Session FW1: Heavy Particle Collisions

Machine learning for modeling the electronic stopping power of ions

The International Atomic Energy Agency (IAEA) stopping power database is a highly valued public resource compiling most experimental measurements published in the last century. The database –accessible to the global scientific community– is continuously updated and has been extensively employed in theoretical and experimental research for over thirty years. In this work, we employ machine learning algorithms on the 2021 IAEA database to construct a model that can accurately predict the electronic stopping power cross sections for any ion and target combination in a wide range of incident energies. The raw values in the database originate from several publications; they were measured using different techniques across several decades. Hence, measurements for the same ion–target collision may show significant discrepancies (much larger than the error of the individual set of experimental data). Cleaning the database is crucial but manually impracticable. The immense difficulties of scrutinizing such an extensive dataset are resolved by implementing a straightforward ML-based method. A clustering-based algorithm was developed to automatically discard suspicious or erroneous data. The method implements a density-based clustering non-parametric algorithm along with three criteria on the data. The filtered values were divided into two sets: the training and test sets. The former dataset was used to train a deep neural network, while the latter was set aside. The converged model can reproduce the input data accurately within a one-digit mean absolute percentage error (MAPE). Considering the spread in some collisional systems and energy ranges, the model's performance is excellent. The neural network results were also compared with the test set (data not used in the training stage), which also showed an outstanding agreement. Exhaustive comparison with other semi-empirical and machine-learning-based methods proved our model to be the most accurate. The first version of the electronic stopping power neural network (ESPNN) code is available to users. The open-access ESPNN code with the forward propagation model runs with Python and has been published in pypi and a public repository.   

Fully Differential Study of Dissociative Capture in p + H2 Collisions

We have measured momentum analyzed protons, emitted in fragmentation of H₂⁺, in coincidence with angular resolved neutralized projectiles for 75 keV p impact.  We extracted fully differential cross sections (FDCS) for dissociative capture.  Data were analyzed for two molecular orientations, one is perpendicular and one parallel to the momentum transfer q.  Based on the kinetic energy release (KER) the dissociative capture channel through nuclear excitation to a vibrational continuum state was selected.

 

In the scattering angle-dependence of the FDCS for the parallel molecular orientation, we observed a two-center molecular interference pattern.  Earlier, we reported that this interference pattern was phase-shifted by π.  The new data, employing improved data analysis techniques, revealed that this phase shift is not constant, but rather depends on the scattering angle q_p.  We did not find any significant dependence on the KER.

 

A phase shift was observed in previous studies of electronic dissociation for excitation to an anti-symmetric molecular state and explained by parity conservation.  But in vibrational dissociation the electron remains passive in the symmetric ground state and this explanation does not hold.

 

We have offered a hypothetical explanation for the phase shift in our data.  As the nuclear wave packet is lifted to the vibrational continuum state it can propagate either towards decreasing or increasing internuclear separation D.  The latter path leads to direct dissociation, for which we do not expect any phase shift.  But for the former path the wave packet first has to be reflected from the molecular potential wall at small D before dissociation can occur, for which a π phase leap is expected.  Depending on which path is stronger, which depends on q_p, the average phase shift can take any value between 0 and π.

 

If this explanation is correct, one would expect additional interference between the direct and the reflection paths because they are indistinguishable.  The phase angle for such an interference depends on the KER.  Indeed, in the KER dependence of the interference term we did observe an oscillating pattern.  Therefore, these data are supportive of our hypothetical explanation, but they do not provide conclusive evidence.   

Integrated total and partial cross sections for dressed carbon-ion collisions with atomic hydrogen

Collisions involving dressed ions is important for applications such as fusion plasma modelling and hadron therapy of cancer. From a theoretical perspective, modelling collisions which involve more than two electrons in a completely ab initio manner is a challenging problem. We employ an effective potential to treat the interactions with the multi-electron projectile ion in a spherically symmetric manner. This reduces the scattering problem of dressed-ion collisions with atomic hydrogen to an effective three-body problem. We have incorporated this potential into the two-centre wave-packet convergent close-coupling (WP-CCC) formalism [1] to study dressed carbon-ion collisions with atomic hydrogen. Specifically, for each charge state of carbon colliding with H, we have calculated the total cross sections for all single-electron processes in the energy region between 1 keV/u to 1 MeV/u, where coupling between the channels is important. We compare our results with the available experimental and theoretical data and present the first set of theoretical calculations for the ionisation cross section in a number of dressed C-ion collisions.

[1] Abdurakhmanov I B et al. 2021 Phys. Rev. A. 104 042820.   

Transport cross sections and collision integrals of atoms/ions: N-H+, H-N+, N2+-H, N+-H+ collisions.

The transport properties of atomic gases (for plasma science and aerothermodynamics) are described by the properties of the relevant elastic collisions. Depending on the approach taken, a various quantities are used: the potential energy curves (molecular dynamics), transport cross sections (DSMC - Direct Simulation Monte Carlo, PIC-MCC - Particle In Cell Monte Carlo Collisions) or collision integrals (CFD - computational fluid dynamics). In most cases such data are not available or are calculated with very significant approximations.

The limitation is the availability of the potential energy curves (which can be numerous), especially for atoms/ions in the excited states. The present work reports potential energy curves for the N-H⁺, H-N⁺, N²⁺-H, N⁺-H⁺ interactions and calculated transport cross sections and collision integrals. The classical mechanics is shown (by comparison to the semiclassical WKB method) to be usually sufficient for the temperatures relevant to ionized gas regime; especially when the excellent performance of the classical mechanics in case of repulsive curves is taken into account. The extrapolation of potentials for higher energies (up to 1keV) is also discussed.

The usefulness of the following approximations will be discussed: use of exponential function for description of repulsive potentials, polarizability approximation for atom-ion interactions, and screened Coulomb potential for ion-ion interactions.

The collision integrals, transport cross sections and potential energy curves are available as supplementary material of publications. Transport cross sections are also stored in the CollisionDB database of IAEA.