Total Capture Cross Sections Research Articles

Cross section sensitivity to perturbation strengths in distorted waves for double electron capture by alpha particles from helium targets

Computer experiments are performed on total cross sections for capture of both electrons from helium targets at 100-10000 keV. Employed are four quantum-mechanical perturbative four-body distorted wave methods (one of the first and three of the second order). The goal is to determine the cross section sensitivity to the perturbation strengths in distorted waves from the second-order methods. The perturbation strength is parametrized by the Sommerfeld factor (the quotient of the nuclear charge and the relative velocity of the colliding particles). At each fixed impact energy, the sought sensitivity is monitored by gradually modifying the nuclear charges in the Sommerfeld factors. These factors reside in the Coulomb distortions of the unperturbed channels states. The focus is on the electronic distortions through the eikonal Coulomb logarithmic phases and the full Coulomb waves. The logarithmic phases are the constituents of the compound phases for the net charges of the two heavy scattering aggregates in relative motions. A striking perturbation strength sensitivity of the obtained total cross sections is recorded.

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 reaction rate of radiative n8Li capture in the range from 0.01 to 10 T9

Within the modified potential cluster model (MPCM) with forbidden states, the total cross sections are calculated for capture in the ground and first excited states of the9Li nucleus in then8Li channel in the energy range from 10−5 eV to 5 MeV based onЕ1 andM1 transitions. The experimentally proved resonance atEc.m.= 0.232 MeV in the4P5/2wave andab initio-predicted4P3/2resonance at 1.32 MeV [Phys. Rev. C 103, 035801 (2021)] are considered. The strong impact of the asymptotic constant and channel spectroscopic factors on the total capture cross sections are responsible for the variation in the absolute values within factor two. As a consequence, the thermal cross sections areσtherm=24–46.8 mb. The evaluation ofσthermbased on the extrapolation ofab initiocross sections yields ∼85 mb. The reaction rate is calculated in the temperature range from 0.01 to 10T9. The reported reaction rates are compared at the benchmark point 1T9. The comparison of two datasets [Phys. Rev. C 103, 035801 (2021) and Phys. Rev. C 105, 064608 (2022)] on reaction rates recently calculated in microscopic models in extended temperature intervals shows the essential quantitative and qualitative differences. The comparative joint analysis of the reaction rates of radiative neutron capture on the lithium isotopes6,7,8Li is suggested for the choice of an optimal interval for the asymptotic constants.

Calculation of Ionization, Excitation and Electron Capture Cross Sections for Be4+ + H(2s,2p) Collisions.

A computational study of Be4+ + H(2s,2p) collisions has been carried out employing the Classical Trajectory Monte Carlo (CTMC) method for the impact energy range from 20 keV/u to 1000 keV/u. The integral n partial cross sections for H(n) excitation and Be3+(n) electron capture and, the total ionization and electron capture cross sections are calculated and compared to recent semiclassical results. A general good agreement is observed for the n partial and total electron capture and ionization cross sections. The comparative study of the three inelastic processes show no significant differences between both excited targets.

High-energy two-electron transfer in ion-atom collisions

Two-electron transfer by fast heavy nuclei from heliumlike targets is studied. A detailed sequence of comprehensive computations is carried out in a large keV–MeV range of the projectile energies. This set is illustrated with total cross sections for double capture by alpha particles from helium atoms using several frequently applied four-body quantum-mechanical distorted wave models with the correct boundary conditions. The sensitivity of the obtained total cross sections is examined for different choices of the bound and continuum states. Especially at high energies, the influence of the compactness of the bound states is investigated by reference to the mechanism of the velocity matching kinematic double electron capture. Also considered is the dependence of these cross sections on the electronic screening of the projectile and the target nuclear charges in the bound and continuum states. The impact of this electronic shielding on total cross sections is assessed by reference to the corresponding bare nuclear charges in the bound and continuum states. Relative to all the available experimental data (100–6000 keV), the found striking model-dependence implies that two-electron transfer is sharply different from the associated one-electron transfer involving the same colliding particles.

Independent-atom-model description of multiple ionization of water, methane, and ammonia molecules by proton impact

We study multiple ionization in proton collisions with water, methane, and ammonia molecules using an independent-atom model. Previous work on total (net) capture and ionization cross sections is extended to treat the multiple-ionization channels explicitly. We present the theoretical framework to treat charge-state correlated processes within the independent-atom-model approach, which uses the geometric screening introduced for different molecular geometries and orientations. A comparison of results is made for the target molecules ${\text{H}}_{2}\text{O}, {\text{CH}}_{4}$, and ${\text{NH}}_{3}$ with an emphasis on $q$-fold electron removal. Coincident measurements of produced molecular fragments can be used to estimate this quantity. We find very good agreement for the model calculations for the water molecule, where data exist for $q=1--4$. For methane we observe reasonable agreement for $q=1,2$ and for ammonia only for $q=1$, i.e., the experimental data show little support for a direct multiple-ionization channel in the latter case.

A theoretical study of fragmentation dynamics of water dimer by proton impact

To investigate the collision processes of proton with the water dimer (H2O)2 at 50 eV, the time-dependent density functional theory coupled with molecular dynamics nonadiabatically is applied. Six specific collision orientations with various impact parameters are considered. The reaction channels, the mass distribution and the fragmentation mass spectrum are explored. Among all launched samples, the probability of the channel of non-charge transfer scattering and charge transfer scattering is about 80%, hinting that the probability of fragmentation is about 20%. The reaction channel of proton exchange process 2 is taken as an example to exhibit the detailed microscopic dynamics of the collision process by inspecting the positions, the respective distance, the number of loss of electrons and the evolution of the electron density. The study of the mass distribution and the fragmentation mass spectrum shows that among all possible fragments, the fragment with mass 36 has the highest relative abundance of 65%. The relative abundances of fragments with masses 1, 35, and 34 are 20%, 13%, and 1.5%, respectively. For the total electron capture cross section, the present calculations agree with the available measurements and calculations over the energy range from 50 eV to 12 keV.

Total, state-selective, and angular-differential cross sections for electron capture in He2++H collisions in warm dense plasmas

The total, state-selective, and angular-differential cross sections for He2++H collision system in warm dense plasmas are studied by using the two-center atomic orbital close-coupling method in the energy range 0.1–300 keV/u. The calculations are performed for plasma density and temperature ranges ne ∼1018 to ∼1021 cm−3, Te = 0.3 eV–1.2 eV, typical for the H- and He-rich white dwarfs. The plasma environments are described by a unified screened potential involving electron degeneracy, finite-temperature gradient, and exchange-correlation effects. The results for H++H cases with the same plasma parameters are also presented for comparison to elucidate the discrepancies of plasma screening effects on the electron capture dynamics for collision systems with different nuclear symmetries. Moreover, classical Debye screening results are also given for comparison to clarify the effects of quantum correlations in warm dense plasmas on the electron capture dynamics. The present work is expected to provide theoretical and data support for the astrophysical plasmas.

Charge transfer of potassium by the impact of proton particle

The total cross section for electron capture is being calculated in this paper for 2s state of hydrogen atom in proton-potassium collision. The energy range chosen for the calculation is 50 keV to 10,000 keV and we have used Coulomb projected Born (CPB) approximation method. Also the differential cross section at different scattering angle has been calculated. The result obtained are compared with available theoretical data and found it to be in good agreement.

State-selective differential and total cross sections for single-electron capture in $$He^{+}$$–He collisions

State-selective differential and total cross sections for single-electron capture in $$He^{+}$$–He collisions

Effective one-electron approach to proton collisions with molecular hydrogen

The two-centre wave-packet convergent close-coupling approach to ion–atom collisions is extended to study proton collisions with molecular hydrogen including electron-capture channels. We use a model potential to represent the molecular target as an effective one-electron spherically symmetric system. This greatly simplifies the target structure, allowing us to use already existing code developed for ion collisions with single-electron targets. Calculated total cross sections for electron capture, single ionisation, and excitation processes generally agree well with experimental data and other theoretical calculations where available. However, the total electron capture cross section is found to overestimate the experimental data at low energies, while the total ionisation cross section is slightly underestimated. Additionally, we present state-resolved cross sections for capture into the 1s, 2ell , and 3ell states of the projectile where deviation between various previous calculations is substantial. Our results lead to overall improvement over previous theoretical studies although discrepancies with experiment are observed for 3p and 3d capture. We conclude that treating molecular hydrogen as an effective one-electron system within the two-centre coupled-channel approach to one-electron targets can give reasonably accurate total cross sections at intermediate and high energies, without the need for a complex and computationally demanding two-electron target representation.

Integrated total and state-selective cross sections for bare beryllium ion collisions with atomic hydrogen

We apply the two-centre wave-packet convergent close-coupling approach to calculate integrated total and state-selective cross sections for electron capture and ionisation in bare beryllium ion collisions with atomic hydrogen. This is done in the energy region between 1 keV/u to 1 MeV/u. Good agreement was achieved in comparison to previous theoretical works for the total electron capture cross section across all energies, however the total ionisation cross section shows disagreement with preceding calculations. We present accurate n and ℓ-resolved (n and ℓ are the principal and the angular momentum quantum numbers of the final state in electron capture processes, respectively) cross sections required for plasma impurity diagnostics where there have been discrepancies between different approaches for n > 5. Otherwise, excellent agreement between our results and previous calculations of state-selective cross sections for electron-capture is observed for a wide number of different n. The calculations have been performed on a fine energy mesh to identify oscillatory structures in the n- and nl-resolved capture cross sections in the low-energy region. Our results show pronounced oscillations in the cross sections for n ⩾ 5 below 20 keV/u.

Electron transfer from atomic hydrogen to multiply-charged nuclei at intermediate and high energies

We report on theoretical total cross sections for electron capture from the ground state of atomic hydrogen H(1s) by fast multiply-charged nuclei H+,He2+,Li3+,Be4+,B5+,C6+,N7+,O8+ and F9+. The prior form of the boundary-corrected continuum intermediate states (BCIS) method is used. For a single fixed initial ground-state (i=1s), comprehensive computations are carried out for a sequence of the transitions to the final state (n,l,m) with 1≤n≤nmax, including all the energy degenerate sub-levels (−l≤m≤l,0≤l≤n−1). The maximal quantum number nmax is respectively set to 4 for H+,He2+ and Li3+, to 5 for Be4+, to 6 for B5+, as well as to 7 for C6+,N7+,O8+ and F9+. The reported nine tables provide these state-selective cross sections (Qif) and their state-summed counterparts (QΣ). The cross sections QΣ for the sum over all the final states are evaluated using the exact results of Qif for n≤nmax and the scaled cross sections for n>nmax. The scaling is based on the Oppenheimer n−3 rule. In addition to these tables, at the same impact energies 20–3000 keV/amu, the cross sections from the BCIS method are presented graphically in eight figures for the nuclei Li3+,Be4+,B5+,C6+,N7+,O8+ and F9+. This complements our recently published cross sections for electron capture by protons (H+) and alpha particles (He2+) from H(1s). In the present figures, whenever available, the corresponding experimental data are compared with our results for QΣ. Also included in these comparisons are the corresponding results for QΣ from the continuum distorted wave (CDW) method. The cross sections tabulated here can be used in versatile applications ranging from plasma physics and astrophysics through fusion research to ion therapy.

Ionization and Electron Capture Cross Sections for Single-Electron Removal from Biological Molecules by Swift Ion

We have studied ionization and electron capture cross sections for single-electron removal from biological molecules (adenine, cytosine, guanine, thymine, and uracil) by proton impact at energies ranging from 30 keV/amu to 10 MeV/amu. In this investigation, the three-body distorted wave method is used. The calculations are based on the independent electron model. For electron capture process, distortion in the final channel related to the Coulomb continuum states of the active electron and the projectile in the field of residual target ion is included. In case of ionization, we take all the pair-wise Coulomb interactions, which treat all interactions on equal footing in the final channel. Moreover, the asymptotic Coulomb logarithmic phase for the relative motion of two colliding nuclei is included in the initial channel. In both processes, the molecular character of the biological target is assumed to be a linear combination of their atomic orbitals (LCAO) and, for all cases, the different atomic orbitals are described with the Roothaan-Hartree-Fock (RHF) approximation. We have also calculated the total capture cross sections using simple Bragg’s additivity rule. For electron capture, the contributions to the TCS from the core orbitals of the molecule have also been explicitly analyzed. The double differential cross sections (DDCS) for electron emission as well as the total cross sections for single ionization of only uracil molecule with fast proton impact are also calculated. The results for capture and ionization cross sections are compared with other theoretical calculations and existing experimental data. We find that our calculated results are in quite better agreement with available experimental data than the other theoretical results.

Nonresonant p -wave direct capture and interference effect observed in the O16(n,γ)O17 reaction

We measured the total capture cross section of the $^{16}\mathrm{O}(n,\ensuremath{\gamma})^{17}\mathrm{O}$ reaction, as well as partial cross sections leading to the ground (${J}^{\ensuremath{\pi}}=5/{2}^{+})$ and first-excited (${J}^{\ensuremath{\pi}}=1/{2}^{+})$ states in $^{17}\mathrm{O}$. The measurement was carried out at average neutron energies of 157, 349, 398, 427, 468, 498, and 556 keV by using pulsed neutrons produced via the $^{7}\mathrm{Li}(p,n)^{7}\mathrm{Be}$ reaction and a $\ensuremath{\gamma}$-ray detection system based on an anti-Compton NaI(Tl) spectrometer. We observed the interference effect between the $3/{2}^{\ensuremath{-}}$ resonance state at 4554 keV of $^{17}\mathrm{O}$, corresponding to a neutron energy of 411 keV in the center-of-mass system, and a nonresonant contribution in the capture process. The measured partial cross sections are in good agreement with theoretical calculations obtained taking into account the interference between the $3/{2}^{\ensuremath{-}}$ resonance and a nonresonant $p$-wave direct radiative capture contribution. Using the present results, together with our previous measurement, we derived the Maxwellian-averaged capture cross sections (MACS) for thermal energies between $kT=5$ and 100 keV, key quantities for $s$ process nucleosynthesis studies in massive stars.

Nuclear Structures of 17O and Time-dependent Sensitivity of the Weak s-process to the 16O(n,γ)17O Rate

Abstract We revisit the radiative neutron capture reaction 16O(n,γ)17O of astrophysical interest, based on the new reevaluated cross-section data. Several potentials are proposed to predict direct capture cross sections. The contributions from single-particle resonances to total capture cross section are quantitatively considered in Breit–Wigner formalism, taking into account the interference term between direct capture and resonant cross sections, which is crucial for the description of the behavior around the resonance energies. A new cross section is achieved based upon χ 2-fittings for optimized resonance parameters using Minuit code, and it has a largely improved agreement with updated experimental data. Statistical errors are also evaluated for the total and Maxwellian-averaged cross sections. It is confirmed that the direct captures dominate the total cross sections; however, resonant contribution also becomes progressively more important as the energy increases to 100 keV. Resonance contribution can increase the reaction rates for energy region 50 keV < E < 100 keV by 5% ± 5%–25% ± 5%, and around 8% ± 5% in comparison with KADoNiS v0.3 rate and the latest data evaluations, respectively. We show a detailed propagation of the uncertainty in the 16O(n,γ) reaction rate to abundances of nuclei, including s-nuclei during the weak s-process with a multi-zone nuclear network calculation. Although an enhanced rate of 16O(n,γ) diminishes the s-process efficiency in the 25 M ☉ stellar model adopted from the Modules for Experiments in Stellar Astrophysics, it can lead to larger abundances of neutrons as well as 22Ne in the late epoch of C burning.

Nonperturbative scaling behavior for net ionization of biologically relevant molecules by multiply charged heavy-ion impact

A recently developed model to describe proton collisions from molecules involving basic atoms such as hydrogen, carbon, nitrogen, oxygen and phosphorus (H, C, N, O, P) is extended to treat collisions with multiply charged ions. The ion-atom collisions are computed using the two-center basis generator method (TC-BGM), which has a proven track record of yielding accurate total cross sections for electron capture and ionization. The atomic net ionization cross sections are then used to assemble two models for ion-molecule collisions: an independent atom model (IAM) that follows the Bragg additivity rule (labeled IAM-AR), and also the so-called pixel-counting method (IAM-PCM). The latter yields reduced cross sections relative to IAM-AR near the maximum, since it takes into account the overlapping nature of effective cross sectional areas. The IAM-PCM for higher-charge projectiles leads to strong reductions of net ionization cross sections relative to the IAM-AR method, and is computed directly for projectile charges $Q=1, 2, 3$. The scaling behavior of the IAM-PCM is investigated over a wide range of energies $E$, and at high $E$ it converges towards the IAM-AR. An empirical scaling rule is established which allows to reproduce these results based on proton impact calculations. Detailed comparisons are provided for the uracil target ($\rm C_4 H_4 N_2 O_2$), for which other theoretical as well as experimental results are available. Based on the scaling model derived from the IAM-PCM data it is shown how the experimental data for uracil and water bombarded by multiply charged ions can be reduced to effective $Q=1$ cross sections respectively, and these are compared to proton impact data.

Target K-shell X-ray emission associated with single and double electron capture for [formula omitted] + Ar collisions

Cross sections for target Ar K-shell ionization associated with single and double electron capture, as well as the same cross sections corresponding to projectile F K X-rays and the total cross sections for single and double capture, were determined for 1.8–2.2 MeV/u F9+,8+,7+ projectiles. This work was performed at Western Michigan University using the tandem Van de Graaff accelerator. Coincidences between emitted X-rays and their corresponding charge-changed particles were detected. The Ar K X-ray coincidence cross section ratios for double to single capture are found to depend strongly on the incident charge state, with the ratios for F9+ well exceeding unity. Possible explanations for this anomalous behavior are discussed but a conclusive explanation is not found. The results are compared to previous experiments using fully-stripped fluorine where coincidence techniques were not employed.

Line intensities for x-ray emission in Mg12+ collisions with H and He atoms

State selective charge transfer cross sections are calculated in Mg12+ collisions with H and He atoms at incident energies of 1.0, 3.0, and 5.0 keV amu−1 using a time-dependent lattice method. Total capture cross sections using the time-dependent lattice method are found to be larger than those previously calculated using the Landau–Zener method. Lyman line ratios are calculated using the time-dependent lattice capture cross sections and standard radiative transitions for both the H and He atoms. Lyman line probabilities are presented for both H and He. The strongest probability for both H and He is the Lyman α emission, but relatively strong probabilities for He at an incident energy of 1.0 keV amu−1 are found for Lyman β, γ, δ, and ϵ emission.

Distorted wave model for sub-shell electron capture cross sections of noble gases by bare ion impact

SynopsisElectron capture from noble gases (He, Ne and Ar) are investigated in the framework of the quantum-mechanical distorted wave model. In this model, we use an independent electron model taking particular care of the representation of the bound and continuum target states. The results for partial and total capture cross sections are compared with other theoretical calculations and experimental data. The present results are found to be in very good agreement with the available experimental findings.