Ion-atom Collisions Research Articles

Dynamic screening and two-center effects in neutral and partially dressed ion-atom collisions

In collisions involving projectiles with bound electrons, partial or total screening of their nuclear charge must be considered. Accordingly, a projectile dynamic effective charge, as a function of the collision momentum transfer, is included in the state-of-the-art continuum distorted wave with eikonal initial state model. This correction, applied in the exit channel, recovers a two-center description from collisions with neutral projectiles. Also, an improvement of both target and projectile ionization double differential cross sections is achieved, especially at the binary encounter and electron capture to the continuum peaks. The results calculated by our analytical model are shown in accordance with previous theoretical and experimental work.

Proposal for measuring line profiles and angular distributions of the radiative-electron-capture transition in low-energy ion-atom collisions: Beyond the impulse approximation

We propose to measure line profiles and angular distributions of the radiative-electron-capture transition in collisions of sub-MeV/$u {\mathrm{Ar}}^{18+}$ with helium. We estimate the line profile and the angular distribution using hydrogenlike and Hartree-Fock wave functions and show that the asymmetry of the line profile and the deviation of the angular distribution from the ${sin}^{2}{\ensuremath{\theta}}_{\mathrm{t}}$ law are magnified in the sub-MeV/$u$ region. Finite detector resolution and ion-beam monochromaticity are considered, and the results show that by using a usual bent-crystal spectrometer and a group of commercial silicon drift x-ray detectors one will be able to obtain sufficiently precise line profile and angular distribution to distinguish different theoretical descriptions of target atoms. The enhanced sensitivity to different theoretical approaches at low energies suggests that the proposed experiment will provide insights into the electromagnetic transition of an electron between a pair of relatively moving nuclei.

Buffer gas cooling of ions in radio-frequency traps using ultracold atoms

Reaching ultracold temperatures within hybrid atom–ion systems is a major limiting factor for control and exploration of the atom–ion interaction in the quantum regime. In this work, we present results on numerical simulations of trapped ion buffer gas cooling using an ultracold atomic gas in a large number of experimentally realistic scenarios. We explore the suppression of micromotion-induced heating effects through optimization of trap parameters for various radio-frequency (rf) traps and rf driving schemes including linear and octupole traps, digital Paul traps, rotating traps and hybrid optical/rf traps. We find that very similar ion energies can be reached in all of them even when considering experimental imperfections that cause so-called excess micromotion. Moreover we look into a quantum description of the system and show that quantum mechanics cannot save the ion from micromotion-induced heating in an atom–ion collision. The results suggest that buffer gas cooling can be used to reach close to the ion’s groundstate of motion and is even competitive when compared to some sub-Doppler cooling techniques such as Sisyphus cooling. Thus, buffer gas cooling is a viable alternative for ions that are not amenable to laser cooling, a result that may be of interest for studies into cold controlled quantum chemistry and charged impurity physics.

Effective single-electron treatment of ion collisions with multielectron targets without using the independent-event model

In ion-atom collisions involving multielectron targets the role of inner-shell electrons becomes important with increasing collision energy. Usually, processes involving the outer-shell and inner-shell electrons are treated using an independent-event model. However, the independent-event model becomes impractical when the number of shells is more than two. We develop an effective single-electron approach to ion collisions with multielectron atomic targets that overcomes this difficulty by treating all the atomic electrons on an equal footing. The approach allows the calculation of single-ionization and single-electron transfer cross sections by including the excitation of any one of the inner- or outer-shell target electrons. Accordingly, the approach does not differentiate which one of the many target electrons is captured or ionized. This is a unique feature of the proposed approach. The ground-state wave function for the target atom obtained in the multiconfiguration Hartree-Fock approach is used to calculate the probability density for the whole atom. The latter is then averaged over the spatial coordinates and spin variables of all of the target electrons except for the position of one electron from the nucleus. The obtained single-electron probability density is then used to derive a pseudopotential describing the interaction of one electron with an effective field produced by the target nucleus and the other electrons. The procedure reduces the many-body Schr\"odinger equation governing the collision system effectively into a three-body one. The reduced Schr\"odinger equation is solved using the two-center wave-packet convergent close-coupling approach. As an illustrative example we calculate integrated cross sections for single-electron transfer and ionization in proton collisions with lithium, sodium, and potassium. The results obtained agree very well with available experimental data for electron transfer. However, we find significant discrepancies with experiment for single ionization of Na and K, which warrant further experimental and theoretical investigations.

Measurement of L-shell X-ray production cross sections in 89Y, 158Gd and 209Bi due to 0.3 MeV/u – 1.0 MeV/u 12C ions

Experimental heavy ion induced X–ray production cross sections in matter continue to be of importance for both fundamental ion-atom collision studies as well as practical applications such as in nuclear analytical techniques. This work presents results of L-shell X-ray production cross section measurements in 89Y, 158Gd and 209Bi due to 4 MeV–12 MeV 12Cq + projectile ions. Experimental data are compared with theoretical calculations based on the ECPSSR, ECPSSR + EC and ECPSSR-UA models. Data show fairly good, albeit energy dependent agreement with the different models for yttrium and gadolinium cross sections. For bismuth, all three models overestimate data by an almost constant factor of two. The effect of multiple ionization on the l-line intensity ratios is also presented for gadolinium and bismuth targets.

Novel Approach to ^{93m}Mo Isomer Depletion: Nuclear Excitation by Electron Capture in Resonant Transfer Process.

A novel approach for isomer depletion in ion-atom collisions is proposed and considered theoretically. Analyses are performed for the depletion of the ^{93m}Mo isomer for which an unexpectedly large probability was measured in the beam-based experiment of Chiara etal. [Nature (London) 554, 216 (2018)NATUAS0028-083610.1038/nature25483]. The subsequent attempt at a theoretical description based on state-of-the-art atomic theory did not reproduce the experimental result [Wu etal., Phys. Rev. Lett. 122, 212501 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.212501] and showed a dramatic disagreement with the experiment (by many orders of magnitude). This conflict calls for further research on the nature of isomer depletion mechanisms occurring in atomic processes. Here, we propose to consider the ^{93m}Mo isomer depletion as the nuclear excitation by electron capture in resonant transfer process taking into account the momentum distribution of the target electrons. Although our results only slightly shift the upper theoretical limit for the total ^{93m}Mo isomer depletion probability toward the experimental value, they show the importance of considering the Compton profile in the theoretical description, in particular for the L shell, for which the depletion probability increases by many orders of magnitude.

Stability of a dust cloud in the radio frequency low-pressure gas discharge

We analyze stability of a three-dimensional cloud of the dust particles in the low-pressure radio frequency discharge under microgravity conditions. The parameters of such complex plasma are assumed to conform to the recently developed ionization equation of state that includes the effects of the ion–atom collisions on the particle charge and of the ion–particle collisions on the ion mean free path. Propagation of the particle number density perturbation in a cloud is treated using the fluid approach. The equation for dust cloud dynamics allows for the electric and ion drag forces that are not compensated in a nonstationary state and yields the wave equation for the dust acoustic waves with either a positive or negative effective friction coefficient. The resulting dispersion relation defines a condition of the instability onset, which is written for the maximum ambipolar field and dust number density gradient. Analysis of the available experimental data reveals a satisfactory correspondence with the theory. In particular, it is demonstrated that the maximum dust density gradient in the cloud increases with the increase in the particle diameter and in the pressure of plasma-forming gas.

Analysis of Multipolar Linear Paul Traps for Ion–Atom Ultracold Collision Experiments

We evaluate the performance of multipole, linear Paul traps for the purpose of studying cold ion–atom collisions. A combination of numerical simulations and analysis based on the virial theorem is used to draw conclusions on the differences that result, by considering the trapping details of several multipole trap types. Starting with an analysis of how a low energy collision takes place between a fully compensated, ultracold trapped ion and an stationary atom, we show that a higher order multipole trap is, in principle, advantageous in terms of collisional heating. The virial analysis of multipole traps then follows, along with the computation of trapped ion trajectories in the quadrupole, hexapole, octopole and do-decapole radio frequency traps. A detailed analysis of the motion of trapped ions as a function of the amplitude, phase and stability of the ion’s motion is used to evaluate the experimental prospects for such traps. The present analysis has the virtue of providing definitive answers for the merits of the various configurations, using first principles.

Direct observation of swap cooling in atom–ion collisions

Direct observation of swap cooling in atom–ion collisions

Direct observation of swap cooling in atom–ion collisions

Collisions with cold particles can dissipate a hot particle’s energy and therefore can be exploited as a cooling mechanism. Kinetics teach us that cooling a particle down by several orders of magnitude typically takes many elastic collisions as each one only carries away a fraction of the collision energy. Recently, for a system comprising hot ions and cold atoms, a very fast cooling process has been suggested (Ravi et al 2012 Nat. Commun. 3 1126) where cooling over several orders of magnitude can occur in a single step. Namely, in a homo-nuclear atom–ion collision, an electron can resonantly hop from an ultracold atom onto the hot ion, converting the cold atom into a cold ion. Here, we demonstrate such swap cooling in a direct way as we experimentally observe how a single energetic ion loses energy in a cold atom cloud. In order to contrast swap cooling with sympathetic cooling, we perform the same measurements with a hetero-nuclear atom–ion system, for which swap cooling cannot take place, and indeed observe very different cooling dynamics. Ab initio numerical model calculations agree well with our measured data and corroborate our interpretations.

Dynamic effective charge in the target continuum within the CDW-EIS model for ionisation in ion–atom collisions: angular dependence

Dynamic effective charge in the target continuum within the CDW-EIS model for ionisation in ion–atom collisions: angular dependence

Rydberg atom-ion collisions in cold environments

Low-energy collisions of Rydberg atom-ion systems are investigated theoretically. We present the parameter space associated with suitable approaches for the dynamics of Rydberg atom-ion collisions, i.e. quantum-, Langevin and classical exchange regimes, showing that for the lowest reachable temperatures a classical treatment is appropriate. A quasi-classical trajectory method is used to study charge exchange cross sections for Li$^*$-Li$^+$ and Li$^*$-Cs$^+$ at collision energies down to $1\,$K. For cold collisions we find the charge exchange cross section deviating from the $n^4$ geometric scaling. Furthermore, for low-energy collisions, we find both an influence of the ionic core-repulsion as well as variations for two different models used for describing the electron-core potential.

Single- and double-ionization processes using Gaussian-type orbitals: Benchmark on antiproton-helium collisions in the keV-energy range

We present a simple and efficient method for computing single and double ionization cross sections in ion-atom and ion-molecule collisions using ${L}^{2}$ Gaussian basis sets. Gaussian functions are widely employed to compute bound states of ions, atoms, and molecules. However, the description of continuum states, and therefore ionization phenomena, remains a theoretical challenge. Our approach is tested on the benchmark system antiproton-helium collisions in the so-called intermediate energy range. A good agreement with numerically exact calculations is observed. The proposed method is general and can thus be employed in any collisional systems in the challenging nonperturbative regime. Our work opens the way to investigate multiple ionization processes by ion impact in multicenter polyelectronic systems.

High-energy-resolution measurements of an ultracold-atom–ion collisional cross section

The cross section of a given process fundamentally quantifies the probability for that given process to occur. In the quantum regime of low energies, the cross section can vary strongly with collision energy due to quantum effects. Here, we report on a method to directly measure the atom-ion collisional cross section in the energy range of 0.2-12 mK$\cdot$ k$_B$, by shuttling ultracold atoms trapped in an optical-lattice across a radio-frequency trapped ion. In this method, the average number of atom-ion collisions per experiment is below one such that the energy resolution is not limited by the broad (power-law) steady-state atom-ion energy distribution. Here, we estimate that the energy resolution is below 200 $\mu$K$\cdot$k$_B$, limited by drifts in the ion's excess micromotion compensation and can be reduced to the 10's $\mu$K$\cdot$k$_B$ regime. This resolution is one order-of-magnitude better than previous experiments measuring cold atom-ion collisional cross section energy dependence. We used our method to measure the energy dependence of the inelastic collision cross sections of a non-adiabatic Electronic-Excitation-Exchange (EEE) and Spin-Orbit Change (SOC) processes. We found that in the measured energy range, the EEE and SOC cross sections statistically agree with the classical Langevin cross section. This method allows for measuring the cross sections of various inelastic processes and opens up possibilities to search for atom-ion quantum signatures such as shape-resonances.

Evaluation of the Charge-Changing Cross Sections for Ion—Atom Collisions

Evaluation of the Charge-Changing Cross Sections for Ion—Atom Collisions

The influence of photo-induced processes and charge transfer on carbon and oxygen in the lower solar atmosphere

ABSTRACT To predict line emission in the solar atmosphere requires models that are fundamentally different depending on whether the emission is from the chromosphere or the corona. At some point between the two regions, there must be a change between the two modelling regimes. Recent extensions to the coronal modelling for carbon and oxygen lines in the solar transition region have shown improvements in the emission of singly and doubly charged ions, along with Li-like ions. However, discrepancies still remain, particularly for singly charged ions and intercombination lines. The aim of this work is to explore additional atomic processes that could further alter the charge-state distribution and the level populations within ions, in order to resolve some of the discrepancies. To this end, excitation and ionization caused by both the radiation field and by atom–ion collisions have been included, along with recombination through charge transfer. The modelling is carried out using conditions which would be present in the quiet Sun. This allows an assessment of the part atomic processes play in changing coronal modelling, separately from dynamic and transient events taking place in the plasma. The effect the processes have on the fractional ion populations are presented, as well as the change in level populations brought about by the new excitation mechanisms. Contribution functions of selected lines from low-charge states are also shown, to demonstrate the extent to which line emission in the lower atmosphere could be affected by the new modelling.

Transport of a Single Cold Ion Immersed in a Bose-Einstein Condensate.

We investigate transport dynamics of a single low-energy ionic impurity in a Bose-Einstein condensate. The impurity is implanted into the condensate starting from a single Rydberg excitation, which is ionized by a sequence of fast electric field pulses aiming to minimize the ion's initial kinetic energy. Using a small electric bias field, we study the subsequent collisional dynamics of the impurity subject to an external force. The fast ion-atom collision rate, stemming from the dense degenerate host gas and the large ion-atom scattering cross section, allow us to study a regime of frequent collisions of the impurity within only tens of microseconds. Comparison of our measurements with stochastic trajectory simulations based on sequential Langevin collisions indicate diffusive transport properties of the impurity and allows us to measure its mobility. Our results open a novel path to study dynamics of charged quantum impurities in ultracold matter.

Strengthening the case for interatomic Coulomb decay as a subdominant reaction channel in slow O3+−Ne2 collisions with independent-atom-model coupled-channel calculations

We report on electron removal calculations for 2.81 keV/amu Li$^{3+}$ and O$^{3+}$ ion collisions with neon dimers. The target is described as two independent neon atoms fixed at the dimer's equilibrium bond length, whose electrons are subjected to the time-dependent bare and screened Coulomb potentials of the classically moving Li$^{3+}$ and O$^{3+}$ projectile ions, respectively. Three mutually perpendicular orientations of the dimer with respect to the rectilinear projectile trajectories are considered and collision events for the two ion-atom subsystems are combined in an impact parameter by impact parameter fashion and are orientation-averaged to calculate probabilities and cross sections for the ion-dimer system. The coupled-channel two-center basis generator method is used to solve the ion-atom collision problems. We concentrate the ion-dimer analysis on one-electron and two-electron removal processes which can be associated with interatomic Coulomb decay, Coulomb explosion, and radiative charge transfer. We find that the calculated relative yields are in fair agreement with recent experimental data for O$^{3+}$-Ne$_2$ collisions if we represent the projectile by a screened Coulomb potential, but disagree markedly for a bare Coulomb potential, i.e., for Li$^{3+}$ impact. In particular, our calculations suggest that interatomic Coulomb decay is a significant reaction channel in the former case only, since capture of a Ne($2s$) electron to form hydrogenlike Li$^{2+}$ is unlikely.

On the Possibility of Heating the Solar Corona by Heat Fluxes from Coronal Magnetic Structures

We estimate the role of heat flux from hot magnetic loops and open flux tubes into the surrounding corona as a possible source of heating of the corona. We show that hot magnetic-flux tubes (Type-II spicules) provide a more efficient source of coronal heating than hot magnetic loops, as the closed magnetic structure of a loop substantially restricts the heat flux into the corona. In order to compensate for radiation and thermal-conduction losses, approximately $10^{4}$ Type-II spicules with a temperature of several million Kelvin are required, which is about 1% of the number of spicules simultaneously observed on the solar disk. Our analysis shows that the principal source of energy that heats the coronal plasma is photospheric convection, which generates electric currents of about $10^{10}$ – $10^{12}$ A in magnetic loops and spicules. Dissipation of the currents increases significantly in the partially ionized plasma, i.e. when ion–atom collisions and the associated Cowling conductivity occur. This results in two important effects: heating of plasma in magnetic structures up to several million Kelvin, and ejection of hot plasma from open magnetic-flux tubes to the corona, replenishing the corona with hot plasma. The ejection of hot plasma results from the heating of the spicule foot-point by electric-current dissipation, which grows with a sporadic increase in the velocity of photospheric convection, for example, due to five-minute oscillations or the Rayleigh–Taylor instability. As a result, the rate of heating the photospheric foot-points of the spicules by ring currents exceeds radiation losses, which leads to a jump in the pressure gradient and the ejection of hot plasma into the corona from the open tips of the magnetic-flux tubes.

Net Electron Capture in Collisions of Multiply Charged Projectiles with Biologically Relevant Molecules

A model for the description of proton collisions from molecules composed of atoms such as hydrogen, carbon, nitrogen, oxygen and phosphorus (H, C, N, O, P) was recently extended to treat collisions with multiply charged ions with a focus on net ionization. Here we complement the work by focusing on net capture. The ion–atom collisions are computed using the two-center basis generator method. The atomic net capture cross sections are then used to assemble two models for ion–molecule collisions: An independent atom model (IAM) based on the Bragg additivity rule (labeled IAM-AR), and also the so-called pixel-counting method (IAM-PCM) which introduces dependence on the orientation of the molecule during impact. The IAM-PCM leads to significantly reduced capture cross sections relative to IAM-AR at low energies, since it takes into account the overlap of effective atomic cross sectional areas. We compare our results with available experimental and other theoretical data focusing on water vapor (H2O), methane (CH4) and uracil (C4H4N2O2). For the water molecule target we also provide results from a classical-trajectory Monte Carlo approach that includes dynamical screening effects on projectile and target. For small molecules dominated by a many-electron atom, such as carbon in methane or oxygen in water, we find a saturation phenomenon for higher projectile charges (q=3) and low energies, where the net capture cross section for the molecule is dominated by the net cross section for the many-electron atom, and the net capture cross section is not proportional to the total number of valence electrons.