Atomic Collisions CCW

Background

High energy collisions among ions and neutral atoms or molecules occur in several settings, for example the interaction of an energetic neutral beam with plasma in a fusion experiment, the interaction of a fast ion beam with a neutralizer gas, the interaction of a highly charged ion beam with residual neutral gas in an accelerator or storage ring and the interaction of solar wind ions with cometary or planetary gas. In these settings, electronic processes — excitation and deexcitation, charge transfer and ionization — can meaningfully be studied in an approximation of fixed velocity, straight line nuclear motion. The present proposed workshop is concerned with methods for computing electronic transition rates in such high energy (fast) atomic collisions.

Two established series of workshops serve as models for the proposed event. The Non-Local Thermodynamic Equilibrium (NLTE) Code Comparison Workshop series started in 1996; the 10th NLTE Workshop (NLTE10) was held in 2017. Inspired by the NLTE series the Spectral Line Shapes in Plasmas (SLSP) Code Comparison Workshop series started in 2012 and the meetings are being held biennially since 2013. For each instance of the NLTE and SLSP code comparison workshops a set of cleanly defined test cases is specified and distributed to the expected participants several months before the event. The researchers do their best calculations and produce results in an agreed format. The code results are assembled before the meeting into a database (accessible to the participants only) and then the contributors come together for 4 or 5 days of intense work during which they seek to understand all their differences. Often a meeting report is produced as a journal article. It has been the custom not to identify the outputs of individual codes in those meeting reports.

The Atomic and Molecular Data Unit at IAEA is currently running a Coordinated Research Project (CRP) on Atomic Processes of Neutral Beams in Fusion Plasma. The code comparison workshop described here supports this project by studying atomic physics codes for fundamental collision processes relevant to neutral beam penetration and beam-based spectroscopy. Test cases for the comparison would include collision processes of relevance to heating and diagnostic neutral beams in fusion plasma, but there would also be test cases motivated by the process of ion beam neutralization, by processes involving residual gas in storage rings, or by interactions of solar wind ions with neutral gas. The quantities of interest for the comparison would be the electronic transition rates only.

Meeting Scope

The practice in the NLTE and SLSP code comparison workshops is that each participant must contribute results for some test cases and each test case is supposed to attract several contributions, but no participant is expected to address all problem classes. The same expectation will apply for the present workshop.

The workshop is devoted to electron dynamics or, more precisely, to electronic transition rates and transition matrix elements for the electronic Schrödinger equation with a time-varying potential. As presently foreseen all the test cases come from the domain of atomic and atom-molecule collisions. Test cases could be included that involve an electronic Schrödinger equation with some other kind of time-varying potential.

The range of test cases that we have in mind starts with collisions between a fully stripped ion and neutral H and assuming straight line motion for the nuclei at a fixed relative velocity. This is a one-electron problem with a prescribed (time-varying) external potential and it is already non-trivial. Test cases having two active electrons would include collisions between a fully stripped ion and neutral He or the H2 molecule. The most complicated systems that we have in mind are still very small by the standards of quantum chemistry; they are collisions between an atomic ion and something like neutral Ne or the CO molecule. We recognize the importance of energetic ion-neutral interactions involving macromolecules or materials, but calculations for such collisions are outside the scope of this workshop.

For any of the classes of test cases the important quantities for applications are cross sections, which are obtained by integrating transition rates over the impact parameter and over the molecular configuration as applicable. However, for a careful comparison of methods and implementations it is appropriate to concentrate on cases where specific nuclear trajectories are singled out; fixed impact parameter and (for molecules) fixed geometry and orientation. For atomic collisions the impact parameter is just one variable, but for collisions between an atomic ion and a rigid diatomic molecule three trajectory parameters are needed to describe the straight line path and for collisions between an atomic ion and a general rigid molecule four trajectory parameters are needed. The purpose of this workshop is to clarify differences among methods and implementations; it is not to evaluate the final data for applications. Maybe for atomic collision test cases the participants will also want to compare cross sections integrated over the impact parameter, but for the cases that involve a diatomic or larger molecule the comparison should almost certainly be restricted to a small set of specific trajectories.

All reaction channels are of interest: state resolved charge transfer, ionization, and simple excitation or deexcitation. The subsequent decay and related photoemission (or autoionizing emission in some cases) from excited reaction products is of great interest for applications, but it is probably not in the scope of this code comparison exercise.

Methods for Comparison

Already within the problem class of electron dynamics for prescribed nuclear motion there is quite a variety of methods being used. There are multiple groups that use classical trajectory Monte Carlo (CTMC). Several groups use Atomic Orbital Close Coupling (AOCC; also the acronym TC-AOCC is used), either based on Slater-type orbitals or on Gaussian orbitals. For the cases of one-electron and two-electron systems several groups evolve the time-dependent Schrödinger equation on a lattice, which can be rectangular or cylindrical, fixed or adaptive, and the acronyms are LTDSE, GTDSE and also just TDSE. Several groups use a Molecular Orbital Close Coupling (MOCC or QMOCC) approach. Time dependent density functional theory (TD-DFT) is used for problems involving more than two electrons. Modelling based on Sturmian functions, time dependent close coupling, and the distorted wave approach are all in scope.

Meeting Objectives

Following the model of the NLTE and SLSP workshop series the primary objective of the workshop is code comparison (i.e., comparison of methods and their implementations) for the benefit of the participating atomic physicists. The workshop should help them to learn more about their method and their implementation in relation to other methods and implementations for the same class of problems.

The workshop will be designed to compare methods and their implementations, but it will not be designed to decide which method is "best" (fastest, most accurate, most convenient, ...) for a given class of problems. Participants may return from the workshop with a keener judgment of the quality of the various methods and implementations for a given class of problems, but they are not asked to produce a consensus report with that judgment.

The code comparison workshop has a further objective to expose atomic data issues to the participants and to help the participants to quantify uncertainties in their calculations of electronic transition rates. This in turn will help them to quantify uncertainties in calculated atomic data for applications including processes of neutral beams in fusion plasma, charged ion beam neutralization, charge transfer from neutral gas in a storage ring, and interaction of solar wind ions with neutral gas.

This is not a data evaluation workshop. In a data evaluation event one would consider a certain collision process, assemble data that are cross sections as a function of energy, assess the uncertainties in those data and finally recommend a best cross section curve and its uncertainty. In this code comparison event we are not comparing cross sections, we are comparing transition rates before integration over impact parameter and molecular configuration. We are not recommending best codes or best data.

Proposed Test Cases

The set of test cases must be more narrowly circumscribed before the workshop to ensure that the calculations will all be done by a sufficient number of participants and that there is adequate time to compare and discuss the results. This is to be discussed with prospective participants.

The balance of emphasis also needs to be discussed with prospective participants. Tentatively, we think that calculations for one-electron and two-electron systems will occupy somewhat more than half the time at the workshop and calculations for systems having three or more active electrons will occupy somewhat less than half the time.

In all the test cases presently foreseen except the final one (that is marked as "borderline for inclusion") the nuclear motion is to be treated as a fixed velocity straight line motion – i.e., in an infinite nuclear mass approximation. The concern is with electronic transition processes and the quantities of interest for comparison are the electronic transition rates.

As presently foreseen all the test cases come from the domain of atomic and atom – molecule collisions. Test cases could be included that involve an electronic Schrödinger equation with some other kind of time-varying potential. This option can be reviewed by the workshop organizers in due time.

Effective one-electron atomic collisions

The simplest model problem for the workshop would be that of collisions between a fully stripped ion, which might be H, He, C, Ne, Ar, Kr or U, and neutral H or a hydrogen-like ion. A limited number of test-cases should be specified: the set of cases should be restricted the minimum that can illustrate different possible issues with the codes. For any specified collision process one specifies several values of the energy and impact parameter and the participants are asked to calculate the electronic transition rate. Maybe in some cases one also asks for a cross section obtained by integrating the transition rate over the impact parameter.

The neutral H or hydrogen-like ion could be H(1s) or it could be excited H(2s) or H(2p) at any polarization or a higher excited state. Transition rates for excited states are important for applications and it probably adds value to the code comparison exercise to include such cases.

Would there be any interest in one-electron atomic collision test cases that involve a hydrogen-like ion other than neutral H? An example would be that of protons colliding with a hydrogen-like ion.

General remark: whenever we speak of a fully stripped ion it could in practice also be a highly charged ion treated in a frozen core approximation. In fast collisions of a highly charged ion with a neutral atom or molecule, if charge transfer takes place then it is to some Rydberg state and therefore a frozen core treatment can be appropriate.

One-electron collisions involving three nuclei

This would be the problem of a fully stripped ion colliding with the H2+ molecular ion. In practice, if the problem class is to be included at all, the fully stripped ion would be H+.

Do we want to include the problem class of energetic collisions between a proton and the H2 molecular ion? Remember that we are not proposing to study rearrangement collisions; these are collisions with prescribed straight line nuclear motion and only the electron dynamics is to be studied. The problem class could be of applied interest in connection with neutralization of a proton beam by passing it through hydrogen gas, if also H2+ is going to be present in the neutralizer chamber.

Effective two-electron atomic collisions

Could be fully stripped ion (probably again H, He, C, Ne, Ar, Kr or U) colliding with the H- anion, He neutral or He-like ion, it could be an H – H collision, or it could be a hydrogen-like ion colliding with H neutral or another hydrogen-like ion.

Collisions among neutral He and fully stripped H or other ion are of interest in connection with use of helium neutral beams in fusion. Which other cases are of applied interest?

Effective two-electron collisions involving three nuclei

The test cases in this problem class would be collisions of a fully stripped ion with an H2 molecule with specification of relative velocity, impact parameter and molecular configuration, all in the approximation of straight line nuclear motion. The relevant data for applications are cross sections integrated over impact parameter and molecular configuration, but that is a three-dimensional integral if the H2 bond length is fixed and a four-dimensional integral if it is not fixed, and we think that it will be too much of a distraction from the core of the comparison exercise to include those integrated data.

Many-electron atomic collisions

The likely problems in this class are collisions between an atomic ion and a neutral atom. An obvious case would be proton collisions with neutral Ne or Ar. In connection with the use of lithium neutral beams in fusion one also thinks of a fully stripped ion colliding with neutral Li. There are countless other cases and we will have to narrow it down to a few that are of broadest interest.

(Borderline for inclusion) Many-electron collisions involving three or four nuclei

Extension to many-electron ion-molecule collisions. Test cases in this class (if they are to be included at all) could be motivated by application to the interaction of solar wind ions with neutral gas, so one would consider collisions of a proton or other atomic ion with a CO molecule or perhaps with H2O or CO2. Like for the problem of atomic collisions with H2, each test case would involve a specified impact parameter and molecular configuration and the nuclear motion would be fully prescribed.

Another many-electron collision system that involves three nuclei is that of the H- negative ion with H2 gas. This process is relevant for the negative ion beam neutralizer for fusion applications.

These many-electron ion – molecule collisions would form the most complicated class of processes to be included in the workshop. At present we judge that it is good to include some such cases, but maybe we will be persuaded otherwise and then these cases will be dropped. Recall that it is not expected that each participant does all the test cases, but each test case must be done by an adequate number of participants and there must be time to discuss the results.

(Borderline for inclusion) One-electron and two-electron atomic collisions with consideration of nuclear dynamics

Any of the previous cases can be extended to include non-trivial nuclear dynamics; the question is mainly if it would have useful synergy with the electron dynamics part of the workshop. At this time we leave it open if there should be some test cases for the simplest systems (two nuclei and at most two electrons) for which the nuclear motion is not prescribed.