The two-center wave-packet convergent close-coupling approach is extended to model dressed ion collisions with atomic hydrogen. This is done by reducing the problem to an effective three-body one and using a model potential to approximate the interactions between the projectile ion with the target electron and target nucleus. The method is applied to calculate the total ionization cross section along with the total and n-resolved electroncapture and target-excitation cross sections in partially stripped C2+ and C3+ ion collisions with ground-state atomic hydrogen. Calculations are performed across a broad projectile energy range from 1 keV/u to 1 MeV/u, where one-electron collision processes are dominant. The calculated total electron-capture cross sections for both systems generally agree very well with available experimental and previous theoretical data. We find that at incident energies above 100 keV/u the total electron-capture cross sections in dressed carbon-ion collisions are larger than the ones corresponding to collisions of bare projectile ions of the same charge. A possible reason for this could be associated with the target-electron radial density and the behavior of the potential of interaction between the target electron and the carbon ion. Our results for ionization in C3+ + H(1s) collisions overestimate the experimental data. We also report a set of calculations for ionization in C2+ + H(1s) collisions.

In the convergent close-coupling method for calculating electron-atom scattering, excitation and ionization are associated with cross sections of negative- and positive-energy target states, respectively. We show that the zero-energy boundary can be continuously accessed from either the negative- or positive-energy side, thereby enabling the estimation, via interpolation, of cross sections of arbitrarily high-level Rydberg target states for the target orbital angular momentum included in the calculations.

State-selective electron capture in collisions of Ar16+ ions with ground-state hydrogen atoms has been modeled using the two-center wave-packet convergent close-coupling approach. The partially stripped He-like projectile ion is represented using a model potential. Experimental measurements are not available for this collision system and to date, only the classical trajectory Monte Carlo (CTMC) method has been applied to calculate cross sections. The calculated total electron-capture cross section (TECS) is in good agreement with the previous CTMC results at the low energies but slightly larger at higher energies. This is likely because, in this work, we account for capture into highly excited states, which contribute significantly to the TECS at the intermediate energies. The n-resolved electron-capture cross sections have also been presented for capture into states with n = 6 - 19, where n is the final-state principal quantum number. The most important of these are the cross sections for capture into the n = 14 - 17 states, which are used in charge-exchange recombination spectroscopy techniques. For these cross sections, a significant difference is observed between the present and previously published data. The cross sections differ by an order of magnitude in the 10-60 keV u(-1) energy range. The agreement between the calculations is observed at the energies above 70 keV u(-1). The nl-resolved electron-capture cross sections have also been presented at 15, 60, 100 and 200 keV u(-1) projectile energies, where is the final-state angular momentum quantum number.

Is there a saddle-point mechanism for ionization in intermediate-energy ion-atom collisions? Since Olson [Phys. Rev. A 33, 4397 (1986)] proposed the idea that the electrons stranded in the potential saddle between the two Coulomb centers dominate the ejected-electron spectra, multiple experimental and theoretical attempts have been made to answer this question. However, the topic has remained controversial. Here we provide a theoretical analysis of this question which can contribute significantly to a definitive answer, at least for intermediate and large projectile energies. To this end we calculate the energy and angular distribution of electrons emitted in proton-helium collisions. We use the two-center four-body wave-packet convergent close-coupling method based on the correlated two-electron structure for the helium target. The doubly differential cross sections obtained at 52 and 103 keV show no sign of a hump near one-half the relative velocity of the collision, which is expected according to the saddle-point ionization theory. At the same time, the results are in excellent agreement with measurements by Meckbach et al. [J. Phys. B 24, 3763 (1991)]. Two mechanisms for the production of electrons are clearly identified: direct ionization (direct knockout) and electron capture to the continuum (ECC) of the projectile. The electron speed (equivalently, energy) where direct ionization peaks is found to be practically independent of the ejection angle. However, the ECC peak is shown to shift towards one-half the relative velocity with increasing electron angle. It is concluded that the signatures of the suggested saddle-point mechanism may actually be due to a shift of the well-known ECC peak when electrons are emitted into angles away from the forward direction. Thus, the answer to the question is in the negative.

We use the two-center wave-packet convergent close-coupling approach to ion-atom collisions to calculate the energy and angular distribution of electrons emitted in proton collisions with atomic hydrogen. Results are provided across a wide range of intermediate energies where many competing reaction channels make calculations challenging. The present data consistently agree with the available experimental measurements and improve upon previously available results based on perturbative and classical methods. Furthermore, we extend the range of electron angles and energies over which theoretical data are available for the doubly differential cross section for ionization. This provides strong evidence that at the level of doubly differential cross sections nonperturbative high-order methods are required to accurately model the ionization process.

Background: The 12 C( alpha, gamma ) 16 O reaction, determining the survival of carbon in red giants, is of interest for nuclear reaction theory and nuclear astrophysics. A specific feature of the 16O nuclear structure is the presence of two subthreshold bound states, (6.92 MeV, 2+) and (7.12 MeV, 1-), that dominate the behavior of the low-energy S factor. The strength of these subthreshold states is determined by their asymptotic normalization coefficients (ANCs), which need to be known with high accuracy. Purpose: The objective of this research is to examine how the subthreshold and ground-state ANCs impact the low-energy S factor, especially at the key astrophysical energy of 300 keV. Method: The S factors are calculated within the framework of the R-matrix method using the AZURE2 code. Results: Our total S factor takes into account the E 1 and E 2 transitions to the ground state of 16O including the interference of the subthreshold and higher resonances, which also interfere with the corresponding direct captures, and cascade radiative captures to the ground state of 16O through four subthreshold states: 0+2 , 3-, 2+, and 1-. To evaluate the impact of subthreshold ANCs on the low-energy S factor, we employ two sets of the ANCs. The first selection, which offers higher ANC values, is attained through the extrapolation process [Blokhintsev et al., Eur. Phys. J. A 59 , 162 (2023)]. The set with low ANC values was employed by deBoer et al. [Rev. Mod. Phys. 89 , 035007 (2017)]. A detailed comparison of the S factors at the most effective astrophysical energy of 300 keV is provided, along with an investigation into how the ground-state ANC affects this S factor. Conclusion: The contribution to the total E 1 and E 2 S factors from the corresponding subthreshold resonances at 300 keV are (71-74)% and (102-103)%, respectively. The correlation of the uncertainties of the subthreshold ANCs with the E 1 and E 2 S (300keV) factors is found. The E 1 transition of the subthreshold resonance 1- does not depend on the ground-state ANC but interferes constructively with a broad (9.585 MeV; 1-) resonance giving (for the present subthreshold ANC) an additional 26% contribution to the total E 1 S (300keV) factor. Interference of the E 2 transition through the subthreshold resonance 2+ with direct capture is almost negligible for small ground-state ANC of 58 fm-1/2. However, its interference with direct capture for higher ground-state ANC of 337 fm-1/2 is significant and destructive, contributing - 27%. The low-energy S E 2 (300keV) factor experiences a smaller increase when both subthfreshold and the ground-state ANCs rise together due to their anticorrelation, compared to when only the subthreshold ANCs increase.

A unified treatment of atomic excitation and ionization in ion-atom collisions is proposed. It is demonstrated that the state-resolved excitation cross sections multiplied by n(3), where n is the principal quantum number of the excited state, and the corresponding partial singly differential ionization cross section form two parts of a single continuous function. This allows one to obtain the excitation cross section for any state including high-lying Rydberg states and the energy-differential ionization cross section at, and arbitrarily close to, the threshold. The proposed method can be used in any theoretical approaches to excitation and ionization and experimental measurements.

In this manuscript we present our experience of porting the code used in the wave-packet convergent-close-coupling (WP-CCC) approach to NVIDIA V100 and AMD MI250X GPUs. The WP-CCC approach is used in the field of ion-atom collision physics to describe various processes such as elastic scattering, target excitation and electron-capture by the projectile. It effectively models collisions between proton or bare ion projectiles and various atomic and molecular targets, particularly those resembling one or two-electron systems. These calculations are used in computational atomic physics, fusion plasma modeling, and hadron therapy for cancer treatment. The main computational cost of the method is solving a set of coupled first-order differential equations. This involves implementing the standard Runge-Kutta method while varying the projectile position along multiple straight-line paths. At each projectile position several millions of matrix elements need to be calculated which is accomplished using the OpenACC programming model. After computing these matrix elements, the next steps involve matrix inversion and multiplication with another matrix. To expedite these operations, a GPU-accelerated LAPACK routine, specialised for solving systems of linear equations, is employed. For AMD GPUs, this routine is accessible through the hipSOLVER library, while for NVIDIA GPUs, it can be obtained from the cuSOLVER library. The portability, performance and energy efficiency of the CPU-only code have been compared with the GPU-accelerated version running on AMD and NVIDIA GPUs. The implementation of GPU-accelerated WP-CCC code opens up avenues for exploring more sophisticated collision processes involving complex projectile and target structures, which were previously considered infeasible.

The differential 3He2+ -He scattering problem is investigated using the two -center wave -packet convergent close -coupling method in the incident energy range of 50-630 keV/u. The present two -electron approach accounts for electron exchange between reaction fragments and uses the configuration -interaction method to treat the target structure. We also apply a simpler method based on the effective one -electron target description. The singly differential cross sections are presented for electron capture, elastic scattering, excitation, and ionization of the target. The paper demonstrates the importance of the electron -electron correlation at lower projectile energies for the electron -capture and elastic -scattering processes. The two -electron results for electron capture into the ground state describe the available experimental data very well at all projectile energies, while the effective single -electron model shows good consistency at energies starting from 300 keV/u. For ionization, we observe a good level of agreement between the two approaches for all types of singly differential cross sections, and they agree well with the experimental data, wherever available. In addition, the angular differential cross sections for ground -state and total electron capture are presented for 4He2+ -He collisions at the projectile energies of 62.5, 125, 187.5, and 250 keV/u. The angular differential elastic -scattering and excitation cross section and all three types of the singly differential ionization cross sections are found to be practically the same as the corresponding results for 3He2 -He collisions.

Differential studies of the proton-helium scattering problem using the two-center wave-packet convergent close-coupling approach is extended to the calculation of the ionization cross section differential in the electron emission energy and the projectile scattering angle. The results obtained using the correlated two-electron and effective one-electron methods are in reasonably good agreement with experiment. While the shape of the doubly differential cross section generally agrees with the results of the experiment, at some emission energies its magnitude does not. This appears consistent with similar disagreement seen in the singly differential cross section at the same emission energies.

Asymptotic normalization coefficients (ANC) determine the overall normalization of cross sections of peripheral radiative capture reactions. In a recent paper [Blokhintsev et al. , Eur. Phys. J. A 58 , 257 (2022)], we con -sidered the ANC C-0 for the virtual decay O-16(0(+); 6.05 MeV)-> alpha +C-12(g.s.). In the present paper, which can be regarded as a continuation of the previous, we treat the ANCs Cl for the vertices O-16(J(pi)) -> alpha +C-12(g.s.) corresponding to the other three bound excited states of O-16 (J(pi) = 3(-) , 2(+) , 1(-) , l = J). ANCs C-l (l = 3 , 2 , 1) are found by analytic continuation in energy of the alpha C-12 l-wave partial scattering amplitudes, known from the phase-shift analysis of experimental data, to the pole corresponding to the O-16 bound state and lying in the unphysical region of negative energies. To determine Cl , the scattering data are approximated by the sum of polynomials in energy in the physical region and then extrapolated to the pole. For a more reliable determination of the ANCs, various forms of functions expressed in terms of phase shifts were used in analytical approximation and subsequent extrapola-tion.

Using the two-centre wave-packet convergent close-coupling approach, we continue our study of the proton–helium collision system. This method uses a correlated two-electron wave function to describe the helium target and discretises the continuum using wave-packet pseudostates. The cross section differential in the electron-emission energy and emission angle is calculated for incident-projectile energies in the intermediate range from 70 to 300 keV, where coupling between various channels and electron–electron correlation effects are important. We also apply an alternative, simpler approach that reduces the target to an effective single-electron system. Overall, the present results from both methods agree well with the available experimental data. This positions both implementations of the two-centre wave-packet convergent close-coupling approach well to further study other doubly differential, as well as fully differential, cross sections of single ionisation in proton–helium collisions. Graphical abstract

We present results of calculations of several processes resulting from positronium (Ps) collisions with antiprotons: antihydrogen formation, Ps breakup, and nPs-changing collisions. Calculations utilize the quantum convergent close-coupling (CCC) method and the classical trajectory Monte Carlo (CTMC) method. We identify a region of Ps principal quantum numbers nPs and Ps energies where the classical description is valid and where the CCC calculations become computationally too expensive. This allows us to present the most complete and reliable set of cross sections in a broad range of nPs and initial orbital momentum quantum numbers lPs which are necessary for experiments with antihydrogen at CERN.

Asymptotic normalization coefficients (ANC) determine the overall normalization of cross sections of peripheral radiative capture reactions. In a recent paper [Blokhintsev et al., Eur. Phys. J. A 58, 257 (2022)], we considered the ANC $C_0$ for the virtual decay $^{16}$O$(0^+; 6.05$ MeV)$\to \alpha+^{12}$C(g.s.). In the present paper, which can be regarded as a continuation of the previous, we treat the ANCs $C_l$ for the vertices $^{16}$O$(J^\pi)\to \alpha+^{12}$C(g.s.) corresponding to the other three bound excited states of $^{16}$O ($J^\pi=3^-$, $2^+$, $1^-$, $l=J$). ANCs $C_l$ ($l=3,\,2,\,1$) are found by analytic continuation in energy of the $\alpha^{12}$C $l$-wave partial scattering amplitudes, known from the phase-shift analysis of experimental data, to the pole corresponding to the $^{16}$O bound state and lying in the unphysical region of negative energies. To determine $C_l$, the scattering data are approximated by the sum of polynomials in energy in the physical region and then extrapolated to the pole. For a more reliable determination of the ANCs, various forms of functions expressed in terms of phase shifts were used in analytical approximation and subsequent extrapolation.

The positron-hydrogen collision system is considered with the one- and two-centre convergent close-coupling methods with a particular focus on initial excited states. The previous limitation on the two-centre method, restricting the Laguerre basis size, has been removed allowing for larger bases, which is necessary for the examination of the near-threshold cross section behaviour for three-body breakup. Excellent agreement with the Wannier–Klar predictions for these systems is found for initial states with principal quantum number n≤ 3 . The accuracy of the presented cross sections is supported by demonstrating internal consistency of the one- and two-centre calculations.

The description of experimental data on energy and angular distributions of electrons produced in intermediate-energy proton collisions with H2 has remained an insurmountable problem for over five decades. A coupled-channel method is developed that provides an accurate solution to the problem. The doubly differential cross section as a function of the energy and angle of the ejected electron is calculated. Excellent agreement between the present results and the experimental data is found. This breakthrough in theoretical modeling of differential ionization in p + H2 collisions paves the way to accurate description of the recent kinematically complete experiments.

The wave-packet convergent close-coupling (WP-CCC) approach is applied to calculate the energy spectrum of electrons ejected in p + H2 collisions as a function of the scattering angle of the projectile. The calculations are performed for projectile energies of 75, 100, and 200 keV. At these incident energies there are many competing reaction channels that play an essential role in the collision dynamics. The target is modeled as an orientationally averaged effective one-electron system. The results are compared with available perturbative calculations and experimental data. Good agreement between the WP-CCC results and experimental data is found for small emission energies, especially when the projectile is scattered at small angles. However, when the electron is emitted with a speed comparable to or greater than the projectile speed we find that our method predicts smaller cross sections near zero scattering angles and a slower fall off than the experimental data. This is in agreement with other calculations. Furthermore, the structure observed in the experimental data at large scattering angles is not supported by our results. Interestingly, we find very good agreement with the continuum-distorted-wave eikonal-initial-state molecular-orbital calculations that use a two-effective center approximation, though our method describes the target as an effective one-electron spherically symmetric system. This suggests that in these models two-center interference effects may have a small effect on this particular cross section. Furthermore, we find that the experimentally observed decrease in average scattering angle in proton collisions with H2 near the electron-projectile matching speed is not reproduced by our results. We also present the doubly differential cross section for ionization as a function of the scattering angle of the projectile at select emission angles.

State-selective non-dissociative electron capture and ionisation cross sections are calculated for collisions between bare helium-ions and molecular hydrogen. The two-centre wave-packet convergent close-coupling approach is used and the hydrogen molecule is represented as an effective one-electron target. For the electron-capture cross section, our results are in good agreement with experimental measurements at energies above 100 keV/u. However, near the peak of the cross section, they are larger than the experimental data. The total ionisation cross section is also in good agreement with experiment, particularly at low and high energies. The results for the state-selective electron-capture cross section are generally in good agreement with the limited experimental measurements. However, we find that our results appear to consistently overestimate the experimental data for electron capture into the s states at intermediate energies. The present results are the first calculations capable of producing electron capture and ionisation cross sections over a wide incident energy range within a single unified theoretical framework. Graphical Abstract