\mathrm{Tl}^{79+}$ ($A=187$, 205, and 207) ions with large ${\ensuremath{\mu}}_{I}$. It is found that the hyperfine-induced effects on the $K{\ensuremath{\alpha}}_{1}$ angular distribution depend strongly on the impact electron energy. When compared with the case of zero-spin ${\mathrm{Tl}}^{79+}$ ions, the $K{\ensuremath{\alpha}}_{1}$ angular distribution becomes much more anisotropic for low impact energies, whereas this anisotropy decreases quickly at intermediate and high impact energies. Such a behavior is in sharp contrast to the results for the fine-structure-resolved $1s2p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}\ensuremath{\rightarrow}1{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$ component [Phys. Rev. A 102, 042813 (2020)]. Therefore, accurate $K{\ensuremath{\alpha}}_{1}$ angular measurements at low impact electron energies could be employed as a sensitive tool to probe the hyperfine interaction in highly charged few-electron ions.

Projectile and target excitation in He+ + He collisions at intermediate energies

We present ab initio calculations of cross sections for projectile and target excitation occurring in the course of He+ + He collisions using a three-active-electron semiclassical nonperturbative approach. Intermediate impact energies ranging from 1 keV to 225 keV/u are considered. The results of our calculations agree well with available measurements for both projectile and target excitation in the respective overlapping energy regions. A comparison of our results with those of other theoretical calculations further demonstrates the importance of a nonperturbative approach that includes a sufficient number of channels. Furthermore, it is found that the cross sections for target excitation into singlet states show a valley centered at about 25 keV/u, resulting from competition with electron transfer to singlet projectile states. By contrast, the cross sections for target excitation into triplet states do not exhibit any such structures.

Single charge exchange in collisions of energetic nuclei with biomolecules of interest to ion therapy

This study is on the theory of single electron capture by fast nuclei from a variety of molecular targets of biological significance with high relevance to ion therapy of deep-seated tumors. The adopted theoretical framework is that of the first principles of quantum physics. As such, no free, adjustable parameters are used. This is in sharp contrast to the associated existing cross section input data to Monte Carlo simulations that all abound with empirical/phenomenological formulae. The present theory has the well-established track of its predictive power. This means that the computed cross sections can confidently be used in the cases for which no experimental data exist. These cross sections are from the full continuum distorted wave method (CDW). We first compute atomic cross sections in the independent electron model and then generate the corresponding molecular cross sections. The latter follow from the former within the independent atom model accompanied by the Bragg additivity rule. The investigated atomic targets are from the backbone of DNA and/or RNA molecules. These are atomic hydrogen, carbon, nitrogen and oxygen (H, C, N, O). Neon is also added to this sequence of targets as an isoelectronic atomic counterpart of water vapor, methane and ammonia molecules. The studied molecular targets are H2O (water vapor), CO (carbon-monoxide), CO2 (carbon-dioxide), CH4 (methane), C2H4 (ethylene), C2H6 (ethane), C4H10 (butane) as well as the DNA/RNA nucleobases C4H4N2O2 (uracil), C5H5N5 (adenine), C5H5N5O (guanine), C5H6N2O2 (thymine) and C4H5N3O (cytosine). The obtained total cross sections for any electronic target shell are compared with the available experimental data and overall favorable agreement is recorded at intermediate and high impact energies, which is the validity domain of the CDW method.

Three-body boundary-corrected continuum-intermediate-state method for single charge exchange with the general transition amplitude (1s→nlm) applied to the p–H(1s), α–H(1s), and p–He(1s2) collisions with n≤4

We derive a general quantum-mechanical transition amplitude in the prior version of the three-body boundary-corrected continuum-intermediate-state (BCIS-3B) method for single charge exchange in collisions of heavy nuclei with atomic hydrogenlike targets. The obtained expression is valid for all the transitions from the initial ground to any final hydrogenlike bound states $(1s\ensuremath{\rightarrow}nlm),$ where ${n,l,m}$ is the usual triple of the quantum numbers (principal, angular, magnetic). The outcome is semianalytical: a judicious combination of an analytical calculation (as far as feasible) and the subsequent numerical computations (quadrature for integrals that could not be reduced to closed formulas). The final results for the $T$-matrix elements are a compact double integration computed by numerical quadratures over real variables in finite intervals. The ensuing total cross section is a single numerical quadrature of the squared absolute value of this transition amplitude integrated over the magnitude of the transverse momentum transfer vector. This can provide detailed information on the cross sections for each individual subshell ${n,l,m}$ of the newly formed hydrogenlike atom or ion comprised of a projectile nucleus and the captured electron. Using these general expressions, we computed a large number of state-selective and state-summed cross sections (both differential and total) for electron capture in the $p\text{\ensuremath{-}}\mathrm{H}$, $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{H}$, and $p\text{\ensuremath{-}}\mathrm{He}$ collisions at intermediate and high impact energies. The energy dependence of the cross sections for the individual shells and their subshells with the fixed quantum numbers $n$, ${n,l}$, and ${n,l,m}$ are reported via detailed tables and figures. Also, differential cross sections (state selective and summed) are computed for the $p\text{\ensuremath{-}}\mathrm{H}$ collisions at 60, 125, and 5000 keV. All the present results from the BCIS-3B method are found to be in very good agreement with the existing experimental data on differential and total cross sections, both state selective (whenever available) and state summed. The provided cross-section database can find important applications in several investigative fields ranging from plasma physics, astrophysics, and heavy-ion transport physics through fusion research and technology to hadron therapy.

Electron capture by fast projectiles from lithium, carbon, nitrogen, oxygen and neon

The three-body boundary-corrected continuum intermediate state method is used to compute total cross sections for single charge exchange in ion-atom collisions at intermediate and high impact energies. Detailed illustrations are given for several scattering systems: H+ + Li, He2+ + Li, H+ + C, He2+ + C, H+ + N, H+ + O and H+ + Ne, He2+ + Ne. An independent particle model and the frozen-core approximation are employed with only one target electron taken as being active. The initial ground state of the active electron in a multi-electron target is described by five wave functions. These are two Roothaan-Hartree-Fock (RHF) wave functions, the single- as well as double-zeta functions and the hydrogen-like functions. Comparisons among the resulting cross sections are made to check their sensitivity to the choice of the initial target wave functions. In the case of a lithium target, the separate cross sections for electron capture from the K-shell and L-shell are reported. The present theoretical total cross sections are compared with the available experimental data and overall good agreement is found, especially when using the RHF wave functions for multi-electron targets.

Differential cross sections for ionization of atomic hydrogen by proton-impact

The process of electron ionization is studied in proton collision with atomic hydrogen in the five initial states (1s, 2s, 2p0, and 2p±1) at intermediate impact energies. The first- and second-Born approximations are applied to calculate the ionization differential cross sections. Double and single differential cross sections are calculated at low electron emission energies. The closured second-Born approximation is applied to calculate the double differential cross sections (DDCSs). At several ejected electron energies, the DDCS is obtained as a function of the projectile scattering angles and also as a function of the electron ejected angles. The single differential cross section (SDCS) is obtained as a function of the ejected electron energy using first-Born approximation. Comparisons are made with available experimental data and previous theoretical calculations.

Water molecule ionization by proton impact experiment and GTO-First Born theory

SynopsisIn this communication we present calculations and measurements of water ionization by protons at intermediate and high impact energies. The main goal of the present theoretical approach is the development of a method to routinely incorporate sophisticated wavefunctions for small and medium-sized molecules in the determination of ionization cross-sections.

Calculation of the triple and double cross sections in the proton-hydrogen impact at the ionization channel by removing singularity in the scattering amplitudes

In the present work, the triple and double cross sections of atomic hydrogen ionization in collision with the proton are calculated. The potential of the interaction is considered as a Coulombic; also, the first and second order Born approximations have been used. The singularity of the Green operator in the second order approximation has been removed for the analytical solution of the scattering amplitude and the triple cross section calculation. Finally, the results for triple and double cross sections have been compared with the available theoretical and experimental results. The first and the second Born approximations are usually applied at intermediate and high impact energy ranges. However, it is shown that it could be successfully applied at lower energies as well.

A dynamical (e,2e) investigation into the ionization of the outermost orbitals of R-carvone.

We report an experimental and theoretical investigation into the dynamics of electron-impact ionization of R-carvone. Experimental triple differential cross sections are obtained in asymmetric coplanar kinematic conditions for the ionization of the unresolved combination of the three outermost molecular orbitals (41a-39a) of R-carvone. These cross sections are compared with theoretical cross sections calculated within a molecular 3-body distorted wave (M3DW) framework employing either a proper orientation average or orbital average to account for the random orientation of the molecule probed in the experiment. Here, we observe that the overall scattering behavior observed in the experiment is fairly well reproduced within the M3DW framework when implementing the proper average over orientations. The character of the ionized orbitals also provides some qualitative explanation for the observed scattering behavior. This represents substantial progress when trying to describe the scattering dynamics observed for larger molecules under intermediate-impact energy and asymmetric energy sharing scattering conditions.

Electron scattering from 1-butanol at intermediate impact energies: Total cross sections.

We report experimental measurements of the absolute total cross sections (TCSs) for electron scattering from 1-butanol at impact energies in the range 80-400 eV. Those measurements were conducted by considering the attenuation of a collimated electron beam, at a given energy, through a gas cell containing 1-butanol, at a given pressure, and through application of the Beer-Lambert law to derive the required TCS. We also report theoretical results using the Independent-Atom Model with Screening Corrected Additivity Rule and Interference approach. Those results include the TCS, the elastic integral cross section (ICS), the ionization total ICS, and the sum over all excitation process ICSs with agreement at the TCS level between our measured and calculated results being encouraging.

Evaluation of differential cross sections using classical two-active electron models for He

Differential cross sections for charge-exchange and single and double electronic emission in collisions of protons with He atoms at intermediate impact energies are theoretically evaluated by means of two classical trajectory Monte Carlo methods. These models incorporate momentum-dependent terms to the Hamiltonian in order to avoid the classical autoionization of He. The theoretical results for single capture and single ionization are compared to available experimental data. The role of the electron–electron correlation effects in double ionization processes is analyzed by inspecting the angular and energetic dependence of the electronic emission spectra at different impact energies.

Magnetically confined electron beam system for high resolution electron transmission-beam experiments.

A novel experimental setup has been implemented to provide accurate electron scattering cross sections from molecules at low and intermediate impact energies (1-300 eV) by measuring the attenuation of a magnetically confined linear electron beam from a molecular target. High-resolution electron energy is achieved through confinement in a magnetic gas trap where electrons are cooled by successive collisions with N2. Additionally, we developed and present a method to correct systematic errors arising from energy and angular resolution limitations. The accuracy of the entire measurement procedure is validated by comparing the N2 total scattering cross section in the considered energy range with benchmark values available in the literature.

Single electron capture into arbitrary states of bare projectiles from multi-electron targets

The prior form of four-body boundary-corrected first Born (CB1-4B) method is applied to calculate the total cross sections for single electron capture from the Kshell of multi-electron atoms (C, N, O, Ar) by fast projectiles (H+, He2+and Li3+). All calculations are carried out for electron capture into the arbitrary n, l, and m final states of the projectiles. The present results are found to be in very good agreement with the available experimental data at intermediate and high impact energies.

Differential and total cross sections for charge transfer and transfer-excitation in ion-helium collisions

Total cross sections for single charge transfer in collisions of multicharged bare ions with ground-state helium atoms at incident energy ranging from 40 to 5000 keV/amu have been calculated in the framework of a four-body model of final channel distorted-wave (FC-DW-4B) approximation. In this formalism, distortion in the final channel related to the Coulomb continuum of the target and the Coulomb interaction between the passive electron in the target with the projectile are included. In all cases, total single electron-capture cross sections have been calculated by summing over all contributions up to $n=3$ shells and subshells. It has been observed that the contribution of the capture cross sections into excited states have insignificant contributions for symmetric collisions. Comprehensive comparisons are made between the four body model of boundary corrected continuum intermediate-state approximations [Phys. Rev. A 83, 032706 (2011)] and the present FC-DW-4B model. The main purpose of the present study is to investigate the relative importance of dynamic electron correlation and the role of passive electron in the target at intermediate and high impact energies. In addition, projectile angular differential cross sections (DCS) for charge transfer and transfer-excitation in $p\text{-He}$ collisions are calculated at different impact energies. At low projectile energies, the present DCS data exhibits the typical steeply decreasing dependence on the projectile scattering angles, whereas at high impact energies, the double-scattering region centered on the Thomas angle is obtained. Detailed comparisons with the available experimental data and other theories are reported with the purpose of further assessing the relevance of the present model at different impact energies. Overall, the calculated cross sections show good agreement with the available experimental findings.

Variational study of atomic hydrogen excitation by proton impact at intermediate velocities: target continuum states contribution

The Schwinger variational principle is used to evaluate the cross section for the excitation and Balmer-α emission of the hydrogen atom. The target is projected by proton impact at energies between 2 and 200 keV. To describe the strong coupling between the excitation and capture channels at intermediate impact energies, the Coulomb wave function, that is, exact continuum states of the hydrogen atom, have been added in the expansion of the scattering wave function. From comparison with the available experimental data and other theoretical findings we remark that taking into account the continuum states of the target is a good choice to describe the capture states at medium and low velocities, thus making the variational approach given in this work an easy way to successfully study the excitation of atoms by ion impacts at intermediate velocities.

Single-electron exchange in H–H and He+–H collisions

The prior version of the four-body Born distorted wave (BDW-4B) approximation is formulated and used to study single-electron capture in H–H and He+–H collisions. The total cross sections are obtained in terms of six-dimensional numerical quadratures at intermediate and high impact energies. The role of dynamic dielectronic correlation is investigated as a function of impact energy. The results of the total cross sections for the post version of the BDW-4B method are also reported and the post–prior discrepancy is estimated. Comparisons of the present results with the available experimental data are made and good agreement is obtained.

Single charge exchange between hydrogen-like projectiles and hydrogen atom: the post version of the BDW-4B approximation

The post version of the four-body Born distorted wave method (BDW-4B) is applied to calculate the total cross section for single electron exchange in the collision of hydrogen-like projectiles with hydrogen atom. The post form of transition amplitude is obtained in terms of two-dimensional real integrals which can be computed numerically. This second-order theory which satisfies the correct boundary conditions is used for the collision of with hydrogen atoms at intermediate and high impact energies. The validity of our results is assessed in comparison with available experimental data and other theories.