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Physics Procedia 66 (2015) 22 - 27

C 23rd Conference on Application of Accelerators in Research and Industry, CAARI 2014

Bare- and Dressed-Ion Impact Collisions from Neon Atoms Studied Within a Nonperturbative Mean-Field Approach

Gerald Schenk, Tom Kirchner

Department of Physics and Astronomy, York University, 4700 Keele Street, Toronto Ontario M3J1P3, Canada

Abstract

We study electron removal processes in collisions of bare and dressed doubly charged ions with neon atoms in the 20 keV/u to 1 MeV/u impact energy regime. The many-electron problem is represented by a single mean field, which in the case of dressed-ion impact includes the projectile electrons. Moreover, the same basis is used to propagate all active orbitals thereby ensuring orthogonality at all times and allowing for a

final-state analysis in terms of standard Slater determinantal wave functions. The same approach was used in a recent work for B 2 + -Ne collisions [Phys. Rev. A 88 012712], in which we examined the role of the projectile electrons for target-recoil-charge-state production. The present study expands on that work by considering additional collision channels and comparing results of equicharged dressed and bare ions in order to shed more light on the role of the projectile electrons.

© 2015 The Authors.Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Selection and peer-review under responsibility of the Organizing Committee of CAARI 2014

Keywords: bare- and dressed ion impact collisions, net recoil ion production, target ionization, electron capture, mean-field model

1. Introduction

Recently, results from collision experiments of dressed 52+ projectiles with atomic neon targets were reported [1, 2]. Collision systems like this are a challenge for theoretical descriptions, since one has to deal with electrons not only on the target, but also on the projectile. One approach to describe such collisions is to only consider the active target electrons while the initial projectile electrons are solely taken into account in terms of a screening potential. Such calculations have been performed in the independent particle model (IPM), for example with the continuum distorted wave with eikonal initial state (CDW-EIS) method [2, 3]. In a recent work we discussed the advantages of considering active electrons on the dressed-ion projectile as well as on the target in the description of projectile charge state coincident multiple ionization of neon [4]. In the present work we compare results of such calculations for dressed-ion impact with those of equicharged bare ion impact, specifically the collisions of B2+ and He2+ with Ne. Atomic units are used throughout this work, unless stated otherwise.

* Corresponding author. Tel.: 416-736-2100, ext. 33695; fax: 416-736-5516.

E-mail address: tomk@yorku.ca

1875-3892 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Selection and peer-review under responsibility of the Organizing Committee of CAARI 2014 doi: 10.1016/j.phpro.2015.05.005

2. Method

The collisions are described in an IPM in which the nuclear potentials are screened by mean-field potentials of their electrons. The collisions discussed here are fast enough to describe the nuclear motion by straight line trajectories. The many-electron system is separated into independent problems for N initial conditions, which correspond to the N orbitals that are occupied on the projectile and the target at an asymptotic time before the collision. All initial states are propagated with the same Hamiltonian

1 - —

h(t) = - - A--i + vUn) - + vHa(rp) (1)

2 rt rp

where - —t/rt and - —p/rp are the nuclear target and projectile potentials, respectively. The projectile is screened by the Hartree potential vHa(rp). At asymptotic distances the effective projectile potential _ — /r + vp (r ) approaches -qp/r^ with the initial

projectile charge state qp. The potential vlcc(rl) includes Hartree and exchange terms, i.e. it compensates self interaction [5], and is therefore asymptotic to - 1/rt. We are using the no-response approximation in which the effective potentials do not change their forms, but reflect the electron configuration at the initial time throughout the collision. The potentials used in our calculations are obtained from the optimized potential method [5].

Using the same Hamiltonian, i.e. a common mean field, preserves orthogonality of the propagated states. The downside of using the Hamiltonian (1) for all initially occupied orbitals is that it is not possible to ensure the correct asymptotic behaviour for both collision centres at the same time. In this work we choose to have the asymptotically correct potential for the target, as our focus is on removal and capture of target electrons. The single-particle equations

id,yv(r, t) = h(t)Wv( r,t), v = 1,...,N (2)

are solved with the two-centre basis generator method (TC-BGM) [6, 7] which is a basis expansion method. The basis is formed by atomic eigenstates of the target, ionic eigenstates of the projectile, and pseudo states to represent the continuum. For the present calculations our basis consists of the 19 neon eigenstates 2s...4f and 20 projectile eigenstates 1s...4f of the hydrogen-like bare helium or the dressed boron ion. In addition 79 pseudostates generated from target orbitals are included.

For each initial condition (index v ) and for all final states (bound target or projectile states), labelled by /d , we obtain

transition amplitudes cv/1 and single-particle probablities pvfi =| cv/1 |2 . The latter can be used for a direct comparison with experiments that provide net recoil ion production cross sections:

The impact parameter b dependent net recoil ion production p^b) is found by summing up the single-particle probabilities pv/1 corresponding to bound target states:

Pn:c(b)=n

v MeT (4)

Nt is the number of electrons initially at the target. For the collisions of Ne with the bare He2+ projectile the inital conditions are the neon 2s to 2p1 orbitals, each occupied by n =2 electrons. For the dressed B2+ projectile the boron 1s and 2s states are propagated in addition. In both calculations the neon 1s orbital is neither propagated nor included in the basis. These K -shell electrons are considered passive and only contribute to the screening potential vete .

We carry out a determinantal analysis to calculate probabilités pk l for a final state where k electrons are found at the projectile and l electrons in the continuum [8, 9]. With this convention and the initial number of electrons on the projectile ion Np the final target charge state is q( = l — Np + k . The q( weighted sum over the total cross sections (JM, corresponding to pM, is equivalent to the net recoil ion production C+ in (3):

N N-k = ■

k=0 I=0

Figure 1: Net recoil ion production CT+ and positive ion production CT+ as functions of projectile velocity. Present theory: Bz+ (solid lines), Hez+ (dashed lines); Previous BGM calculation as described in the text [10] (dash-dotted lines); Experiment: B2+ [2] (triangles); He2+ [11] (open squares), [12] (lozenges).

As probability has to be conserved with regard to equation 5 unlikely and unphysical collision channels, which correspond to negative ion production and are a side-effect of the statistical final-state analysis, are also included in this summation.

3. Results and Discussion

Our results for the net recoil ion production C+ by the dressed and the bare projectile are displayed in Figure 1. For the He2+ projectile our results overestimate the experiments [11, 12] somewhat. This can be attributed to the no-response approximation used. Our present He2+ results - calculated with the two-centre extension of the BGM - closely resemble a previous no-response BGM calculation, in which projectile states were not included explicitly in the basis [10]. However, reference [10] compared a response model with the no-response approximation, and found response results in very good agreement with the experiments [11, 12].

The comparison of the B2+ and He2+ curves shows an interesting aspect of Figure 1: While the net recoil ion production by dressed ion impact exceeds that for the bare ion at medium to high collision energies, the B2+ curve intersects with the He2+ curve near a velocity of v = 1.75, corresponding to an impact energy of E = 75 keV/u.

Unfortunately, unlike for helium ion impact, it appears there is no data available for B2+-Ne net recoil ion production CT+ . There is, however, for a projectile charge state coincident quantity: the positive ion production

= Yl^ki for k = Np

in which the charge state of the projectile at the final time is the same as at the initial time, qp = qf, and hence, qf = l. The CT+ results of our dressed- and bare-ion calculations are shown in Figure 1 as well. For B2+ impact these cross sections have been published previously [4]. To be consistent with the experimental data for He2+ shown in Figure 1 the sum in (6) has been truncated at l = 4, unlike in references [4] and [2] where five-fold ionization was also included.

For both collision systems the present C+ results are in good agreement with the experiments. In slow collisions (v < 2 ) positive ion production CT+ by B2+ is slightly underestimated. Unlike for the net recoil ion production, where the lines intersect, the bare ion cr+ curve and experiment always remain below those for the dressed ion.

E (keV/u)

10 100 200 500 1000

0 12 3 4 5 6

Figure 2: Total cross sections CT 3/ and CT0/ for / -fold target ionization coincident with unchanged projectile charge state, for B2+ (solid line) and He2+ (dashed

line) impact respectively, as functions of projectile velocity. Also shown are results of a CDW-EIS calculation for B1+ (double-dashed line) that accompanied the experimental data of [2]. Experiment: B2+ triangles [2]; He2+ open squares [11], lozenges [12].

In Figure 2 the charge state coincident collision channels Cu contributing to C+ (c.f. equation 6) are shown. Also included

are results of a CDW-EIS calculation for the B2+-Ne collision system published together with the experimental results [2]. We already discussed the differences between these results and ours in our previous article [4], and argued that a passive projectile electron IPM description does not address projectile electron loss and exchange processes. As a consequence, it leads to an overestimation of pure target ionization in fast collisions and an underestimation of ionization in slow collisions. When comparing all three theoretical results included in Figure 2 with the experiments, the agreement is good for small l but worsens as l increases. This is an inherent shortcomming of the IPM, as it addresses multi-particle processes through statistical models. As a rule of thumb, one can expect good results for multiple ionization until I equals the initial projectile charge state plus one. But the picture looks better for B2+ impact for which the present theory is still in good agreement with the experiment up to I = 4 . By contrast, for He2+ the cross section <T04 is strongly overestimated.

While B2+ and He2+ total cross sections for single ionization (CT31 and CT01 respectively) do not differ very much, at least not above 100 keV/u, four-fold ionization of neon by B2+ impact is significantly increased compared to He2+ impact. Such multiple ionization processes are happening predominantly at small impact parameters b . In these close collisions the three projectile electrons screen the boron nucleus only partially such that the total projectile potential is stronger than - 2/rp.

E (keV/u) 100 200

r f KK

double capture \ 5 \

0 1 2 3 4 5

v (au)

Figure 3: Total cross sections for (a) single- and (b) double-capture (7) for B2+ (solid lines) and He2+ (dashed lines) impact, as functions of projectile velocity. Experimental data: B2+ [1] (solid triangles), [13] (solid pentagons); He2+ [11] (open squares), [12] (open lozenges)

Our results for single capture <Tsc and double capture CTdc are compared with experiments in Figure 3. The cross sections

iVt-1 iVt-2

^ = XCT«for k=V +1; CTdc = X for k=V +2, (7)

1=0 1=0

are indiscriminate of the final target charge state, i.e. collision channels with and without additional ionization are summed up without weighting. For the B2+ projectile the present theory underestimates the experimental single capture data of [1]. However, it lies above the two experimental data points of [13]. The results for He2+-Ne are in better agreement with the experiment. The present TC-BGM calculation with a determinantal final state analysis also closely reproduces the previous BGM calculations with a multinomial final state analysis [10]. While the double capture calculations for both collision systems (Figure 3 b) overestimate the experiments, the B2+ curve is consistently below the He2+ curve. The higher net recoil ion production by He2+ impact, compared to B2+ impact, in slow collisions noticed in Figure 1, is partly a consequence of this.

Future work will be concerned with the investigation of response effects in these collision systems and with an extension of the methods to triply-charged ion impact on neon, for which experimental data have been published recently [14].

Acknowledgment

This work has been supported by the Natural Sciences and Engineering Research Council of Canada.

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