Electron capture and ionization cross-section calculations for proton collisions from methane and the DNA and RNA nucleobases
aa r X i v : . [ phy s i c s . a t m - c l u s ] J u l Electron capture and ionization cross-section calculations forproton collisions from methane and the DNA and RNA nucleobases
Hans Jürgen Lüdde ∗ Frankfurt Institute for Advanced Studies (FIAS), D-60438 Frankfurt, Germany
Marko Horbatsch † and Tom Kirchner ‡ Department of Physics and Astronomy,York University, Toronto, Ontario M3J 1P3, Canada (Dated: July 17, 2019)
Abstract
Net ionization and net capture cross-section calculations are presented for proton collisions frommethane molecules and the DNA/RNA nucleobases adenine, cytosine, guanine, thymine, and uracil.We use the recently introduced independent-atom-model pixel counting method to calculate thesecross sections in the 10 keV to 10 MeV impact energy range and compare them with results obtainedfrom the simpler additivity rule, a previously used complete-neglect-of-differential-overlap method,and with experimental data and previous calculations where available. It is found that all theoreticalresults agree reasonably well at high energies, but deviate significantly in the low-to-intermediateenergy range. In particular, the pixel counting method which takes the geometrical overlap ofatomic cross sections into account is the only calculation that is able to describe the measurementsfor capture in proton-methane collisions down to 10 keV impact energy. For the nucleobases it alsoyields a significantly smaller cross section in this region than the other models. New measurementsare urgently required to test this prediction.
PACS numbers: 34.10.+x, 34.50.Gb, 34.70.+e, 36.40.-c ∗ [email protected] † [email protected] ‡ [email protected] . INTRODUCTION Collisions involving complex molecules pose a significant challenge to theory owing to theirlarge number of degrees of freedom and their multi-center geometry. A convenient frameworkfor a simplified discussion is offered by the independent atom model (IAM) according towhich certain properties and quantities of a molecule are constitutive , i.e., can be obtainedby adding up atomic contributions. When applied to collisions, the simplest version of theIAM consists in adding up the cross sections of the atomic constituents of a given moleculein order to obtain the molecular cross section. This procedure is usually referred to as theadditivity rule (AR). It goes back to Bragg [1] and was first studied in a more systematicfashion in the 1950s for electron-impact ionization of medium-sized molecules [2]. The IAM-AR has since been applied to many electron- and ion-impact collision systems, typically withgood success at high impact energies, while larger discrepancies with experimental data havebeen found in the low-to-intermediate energy region. This has been taken as an indicationthat molecular structure effects gain importance with decreasing collision energy [3].Accordingly, extensions and alternatives have been considered, such as ARs with weightfactors (see, e.g., [4] and the review article [5] and references therein) and a complete-neglect-of-differential-overlap (CNDO) approach (see, e.g., [3, 6, 7]. The latter starts fromthe assumption that a molecular net cross section can be expressed as a sum of partial crosssections for all initially occupied molecular orbitals (MOs) and then approximates thosepartial cross sections as linear combinations of atomic-orbital (AO) specific cross sectionswith weight factors that are obtained from a Mulliken population analysis [8]. In this way,the CNDO approach takes molecular structure information into account to some extent.However, CNDO cross sections do not depend on the orientation of the molecule relativeto the projectile beam direction, i.e., they are to be interpreted as orientation-averagedquantities. The same is, of course, true for the simple IAM-AR. Moreover, none of thesemethods account for the ro-vibrational motion of the molecule, but this is uncritical for theimpact energy ranges considered.We have recently introduced an amended AR with orientation-dependent weight factors [9,10]. The weights are obtained from a geometrical interpretation of a molecular cross sectionas an effective area made up of overlapping atomic cross sections. The atomic cross sectionsare calculated using a first-principles-based method with ground-state density-functional-2heory (DFT) potentials [11], and the effective area encountered by the impinging projectileis computed using a pixel counting method. The latter step is repeated for a large numberof orientations so that the orientation average can be compared with experimental data forrandomly oriented molecules. We refer to this model as IAM-PCM [10].Previous applications of the IAM-PCM to proton collisions from medium-sized moleculessuch as H O and from larger compounds such as water clusters and a variety of biomoleculeshave shown promising results [9, 10, 12]. At high impact energies where the simple IAM-ARworks well, the overlap effects are small and the IAM-PCM cross sections agree with theIAM-AR results. Toward lower energies they deviate and tend to be in better agreementwith the (scarce) experimental data, i.e., our results suggest that the IAM-PCM representsan improvement compared to the IAM-AR.The purpose of the present work is to further establish the IAM-PCM as a viable toolfor net ionization and capture cross section calculations for ion-molecule collision systems.Our focus is proton impact on methane molecules (CH ) and the five DNA and RNA nucle-obases adenine (C H N ), cytosine (C H N O), guanine (C H N O), thymine (C H N O )and uracil (C H N O ), for which some experimental data and previous theoretical results,mostly obtained within the CNDO approach, are available for comparison. We also presentCNDO results based on our own first-principles atomic cross section calculations and demon-strate that they disagree with the IAM-PCM predictions in regions in which overlap effectsare strong. The discrepancies are most pronounced for electron capture at relatively lowimpact energies where the projectile speed is similar to or smaller than the average orbitalspeed of the molecular valence electrons. We call for experimental efforts to validate (orrefute) the IAM-PCM predictions for the nucleobases.The paper is organized as follows. We briefly summarize the IAM-PCM and contrastit with the CNDO approach in Sect. II. Results are presented in Sect. III. We start witha look at net ionization and capture in the proton-methane collision system to illustrate afew general trends and then discuss our results for proton collisions from the DNA/RNAnucleobases. The paper ends with a few concluding remarks in Sect. IV. Atomic units,characterized by ~ = m e = e = 4 πǫ = 1 , are used unless otherwise stated.3 I. THEORETICAL MODELS
The IAM-PCM amounts to representing a net cross section for a molecular target atprojectile energy E and for process x , where x stands for capture ( x = cap ) or ionization( x = ion ), as a weighted sum of atomic cross sections σ net x IAM − PCM ( E, α, β, γ ) = N X j =1 s xj ( E, α, β, γ ) σ net xj ( E ) (1)with weight factors ≤ s xj ≤ for the N atoms that make up the molecule, and theEuler angles α, β, γ which characterize the orientation of the molecule relative to the pro-jectile beam axis. The atomic cross sections are calculated in a DFT-inspired framework inthe semiclassical approximation with straight-line projectile trajectories [11]. The initiallyoccupied atomic orbitals (AOs) are propagated in a mean-field potential composed of a (time-dependent) Coulombic projectile potential and an atomic target ground-state potential atthe exchange-only level of DFT, i.e., correlation and time-dependent screening and exchangeeffects are neglected. The propagation is carried out using the coupled-channel two-centerbasis generator method (TC-BGM) [13] and the net cross sections for ionization and captureare obtained by summation of the corresponding orbital-specific transition probabilities andintegration over the impact-parameter plane.The weights in Eq. (1) are obtained by picturing the atomic cross sections as circulardisks around the equilibrium nuclear positions in the molecule and with radii r j ( E ) =[ σ net xj ( E ) /π ] / in a plane perpendicular to the ion beam axis. The combined area of over-lapping circles that is “visible” to the impinging projectile is interpreted as the molecularcross section and computed by a pixel counting method [10]. The procedure is carried outfor a large number of Euler angle triples to obtain an orientation-averaged cross section thatcan be compared with experimental data for randomly-oriented molecules.Keeping in mind that the atomic cross sections are composed of AO-specific contributionswe can write for the orientation average ¯ σ net x IAM − PCM ( E ) = X j ¯ s xj ( E ) X k n ao k,j σ ao xk,j ( E ) , (2)where the sum over k includes all AOs on the j th atom with nonzero occupation numbers n ao k,j and the ¯ s xj are orientation-averaged weight factors. Since the occupation numbers and4he orbital-specific cross sections are the same for each atom of a certain species, Eq. (2)can be cast into the simpler form ¯ σ net x IAM − PCM ( E ) = X i η xi ( E ) σ ao xi ( E ) , (3)where the index i enumerates the occupied AOs of different atomic species only and η xi is acoefficient that is composed of occupation numbers and orientation-averaged weight factors.In the limiting case of zero overlap in which ¯ s xj = 1 for all j and x one obtains σ net x IAM − AR ( E ) = X i n ao i σ ao xi ( E ) , (4)where n ao i is the total occupation number of the i th AO in the molecule. Note that byconstruction the IAM-AR result (4) represents an upper bound for the IAM-PCM crosssection (3).Let us compare these equations with the CNDO approach, which starts from the assump-tion that the net cross section is composed of MO-specific contributions σ net x CNDO ( E ) = X l n mo l σ mo xl ( E ) (5)with occupation numbers n mo l . In a second step the MO-specific cross sections σ mo xl areexpressed as linear combinations of AO-specific cross sections. If the latter are independentof the MOs to which they contribute the CNDO net cross section can be written as σ net x CNDO ( E ) = X i ξ i σ ao xi ( E ) , (6)where ξ i is the (fractional) gross population in the i th AO due to all initially occupiedMOs [8] and the sum includes all AOs that are (partially) populated by at least one ofthe MOs. If one restricts the population analysis to the minimal atomic basis used in theexpansion of the MOs, the index ranges in Eqs. (6), (4), and (3) are the same. Hence,the only difference between the CNDO approach, the IAM-AR and the IAM-PCM is thenature of the coefficients in these linear combinations of AO-specific cross sections. In theIAM-AR they are simply the atomic occupation numbers. In the CNDO approach theyinclude molecular structure information via the Mulliken analysis, while in the IAM-PCMthey depend on the impact energy and the process under study, because the atomic crosssection overlaps do. 5 caveat of the foregoing analysis is that in the previously reported CNDO calculationsthe AO-specific cross sections are not completely independent of the MOs to which theycontribute. In those works, the AO-specific calculations were carried out in some variant ofthe first-order Born approximation or a distorted-wave model, all of which involve the useof effective target charges in the construction of the final (continuum or bound projectile)states of interest. These effective charges were determined using molecular binding energiesin Bohr’s energy formula, thereby introducing an MO dependence into the AO-specific crosssections (see, e.g., [7, 14]). By contrast, there is no room for such a choice in the coupled-channel TC-BGM and, accordingly, our own CNDO calculations, reported here, do satisfyEq. (6). III. RESULTS AND DISCUSSION
Before we look at the DNA/RNA nucleobases let us exemplify the different theoreticalmodels discussed above for the proton-methane collision system as a test case. Table I liststhe total atomic occupation numbers and the fractional gross populations obtained from aMulliken analysis for CH [15] together with the AO binding energies [16]. Given that thegross population of the most weakly bound orbital ξ C(2 p ) = 3 . is significantly larger thanthe AO occupation number n aoC(2 p ) = 2 and ionization tends to increase with decreasing ε i ,one can expect the total net ionization cross section calculated within the CNDO approachto be larger than its IAM-AR counterpart.Figure 1 shows that this is indeed the case. However, the enhancement is relatively small(approximately 10%) and insignificant for the comparison with the experimental data and theother calculations included in the figure. At impact energies E ≥ keV all data, includingthe IAM-AR and CNDO results, are in reasonable agreement, corroborating the previousconclusion that molecular structure effects are unimportant in this region [3]. Toward lowerenergies the present IAM-AR and CNDO results overestimate the data recommended byRudd and coworkers [17], except at very low energies in the E = 10 − keV range whereionization is a relatively weak process. This implies that the atomic cross section overlaps aresmall in this region, and indeed, IAM-AR and IAM-PCM results appear to merge, similarlyto what is observed at high energies ( E > MeV).At intermediate energies the atomic cross sections are sufficiently large for overlap effects6
ABLE I. Atomic occupation numbers n ao i , gross atomic populations ξ i , and atomic bindingenergies ε i (in a.u.) for CH ( i = 1 , . . . , ) The gross populations are obtained from the informationprovided in Table III of [3] whch in turn is based on the Mulliken population analysis of [15]. Thebinding energies for atomic carbon are from the optimized effective potential calculations of [16] onwhich the present TC-BGM cross section calculations are based.H( s ) C( s ) C( s ) C( p ) n ao i ξ i ε i to be substantial. Around the maximum the IAM-PCM net ionization cross section is lessthan 60% of the IAM-AR value and in agreement with the recommended data within thereported uncertainties. A continuum distorted-wave eikonal initial-state (CDW-EIS) calcu-lation in which instead of the IAM or the CNDO approach a spherical-basis representationof the initial-state MOs was used [18] also agrees with the data, but results in somewhatlarger cross section values than the IAM-PCM and shows a different energy dependence withthe maximum shifted toward higher energies. The latter might at least in part be due tothe limited validity of the perturbative CDW-EIS model at impact energies E < keVwhere electron capture gains importance as a competing reaction channel.We have also included (absolute) electron impact measurements from [19] in Fig. 1 usingequivelocity conversion. These measurements agree very well with the recommended datafor proton impact above E = 500 keV, i.e., at projectile speeds v ≥ . a.u. or charge-magnitude-to-speed ratios η = 1 /v ≤ . a.u. One can infer from this agreement thatfirst-order perturbation theory in which cross sections do not depend on the sign of theprojectile charge is valid in this region. Toward lower energies, higher-order contributionsbecome important, as do projectile mass and, for electron projectiles, exchange effects, allof which contribute to the differences in the electron- vs. proton-impact cross sections.It is interesting to see how the CDW-EIS-MO calculation of Ref. [18] appears to be ableto capture the higher-order contributions quite well and agrees with the (proton-impact)measurements down to energies which correspond to η -values between 0.5 and 0.6.Figure 2 shows results for net capture using both double- and single-logarithmic scales to7 + CH IAM-PCMIAM-ARCNDOCDW-EIS-MORudd85Rapp65
FIG. 1. Total cross section for net ionization in p-CH collisions as a function of impact energy. IAM-PCM, IAM-AR, and CNDO: present calculations, CDW-EIS-MO [18]; experiments: Rudd85 [17],Rapp65 [19] for electron impact using equivelocity conversion. emphasize different impact energy regions. The present IAM-AR and CNDO calculationsyield very similar results at all energies and agree nicely with the experimental data at E ≥ keV. The close proximity of both calculations indicates that, unlike ionization,capture does not simply increase with decreasing binding energy and more than one initiallyoccupied AO may contribute significantly. The details of the calculations show that at lowimpact energies the resonant capture from H( s ) dominates, while capture from the carbonAOs gains relative importance toward higher energies. The differences in the orbital-specificcross sections and those between the gross populations and occupation numbers listed inTable I balance out and result in very similar IAM-AR and CNDO cross sections.Figure 2 also includes two previous CNDO calculations; the calculation by Quinto and co-workers [7] uses the CDW-EIS model and the one by Purkait et al. [20] a different distorted-wave (DW) approach to calculate the AO-specific cross section contributions. Both worksyield somewhat smaller cross section values than the present CNDO calculation, but show8 + CH IAM-PCMIAM-ARCNDOCDW-EIS-CNDODW-CNDORudd83Toburen68Sanders03
FIG. 2. Total cross section for net capture in p-CH collisions as a function of impact energy.IAM-PCM, IAM-AR, and CNDO: present calculations, CDW-EIS-CNDO [7], DW-CNDO [20];experiments: Rudd83 [21], Toburen68 [22], Sanders03: [23]. a similar impact energy dependence, at least down to E = 50 keV where the CDW-EIScalculation terminates. The cross-section curve from [20] extends further down to E = 25 keV and indicates an even stronger increase toward low energies than the present CNDOcalculation, which significantly overestimates the measurements in this region. We note thatPurkait et al. also reported IAM-AR calculations in their work which for p-CH collisionsare in close agreement with their CNDO results. Similarly, an earlier publication of the Ar-gentinian group reported very similar CDW-EIS IAM-AR and CNDO capture cross sectionsfor a number of molecules, including CH [14], confirming our present finding regarding thecomparison of both descriptions. This suggests that the choice of molecular binding ener-gies in the construction of the final states in the perturbative models has but a very smallinfluence on the magnitude of the total capture cross section.The present IAM-PCM results agree with the IAM-AR and CNDO calculations at highenergies. They begin to deviate from the latter at E ≈ keV and follow the experimental9ata closely down to E = 10 keV where the IAM-AR capture cross section is more thantwice as large. This is similar to what was found for other collision systems such as p-COand p-H O [9] and gives us confidence in the validity of the IAM-PCM. The key to its successfrom low- to high-velocity collisions is the impact-energy dependence of the weight factorsin Eq. (3). By contrast, the applicability of methods with energy- independent weights suchas the IAM-AR and the CNDO approach appears to be more limited.We now turn to the DNA/RNA nucleobases adenine, cytosine, guanine, thymine, anduracil. Since the observations and conclusions are very similar for all five targets, we restrictthe graphical discussion and comparison with previous results to the proton-adenine collisionsystem and provide our IAM-PCM results for the other target molecules in tabular formonly. The molecular geometry information required for these calculations is taken from dataavailable through the Molview project [24].Experimental data for proton impact are rather scarce. For this reason, we includethe recent electron-impact ionization measurements of Ref. [25] in the discussion. We donot compare the present results with the (proton-impact) cross sections obtained from aprevious model calculation which combines the classical-trajectory Monte Carlo (CTMC)method with the classical over barrier model (COB) [26] to avoid overburdening the figures.The reader is referred to Refs. [6, 27] for comparisons of the CTMC-COB results withperturbative CNDO calculations and the measurements for proton impact.Figure 3 shows the net ionization cross section for adenine target molecules. We notethat this cross section was measured by Tabet et al. at E = 80 keV [28], but the data pointis so high (at 155 Å ) that it is outside the scale of the figure. The only other measurementsfor proton impact were reported by Iriki et al. [29, 30]. Their data are included in Fig. 3and appear to be somewhat lower than the electron-impact measurements of [25]. If wemultiply the latter by a factor of 0.75 they almost perfectly match the proton data pointat E = 1 MeV, which is well described by most of the theoretical calculations included inthe figure. Toward lower E , the renormalized electron-impact data agree very well with thepresent IAM-PCM calculations in the energy range in which one would expect the proton-and electron-impact ionization cross section to be indistinguishable or very nearly so.By contrast, all other calculations predict a larger cross section below E ≈ MeV. Simi-larly to the proton-methane case the present IAM-AR results are slightly below the CNDOand overestimate the IAM-PCM cross section values significantly (by more than a factor of10 +adenine C H N IAM-PCMIAM-ARCNDOCB1-CNDOCDW-EIS-CNDOIMM-ARIriki11Rahman16Rahman75%
FIG. 3. Total cross section for net ionization in p-adenine (C H N ) collisions as a function ofimpact energy. IAM-PCM, IAM-AR, and CNDO: present calculations, CB1-CNDO and CDW-EIS-CNDO [27], IMM-AR [31]; experiments: Iriki11 [29, 30], Rahman16 [25] for electron impact usingequivelocity conversion, Rahman75% are the data of [25] multiplied by 0.75. two around the maximum). Some indirect confirmation that the overlaps incorporated intothe IAM-PCM mimic molecular effects appropriately comes from the independent-molecule-model (IMM) AR results included in Fig. 3. In this model, experimental cross sections forsmall molecules are used to assemble the cross section for the larger molecule of interest [31].The results for adenine lie in between the IAM-PCM and IAM-AR cross sections suggestingthat one can view the IMM-AR as capturing overlap effects partially, i.e., within the smallmolecules used to assemble the adenine ionization cross section, while overlaps between thosesmall-molecule cross sections are not accounted for.The present CNDO calculations are based on the Mulliken populations provided inRef. [27], which were also used for the CDW-EIS and the first-Born with corrected boundaryconditions (CB1) calculations reported in the same paper and included in Fig. 3. The twoperturbative calculations are in reasonable agreement with each other down to E ≈ keV11here the CDW-EIS cross section assumes its maximum, while the CB1 cross section keepsincreasing toward lower energies. Both methods predict significantly smaller cross sectionvalues than the present CNDO calculations in most of the impact energy interval shown inFig. 3. This may be due to (i) the perturbative frameworks used in the CDW-EIS and CB1methods vs. the nonperturbative nature of the TC-BGM, (ii) the fact that in the perturba-tive CNDO calculations the AO-specific cross sections include some molecular informationthrough the choice of the final states, while the present calculations do not. Given the anal-ysis of net capture in p-CH collisions presented above the latter is unlikely, but it wouldbe interesting to see a CDW-EIS or CB1 calculation which uses atomic instead of molecularenergies for the determination of the final (continuum) states to settle this issue.Results for net capture are shown in Fig. 4. We compare the present CNDO, IAM-ARand IAM-PCM data with the CDW and CDW-EIS CNDO calculations of Ref. [6] and theonly reported experimental data point at E = 80 keV [28]. The CDW-EIS model produceslower cross section values than the present CNDO calculation at all impact energies exceptaround E = 10 keV which is probably outside the region of validity of the perturbativemodel. By contrast, the CDW model, which differs from the CDW-EIS in the choice of thedistortion factor in the initial state, results in much larger cross section values which mergewith the other theoretical results only at energies E ≥ keV.As for p-CH collisions, the IAM-AR is in good agreement with the present CNDOresults over most of the energy range shown. Only below E ≈ keV do the results of bothmodels deviate somewhat more strongly than for methane. This is not surprising given thelarger number of contributing electron subshells in adenine, which makes it less likely thatthe differences in orbital-specific capture cross sections and gross populations vs. atomicoccupation numbers balance out.The experimental data point of [28] at E = 80 keV is higher than all theoretical resultsincluded in Fig. 4. The discrepancy with the CDW CNDO calculation is perhaps acceptable,but this may be fortuitous given that the CDW model is sometimes considered inferior to theCDW-EIS because of its use of non-normalized initial-state wave functions [32]. The authorsof Ref. [6] deemed the seemingly good performance of the CDW model “unexpected” andconcluded that new measurements would be welcome. The present calculations reinforce thelatter point. In particular, it would be of great interest if new measurements were extendedto lower impact energies where the IAM-PCM predicts a much smaller capture cross section12 +adenine C H N IAM-PCMIAM-ARCNDOCDW-EIS-CNDOCDW-CNDOTabet 10
FIG. 4. Total cross section for net capture in p-adenine (C H N ) collisions as a function of im-pact energy. IAM-PCM, IAM-AR, and CNDO: present calculations, CDW-EIS-CNDO and CDW-CNDO [6]; experiment: Tabet10 [28]. than all other theoretical models. Given the good agreement of the IAM-PCM net capturewith experimental data for smaller molecules such as CH (cf. Fig. 2) it would be surprisingif the prediction for proton-adenine collisions would be off.We have checked that the situation is similar for the other DNA/RNA nucleobases. Infact, all the features seen in Figs. 3 and 4 for adenine are also present for cytosine, guanine,thymine and uracil. This can be explained by the similar atomic building blocks and struc-tures of these molecules. In lieu of figures we provide tables with the present IAM-PCMresults: Table II lists the net capture and ionization cross sections for the pyrimidines cyto-sine, thymine, and uracil and Table III the results for the purines adenine and guanine. Wenote that the ionization cross sections were previously included in tables presented in [12],in which scaling properties were studied for larger classes of systems. We repeat these datahere for the convenience of the reader. 13 ABLE II. Orientation-averaged IAM-PCM net capture and ionization cross sections for protoncollisions with the pyrimidines cytosine, thymine, and uracil (in Å ).Cytosine (C H N O) Thymine (C H N O ) Uracil (C H N O )E [keV] Capture Ionization Capture Ionization Capture Ionization10 37.71 9.34 41.03 10.62 35.80 8.9220 29.32 15.42 32.28 17.41 27.74 14.8350 15.95 19.44 18.00 21.93 15.44 18.90100 4.99 18.75 5.58 21.17 4.94 18.23200 0.61 15.49 0.69 17.63 0.65 15.13500 0.029 10.28 0.031 11.72 0.028 9.991000 0.0026 6.46 0.0029 7.35 0.0026 6.212000 3.76 4.26 3.655000 1.80 2.03 1.7610000 1.02 1.14 0.98 IV. CONCLUSIONS
We have presented IAM-PCM calculations for proton collisions from methane moleculesand the nucleobases adenine, cytosine, guanine, thymine, and uracil over wide ranges ofimpact energy from E = 10 keV to E = 1 MeV for net capture and up to E = 10 MeV fornet ionization. Like the simpler IAM-AR and the widely-used CNDO approach the IAM-PCM is based on atomic cross-section calculations, but in contrast to the former it weighs theatomic contributions in an impact-energy-dependent way. The weight factors are obtainedfrom the geometrical overlaps which arise when one pictures the atomic cross sections ascircular disks in the impact-parameter plane. The overlaps can be substantial thereby leadingto a significant reduction of IAM-PCM compared to IAM-AR cross sections. This effect ismost pronounced for electron capture at low energies where we found discrepancies betweenIAM-PCM and IAM-AR cross sections of up to a factor of three to four. We have shownthese discrepancies for proton-adenine collisions only, but have checked that they are similarfor the other nucleobases. New measurements are required to test these predictions.In the case of ionization the discrepancies between different theoretical models are less14
ABLE III. Orientation-averaged IAM-PCM net capture and ionization cross sections for protoncollisions with the purines adenine and guanine (in Å ).Adenine (C H N ) Guanine (C H N O)E [keV] Capture Ionization Capture Ionization10 43.59 11.32 45.12 12.0420 34.12 18.53 35.58 19.7050 19.04 22.96 20.50 24.52100 5.98 22.17 6.79 23.68200 0.69 18.41 0.82 19.91500 0.032 12.40 0.036 13.331000 0.0033 7.86 0.0036 8.472000 4.58 4.965000 2.18 2.3910000 1.23 1.33 dramatic, but they are sizable, especially around the cross section maximum. Again, thesetrends are similar for all nucleobases and an experimental study that would test this sim-ilarity in a systematic way would be of great interest. As for capture, the only existingexperimental data points in this region appear to be too high.In contrast to the IAM-PCM, the CNDO approach, when coupled with the present (non-perturbative) atomic-orbital-specific cross section calculations, does not lead to significantdifferences to the simple IAM-AR. Previous (perturbative) work provided some evidencethat the differences between both models become more pronounced when differential crosssections are calculated [3]. In the context of the present analysis it would be interestingto know if the deviations in the differential cross-section results are related to the use ofmolecular instead of atomic binding energies in the determination of the final continuumstates in the perturbative CNDO calculations. On the level of total cross sections this choiceappears to be of minor importance.Our own future work will focus on IAM-PCM studies of collisions involving multiply-charged ions. Preliminary calculations show, not surprisingly, that the overlap effect isstronger and IAM-PCM total cross sections merge with IAM-AR results at higher impact15nergies than for proton impact. The role of multi-electron processes will be enhanced aswell. These processes require an extension of the model to allow for the calculation of impact-parameter-dependent probabilities which can be fed into a multinomial analysis of multiplecapture and ionization processes. Work in this direction is in progress.
ACKNOWLEDGMENTS
This work was supported by the Natural Sciences and Engineering Research Councilof Canada (NSERC). One of us (H. J. L.) would like to thank the Center for ScientificComputing, University of Frankfurt for making their High Performance Computing facilitiesavailable. [1] W. H. Bragg and R. Kleeman, Phil. Mag. , 318 (1905).[2] J. W. Otvos and D. P. Stevenson, J. Am. Chem. Soc. , 546 (1956).[3] M. E. Galassi, R. D. Rivarola, M. Beuve, G. H. Olivera, and P. D. Fainstein,Phys. Rev. A , 022701 (2000).[4] F. Blanco and G. García, Phys. Lett. A , 458 (2003).[5] H. Deutsch, K. Becker, S. Matt, and T. D. Märk, Int. J. Mass Spectrom. , 37 (2000).[6] C. Champion, P. F. Weck, H. Lekadir, M. E. Galassi, O. A. Fojón, P. Abufager, R. D. Rivarola,and J. Hanssen, Phys. Med. Biol. , 3039 (2012).[7] M. A. Quinto, P. R. Montenegro, J. M. Monti, O. A. Fojón, and R. D. Rivarola,J. Phys. B , 165201 (2018).[8] R. S. Mulliken, J. Chem. Phys. , 1833 (1955).[9] H. J. Lüdde, A. Achenbach, T. Kalkbrenner, H.-C. Jankowiak, and T. Kirchner,Eur. Phys. J. D , 82 (2016).[10] H. J. Lüdde, M. Horbatsch, and T. Kirchner, Eur. Phys. J. B , 99 (2018).[11] T. Kirchner, L. Gulyás, H. J. Lüdde, E. Engel, and R. M. Dreizler,Phys. Rev. A , 2063 (1998).[12] H. J. Lüdde, M. Horbatsch, and T. Kirchner, (2019), submitted to J. Phys. B.,arXiv:1905.02273 [physics.atm-clus].
13] M. Zapukhlyak, T. Kirchner, H. J. Lüdde, S. Knoop, R. Morgenstern, and R. Hoekstra,J. Phys. B , 2353 (2005).[14] M. E. Galassi, P. N. Abufager, P. D. Fainstein, and R. D. Rivarola,Phys. Rev. A , 062713 (2010).[15] R. Hoffmann, J. Chem. Phys. , 1397 (1963).[16] K. Aashamer, T. M. Luke, and J. D. Talman, At. Data Nucl. Data Tables , 443 (1978).[17] M. E. Rudd, Y. K. Kim, D. H. Madison, and J. W. Gallagher, Rev. Mod. Phys. , 965 (1985).[18] L. Gulyás, I. Tóth, and L. Nagy, J. Phys. B , 075201 (2013).[19] D. Rapp and P. Englander-Golden, J. Chem. Phys. , 1464 (1965).[20] K. Purkait, S. Samaddar, S. Halder, C. R. Mandal, and M. Purkait,Braz. J. Phys. , 473 (2019).[21] M. E. Rudd, R. D. DuBois, L. H. Toburen, C. A. Ratcliffe, and T. V. Goffe,Phys. Rev. A , 3244 (1983).[22] L. H. Toburen, M. Y. Nakai, and R. A. Langley, Phys. Rev. , 114 (1968).[23] J. M. Sanders, S. L. Varghese, C. H. Fleming, and G. A. Soosai, J. Phys. B , 3835 (2003).[24] MolView: http://molview.org [Online; accessed 2019-13-07].[25] M. A. Rahman and E. Krishnakumar, J. Chem. Phys. , 161102 (2016).[26] H. Lekadir, I. Abbas, C. Champion, O. Fojón, R. D. Rivarola, and J. Hanssen,Phys. Rev. A , 062710 (2009).[27] M. E. Galassi, C. Champion, P. F. Weck, R. D. Rivarola, O. A. Fojón, and J. Hanssen,Phys. Med. Biol. , 2081 (2012).[28] J. Tabet, S. Eden, S. Feil, H. Abdoul-Carime, B. Farizon, M. Farizon, S. Ouaskit, and T. D.Märk, Phys. Rev. A , 022703 (2010).[29] Y. Iriki, Kikuchi Y., M. Imai, and Itoh A., Phys. Rev. A , 032704 (2011).[30] Y. Iriki, Kikuchi Y., M. Imai, and Itoh A., Phys. Rev. A , 052719 (2011).[31] S. Paredes, C. Illescas, and L. Méndez, Eur. Phys. J. D , 178 (2015).[32] L. Gulyás, A. Igarashi, and T. Kirchner, J. Phys. B , 085205 (2012)., 085205 (2012).