Eur. Phys. J. D (2014) 68: 161DOI: 10.1140/epjd/e2014-40820-5

Regular Article

THE EUROPEANPHYSICAL JOURNAL D

Differential and integral electron scattering cross sectionsfrom tetrahydrofuran (THF) over a wide energy range:1–10 000 eV�,��

Martina C. Fuss1, Ana G. Sanz2, Francisco Blanco2, Paulo Limao-Vieira3,Michael J. Brunger4,5, and Gustavo Garcıa1,6,a

1 Instituto de Fısica Fundamental, Consejo Superior de Investigaciones Cientıficas, Serrano 113-bis, 28006 Madrid, Spain2 Departamento de Fısica Atomica Molecular y Nuclear, Universidad Complutense de Madrid, Ciudad Universitaria,

28040 Madrid, Spain3 Laboratorio de Colisoes Atomicas e Moleculares, CEFITEC, Departamento de Fısica, Faculdade de Ciencias e Tecnologia,

Universidade Nova de Lisboa, 2829-516 Caparica, Portugal4 ARC Centre for Antimatter-Matter Studies, School of Chemical and Physical Sciences, Flinders University, G.P.O. Box 2100,

Adelaide, South Australia 5001, Australia5 Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia6 Centre for Medical Radiation Physics, University of Wollongong, NSW2522, Australia

Received 21 December 2013 / Received in final form 3 March 2014Published online 27 June 2014 – c© EDP Sciences, Societa Italiana di Fisica, Springer-Verlag 2014

Abstract. Total, integral inelastic and integral and differential elastic cross sections have been calculatedwith the screening-corrected additivity rule (SCAR) method based on the independent atom model (IAM)for electron scattering from tetrahydrofuran (THF). Since the permanent dipole moment of THF enhancesrotational excitation particularly at low energies and for small angles, an estimate of the rotational ex-citation cross section was also computed by assuming the interaction with a free electric dipole as anindependent, additional process. Our theoretical results compare very favourably to the existing experi-mental data. Finally, a self-consistent set of integral and differential interaction CSs for the incident energyrange 1 eV–10 keV is established for use in our low energy particle track simulation (LEPTS). All crosssection data are supplied numerically in tabulated form.

1 Introduction

Since pioneering studies of Sanche and coworkers in2000–2003 [1–3] showed how low energy electrons may in-duce structural alterations in biomolecular systems, thenumber of theoretical and experimental publications de-voted to obtain electron scattering cross section data forDNA and RNA components, as well as for other biologi-cally relevant targets, has significantly increased. In par-ticular, recent experiments are evaluating the indirectlyinduced damage by secondary electrons in complex bio-logical targets [4]. From the experimental point of view,these targets are not easy to measure as they are com-monly solids at room temperature requiring to use ovens

� Contribution to the Topical Issue “Nano-scale Insights intoIon-beam Cancer Therapy”, edited by Andrey V. Solov’yov,Nigel Mason, Paulo Limao-Vieira, Malgorzata Smialek-Telega.�� Supplementary material in the form of four “.xlsx” filesavailable from the Journal web page athttp://dx.doi.org/10.1140/epjd/e2014-40820-5

a e-mail: g.garcia@iff.csic.es

with restricted temperature operation ranges (to avoidthe thermal dissociation of the target) in order to pro-duce an appropriate molecular beam. In addition, most ofthem are polar molecules, implying high probabilities toinduce molecular rotations associated to low angle elec-tron scattering processes which are almost impossible tobe detected with the standard energy and angular res-olution used in electron scattering experiments [5]. Thepermanent dipole moment also causes complications intheoretical studies. In fact, the most common “ab initio”methods used for electron-molecule scattering calculations(R-matrix methods [6], Single Centre Expansion proce-dures [7], and Schwinger Multichannel Methods [8]) re-quire an additional approximate treatment to fully ac-count for rotational excitations. An important limitationfor these calculation methods comes from the increas-ing complexity of the biomolecular targets, restrictingtheir applicability to low energy ranges, where the num-ber of inelastic channels is low enough to ensure accept-able uncertainties of the numerical results. For these rea-sons, both theoreticians and experimentalists have been

Page 2 of 8 Eur. Phys. J. D (2014) 68: 161

looking for prototype targets to benchmark electron scat-tering cross sections. One of these benchmark moleculesis tetrahydrofuran (THF, C4H8O), whose molecular struc-ture is similar to the ribose in the DNA backbone. THFis a liquid at room temperature with high vapour pres-sure, so it is easy to determine its density during theexperiments. It presents a permanent dipole moment of1.63 D, high enough to allow the calculation of rotationalexcitation cross sections and to check their influence inmeasurements.

Concerning experimental data, total electron scatter-ing cross sections (TCS) of THF were measured by Zeccaet al. [9] and Mozejko et al. [10] by using two differentconfigurations of transmission beam experiments. Later,measurements with similar techniques were performed byFuss et al. [11] and Baek et al. [12]. Experimental ion-isation cross sections can be found in references [11,13],generally derived by analyzing the ion fragmentation in-duced by electron impact and using different normaliza-tion procedures to put data on an absolute scale. Dif-ferential electron scattering cross sections were obtainedthrough angular resolved crossed beam experiments bydifferent groups [14–19]. Again, they are relative mea-surements and require some normalization procedure togive absolute values. Electronic and vibrational excitationcross sections were derived from angular resolved energyloss spectra in combination with normalization proceduresby references [20] and [16].

As for theoretical data, low energy electron (below20 eV) elastic scattering, including resonance analysis,were calculated by Bouchiha et al. [21] using the R-matrixprocedure. This method accounts for some rotational ex-citation channels but it requires an additional correction,based on the Born approximation, to include transitionsnot considered by the ab initio procedure. Furthermore,differential elastic and momentum transfer cross sectionscan be found in references [19,22] calculated with aSchwinger method and in reference [23] by using the Kohnmethod. For intermediate and high energies different opti-cal potential methods have been applied [12,18,24] to de-rive elastic and inelastic cross section data. In particular,ionisation cross sections calculated by employing differentBorn-based methods can be also found in [24,25].

In this study, we use our latest formulation of the in-dependent atom representation-based screening correctedadditivity rule (IAM-SCAR) method in combination withan approximate differential and integral rotational exci-tation cross section calculation based on the Born ap-proximation. Preliminary total electron scattering crosssections by THF calculated with this technique were al-ready published [26,27] to complement a positron scatter-ing study and as tentative input data for electron trackmodelling, respectively. Some details of the present cal-culation procedure are given in Section 2. The presentresults are compared to available experimental and theo-retical data in Section 3 and the complete set of differentialand integral cross sections calculated for energies rangingfrom 1 to 10 000 eV are made available in Tables S1–S3∗∗.The consistency of the available electron scattering cross

section values for THF is discussed in Section 4 before weselect a set of input parameters (including integral elasticand partial inelastic cross sections and elastic differentialcross sections) covering the energy range 1 eV–10 keV tobe used in our LEPTS (Low Energy Particle Track Simu-lation) code. Finally, we draw some conclusions from thepresent study.

2 Calculation procedure

The present calculation method permits to study theinteraction of intermediate and high energy electronswith molecules. It is based on a corrected form ofthe Independent-atom model (IAM) known as SCAR(screening-corrected additivity rule). Details of thismethod have been presented in previous works [28–32],therefore only a brief description is given here.

Initially, this approximation does not consider themolecule as a single target but as an aggregate of atomswhich scatter independently, assuming that molecularbinding does not affect the electronic distribution of theatoms. The first subjects of these calculations are there-fore the constituent atoms, namely C, H and O. Eachatomic target is represented by an interacting complex(optical) potential, Vopt(r), whose real part accounts forthe elastic scattering of the incident electrons while theimaginary part represents the inelastic processes that areconsidered as “absorption” from the incident beam. Thisoptical potential can be expressed as:

Vopt(r) = Vs(r) + Vex(r) + Vpol(r) + iVabs(r), (1)

where Vs(r) is the static term derived from the Hartree-Fock calculation of the atomic charge density [33]. Vex(r) isthe exchange term which accounts for the indistinguisha-bility between the incident and target electrons. The ex-pression chosen for this term is the semiclassical energy-dependent formula derived by Riley and Truhlar [34].Vpol(r) is the polarization term which describes the long-range interactions and depends on the target dipole po-larizibility, in the form given by Zhang et al. [35]. Fi-nally, the absorption potential Vabs(r), which accounts forthe inelastic processes, is based on Staszewska’s quasifreemodel [36]. Initially some divergences were found whenresults were compared to the available atomic scatteringdata. After including some improvements such as many-body and relativistic corrections, screening effects insidethe atom, local velocity correction and in the descriptionof the electrons’ indistinguishability, the model proves toprovide a good approximation for electron-atom scatter-ing [30,31] over a broad energy range. An excellent exam-ple of this was our calculation of elastic electron-atomic io-dine (I) scattering [37], where the optical potential resultscompared very favourably with those from a sophisticatedDirac-B-spline R-matrix computation.

Within this model we also numerically integrate theradial scattering equation, from where we obtain the com-plex partial wave phase shifts δl. Using these phase shifts,in combination with the optical theorem, we can generate

Eur. Phys. J. D (2014) 68: 161 Page 3 of 8

the atomic scattering amplitudes (f(θ)), which providedifferential (dσel/dΩ) and integral (σel) elastic cross sec-tions, as well as the total (σtot) scattering cross sections asa function of the scattering angle (θ) and the momentumof the incident electrons (k):

f(θ) =1

2ik

lmax∑

l=0

(2l + 1)(e2iδl + 1

)Pl(cos θ),

dσel

dΩ= |f(θ)|2 (2)

σel =∫

dσel

dΩdΩ, σtot =

4π

k2Imf(θ = 0), (3)

where Pl are the Legendre polynomials.In order to obtain molecular cross sections, the IAM

has been followed by applying a coherent addition pro-cedure, commonly known as the additivity rule (AR). Inthis approach, the molecular scattering amplitude (F (θ))is derived from the sum of the above atomic amplitudes,which lead to the differential elastic cross section for themolecule (dσmolecule/dΩ), according to:

F (θ) =∑

atoms

fi(θ)eiq.ri ,

dσmoleculeel

dΩ=

∑

i,j

fi (θ) f∗j (θ)

sin qrij

qrij, (4)

where q is the momentum transferred in the scatteringprocess and rij is the distance between atoms i and j.

Integral elastic cross sections for the molecule can bedetermined by integrating equation (4). Alternatively elas-tic cross sections can be derived from the atomic scatteringamplitudes in conjunction with the optical theorem [30]giving

σmoleculeel =

∑

atoms

σatomel . (5)

Unfortunately, in its original form, we found an inher-ent contradiction between the integral cross section de-rived from those two approaches, which suggested thatthe optical theorem was being violated [38].

The main limitation of the AR is that no molecularstructure is considered, thus it should only be appliedwhen the incident electrons are fast enough to effectively“see” the target molecule as a sum of the individual atoms(typically above ∼100 eV). To reduce this limitation wedeveloped the SCAR method [31,32] which considers thegeometry of the corresponding molecule (atomic positionsand bond lengths) by introducing some screening coeffi-cients which modify both differential and integral crosssections, especially for low incident energies [31,32]. Withthis correction the range of validity of the IAM-SCARmethod can be extended down to about 30 eV. For in-termediate and high energies (30−5000 eV) this methodhas been proven to be a powerful tool for calculatingelectron scattering cross sections from a large variety ofmolecules of very different sizes, from diatomic ones tocomplex biomolecules [39].

From the above description of the IAM-SCAR proce-dure it is obvious that vibrational and rotational excita-tions are not considered in this calculation. However, forpolar molecules such as THF, additional dipole-inducedexcitation cross sections can be calculated following theprocedure suggested by Jain [40]. Basically it calculatesdifferential and integral rotational excitation cross sec-tions for a free electric dipole in the framework of thefirst Born approximation (FBA) which can be incorpo-rated into our IAM-SCAR calculation in an incoherentway, simply adding the results as an independent chan-nel. Although rotational excitation energies are, in gen-eral, very low (typically a few meV) in comparison withthe incident electron energies, in order to validate the Bornapproximation the latter energies should be higher thanabout 20 eV. Under these circumstances, rotational exci-tation cross sections J → J ′ were calculated by weightingthe population for the Jth rotational quantum number at300 K and estimating the average excitation energy fromthe corresponding rotational constants. For THF the aver-age excitation energy resulted 1.20 meV. We can call thewhole procedure the IAM-SCAR + Rotations method andit has been successfully applied to other polar moleculessuch as H2O [41] and HCN [42].

Note that the integral and differential IAM-SCAR re-sults derived by the present calculational approach arecompletely self-consistent. In particular, the normalizationof interference terms [35] ensures that the elastic and rota-tional excitation differential CS, when integrated over thecomplete angular range 0–180◦, give exactly the integralCS for elastic and rotationally inelastic scattering, respec-tively. Similarly, the total CS is obtained as the exact sumof all integral CS (elastic, rotationally inelastic, and elec-tronically inelasic), making it an accurate prediction ofthe molecular scattering cross section for the totality ofprocesses included.

3 Results and discussion

A complete set of differential and integral cross sectionsfor electron scattering by THF for collision energies from 1to 10 000 eV, calculated in this study, is available in nu-merical form in Tables S1–S3∗∗. In order to compare thepresent results with previous theoretical and experimentaldata, some selected processes and energies receive specialattention in this section. Differential electron elastic scat-tering plus rotational excitation cross sections are plot-ted in Figure 1 for 10, 20, 30, 50, 100 and 1000 eV inci-dent energies. Note that we added the differential elasticand the differential rotational cross sections in order toget a quantity directly comparable to experimental data.Certainly, as the rotational excitation energy is not re-solved by any of the experimental systems used to ob-tain those measurements, what they collect for a givenscattering angle is the sum of these two scattering pro-cesses which is identified as the observed elastic intensityin that direction. As can be seen in this figure, our IAM-SCAR +Rotations calculation does not reproduce well the

Page 4 of 8 Eur. Phys. J. D (2014) 68: 161

0m

2 /sr)

c�on

(10-

20alcrossse

Differen�

Sca�ering angle (deg)Fig. 1. Comparison of the present elastic plus rotational excitation differential cross sections to previous experimental andtheoretical results at different incident energies. Thick solid line (red), present IAM-SCARD calculation; dashed blue line,uncorrected SMC elastic CS from Gauf et al. [19]; dash-dotted purple line, Born-corrected SMC elastic CS from Gauf et al. [19];dash-double-dotted green line, Trevisan et al. [23]; black bullets, Allan [16]; black open circles, Dampc et al. [17]; black crosses,Colyer et al. [15]; black open diamonds, experiment of Gauf et al. [19].; black full triangles, Milosavljevic et al. [14]; blackupwards-pointing open triangles (20 and 30 eV), Baek et al. [12]; thin solid line (orange), theory in Homem et al. [18]; blackdownwards-pointing open triangles (50–1000 eV), experiment in Homem et al. [18].

experimental data at 10 eV for intermediate angles (45–90◦). As expected, our calculation fails, in general, for in-cident energies below typically 20 eV. However, calcula-tions using the SMC method [19,22] and the Kohn varia-tional method [23] show a generally good agreement withthe experimental data. For increasing energies, the situ-ation changes substantially. Our calculation for energiesabove 20 eV shows excellent agreement with available ex-perimental data whereas low energy calculation methodstend to overestimate the cross sections for large anglesabove 20 eV in the case of [23] and above 30 eV for refer-ences [19,22]. Above 100 eV, recent model potential cal-culations assuming an independent atom representationcan be found in [12,18]. To illustrate these results, calcu-lations of Homem et al. [18] are also plotted in Figure 1.As this figure shows, for 100 eV some discrepancies be-tween the present calculation and the experimental datastill remain but as the energy increases the IAM modelbecomes a good representation of the electron-moleculescattering process reaching an excellent agreement withthe experimental data at 1000 eV.

Present integral electron scattering cross section dataare shown in Figure 2 together with available experimentalvalues and with the theoretical R-matrix results ofBouchicha et al. [21] and the SMC results reportedin [19,22]. As far as integral cross sections are concerned,we can only consider the total scattering cross sectionsand the ionisation cross sections as purely experimentaldata. Total cross sections are relevant parameters as theyrepresent the sum of the cross sections of all the possi-ble scattering processes at a given energy, like they arederived from the calculations. However, from the experi-mental point of view total cross sections can be directlydetermined by measuring the attenuation of the incidentelectron beam after the interaction with a molecular tar-get whose density is well known. As shown in Figure 2,there is an excellent agreement between all available to-tal cross section measurements and the present calcula-tion for energies above 10 eV. This confirms our predic-tions, based on previous calculations, which establishedthat the IAM-SCAR procedure is reliable, within 10%,for incident energies above 20–30 eV. Below 10 eV our

Eur. Phys. J. D (2014) 68: 161 Page 5 of 8

Fig. 2. Comparison of the present IAM-SCAR+Rotationscalculation results to experimental and theoretical data avail-able from different groups. Black solid line, TCS; red solid line,integral elastic cross section; blue line, electronically inelasticCS; green line, rotational excitation CS; gray open diamonds,experimental TCS obtained by Mozejko et al. [10]; black opentriangles, experimental TCS from Baek et al. [12]; black full tri-angles, experimental TCS from Fuss et al. [11]; purple dashedline, BEB calculation [24]; black full circles, ionisation CS [11];red full diamonds, elastic CS [18]; red full squares, elasticCS [12]; black dashed line, dipole-corrected model B theoryof Bouchiha et al. [21]; red dashed line, uncorrected model Btheory [21]; black dash-dotted line, Born-dipole-corrected SMCelastic CS [19]; red dash-dotted line, uncorrected SMC elasticCS [19].

IAM-SCAR + Rotations calculation tends to overestimatethe experimental data from Mozejko et al. [10] reachinga factor three deviation at 1 eV. We can expect this ten-dency of our calculation at low energy due to the failureof the IAM-SCAR approach but this large discrepancycan be only explained if any experimental systematic er-ror additionally affects the measurements. Note that theangular acceptance of the scattering apparatus, <2 de-grees in this case [43], limits the ability of the exper-imental system to distinguish between unscattered andelastically or rotationally scattered electrons within theacceptance angle of the apparatus. This limitation leadsto an underestimation of the measured total cross section,especially due to the dipole-induced rotational excitationswhich preferentially scatter the electrons in the forwarddirection. Note also that the average rotational excitationenergy of THF is 1.20 meV at room temperature, muchlower than the experimental energy resolution (80 meV).To quantify this effect, we have introduced in the com-parison the R-matrix calculation carried out by Bouchihaet al. [21] for low energy (0–10 eV) electrons includingelastic collisions and elastic plus rotationally inelastic scat-tering, labelled by them as Model B and dipole-correctedmodel B (see Ref. [21] for details), as well as the Born-

dipole-corrected and uncorrected SMC elastic CS [19]. Asshown in Figure 2, the dipole-corrected (elastic plus rota-tional excitations) calculation from [21] agrees very wellwith our IAM-SCAR + Rotations data at 10 eV. Below10 eV, as expected, our calculation gives higher resultsreaching a maximum discrepancy of about 60% at 1 eV.Compared to the experimental data this low energy calcu-lation gives still 70% higher results than those measuredin [10] at 1 eV. However, data given in [21] without dipolecorrection, which are essentially integral elastic cross sec-tions, agree very well with the experimental data belowthe electronic excitation threshold, i.e. below 6 eV [44].This proves that experimental TCSs are somewhat under-estimated for incident energies below 10 eV (about 70%at 1 eV). A very similar behaviour can be observed inFigure 2 for the corresponding SMC results including andexcluding the Born-dipole correction [19]. Regarding theelectronically inelastic CS, good agreement is observed be-tween our calculated values and the sum of experimentalionisation [11] and electronic excitation [20] data at theonly common energy value, 50 eV.

Note that integral elastic experimental data are not in-cluded in this discussion. It has to be borne in mind thatelastic experimental values [12,15,18,19] do generally in-clude the rotationally inelastic collisions due to the finiteenergy resolution and the very small energy losses (typ-ically, a few tens of eV at most) expected in rotationalexcitations, and that this contribution can be quite signif-icant in the case of polar molecules such as THF. In fact,the large integral values found for “elastic” scattering byGauf et al. [19] (not shown) do closely match the dipole-corrected SMC theoretical values but exceed the experi-mental total CS from [10,12] for some energies. However,the integral elastic cross sections found in the literatureare in fact not completely experimental values but semi-empirical in nature, since they build on some additionaltheoretical assumptions in order to extrapolate data atleast for small angles. These low angles are prevalent inthe integration procedure for polar species and thereforethe integrated values strongly depend on the extrapolateddata, hindering a meaningful comparison to the presentresults.

4 Data consistency and compilation

As mentioned above, consistency of electron scatteringcross section databases can be checked through the in-tegral cross sections by comparing the sum of data corre-sponding to all possible processes with a reference TCS.The self-consistency of any data set, experimental or the-oretical, is a very critical aspect and should be confirmedbefore any potential recommendation or use, e.g. for mod-elling purposes. In the case of THF, as discussed above, theconsiderable permanent dipole moment (1.63 D) causessome discrepancies between data from different sources,particularly for the lower incident energies, due to thedifficulties of experimental measurements to energeticallyand angularly resolve/discriminate rotational excitations.In order to compile a set of interaction CSs that serve as

Page 6 of 8 Eur. Phys. J. D (2014) 68: 161

the input parameters for our LEPTS model in the inci-dent energy range 1 eV–10 keV, we therefore proceededas follows.

In the energy range noticeably affected by the dipole-induced enhancement of rotational scattering (0–30 eV),the most accurate and reliable partial cross sections (forthe different processes) are first identified as the primaryreference and are then summed up in order to obtainthe total scattering CS. The resulting total CS value ismuch higher than the experimental ones [10–12], beingmore similar to the theoretical predictions when includingdipole-induced rotations. However, for incident energies�40 eV, the experimental total CSs of Mozejko et al. [10](40 and 50 eV) and Fuss et al. [11] (70–5000 eV and theirextrapolation up to 10 000 eV) are very well consistentwith the sum of the individual partial CSs obtained asoutlined (see details below). These values are also in verygood agreement with the experimental total CS recentlyreported by Baek et al. [12] in the overlapping energyrange, so that they are selected as the total CS parameterfor those energies.

The pure elastic scattering cross section is derived af-ter a rigorous comparison of the Schwinger multichannel(SMC) calculations of [19,22], found to be the theoreti-cal results best emulating experimental differential datafor energies �20 eV, to the available experimental elas-tic DCSs [12,14–19]. The fact that the SMC prediction ofthe elastic differential CSs, when including a Born-dipole-correction, reproduces the experimental angular distribu-tions extraordinarily well (particularly at the lower in-cident energies and for small angles, see also Figure 1in [19]) confirms the conclusion that indeed, the cited ex-periments suffer from a pronounced contamination of ro-tationally inelastic collisions. In consequence, the LEPTSinput pure integral elastic CS up to energies of 20 eVis taken from the un-Born-corrected version from [19,22].For the intermediate incident energy range, a compari-son of the different theoretical and experimental integralelastic cross sections is not conclusive in a straight man-ner, since the experimental results reported in [12,15,18]appear quite scattered and show rather poor agreementwith the present IAM-SCAR calculations or the IAM-ARresults of Homem et al. [18]. Nonetheless, at energies of�200 eV measurements [12,18] are in satisfactory accor-dance with the present results so that our theoretical datacan be selected for use and a numerical interpolation func-tion is used for deriving integral elastic CS values in theenergy range 30–150 eV.

The ionisation CS selected as LEPTS data input origi-nates from the Madrid measurements in Fuss et al. [11] forE � 70 eV, including an extrapolation towards 10 keV,and from the calculation of Mozejko et al. [24] which showsvery good agreement with the first data. The integral CSfor electronic excitation is based on the measurements ofDo et al. [20] and an extrapolation of these values to-wards higher energies. These data may fall short of thetrue value of integral electronic excitation since excita-tion levels above ∼8.5 eV are ignored. However, one canargue that this might be approximately compensated for

by the fact that some excitations lead to neutral dissocia-tion which is accounted for separately in its own channel.Next, the vibrational excitation CS values are derived asan estimation based on the absolute integral values re-ported by Dampc et al. [17] and Allan [16], for incidentenergies between 6 eV and 10 eV, and the differential exci-tation functions for the most prominent modes publishedin [16] due to the lack of integral values over a sufficientlyextended energy range. The recommended values for rota-tional excitation are taken from our calculation but nor-malized to the corresponding SMC result of [19] at 1 eVwhich lies lower in absolute magnitude. This proceduregives the best overall consistency with the other interac-tion channels (particularly, it guarantees a smooth contin-uation of the total CS at 30–40 eV). Finally, the remainingCS (σtot-σel-σvib-σrot-σion-σexc) for energies �40 eV is at-tributed to neutral dissociation not otherwise accountedfor and the resulting curve is extrapolated towards lowerenergies. The complete integral cross section data set se-lected for electron scattering from THF and included inthe LEPTS data base is presented in Table 1.

Due to the very good agreement between the IAM-SCAR elastic DCSs and the experiments at intermedi-ate and high energies [12,15,18,19], it is recommendedto use the present results for incident energies �30 eV.For the lower energies (approximately �20 eV), the elas-tic DCSs included in our LEPTS input data are basedon the experimental data [12,14–19], using the particu-lar source that best combines the typical shape and ab-solute values of all the different measurements for eachincident energy and angular range. As a result, most ofthe data points result from the numerical interpolation toa 1◦ grid of the DCSs values given by Colyer et al. [15],Gauf et al. [19] and Dampc et al. [17]. However, for thesmall-angle range where experiments diverge from (non-dipole-corrected) theory, we rely on the SMC calculationwithout Born-dipole-correction as reported in [19,22]. Theresulting absolute elastic DCS values selected for the en-tire incident energy range can be found in Table S4∗∗.

5 Conclusions

In this article, we have presented our IAM-SCAR cal-culation on electron scattering from tetrahydrofuran(C4H8O) in the energy range 1–10 000 eV. In compari-son to experimental total cross section data from differentsources [10–12], we find excellent agreement for incidentenergies �10 eV and up to 5000 eV (the highest inci-dent energy studied experimentally). Also the calculatedinelastic CS agrees well with the available experimentswhere a comparison can be made. The validity of our the-oretical IAM-SCAR + Rotations approach in THF is thusconfirmed in its recommended energy range, 10–5000 eV.Complete numerical data are made available in Tables S1–S3∗∗. Additionally, a self-consistent electron-THF interac-tion data set comprising partial integral CSs for elasticand different types of inelastic scattering, as well as elas-tic differential CSs throughout the entire incident energyrange 1–10 000 eV has been selected for inclusion in the

Eur. Phys. J. D (2014) 68: 161 Page 7 of 8

Table 1. Integral cross sections selected for our LEPTS code for electron scattering from tetrahydrofuran, in 10−20 m2.

Energy Total Elastic Rotation Vibration Electronic Ionisation Neutral(eV) excitation dissociation

1 105.5 26.9 77.4 1.22 0 0 0

1.5 82.8 27.4 54.3 1.16 0 0 0

2 70.7 27.4 42.0 1.29 0 0 0

3 57.1 26.0 29.36 1.76 0 0 0

4 52.1 26.5 22.78 2.80 0 0 0

5 52.4 29.4 18.51 4.54 0 0 0

7 60.2 40.7 13.74 5.74 0 0 0

10 56.0 40.4 9.95 5.6 0 0 0

15 52.0 38.2 6.90 3.28 2.00 1.63 0.000

20 50.7 33.9 5.32 1.91 5.06 4.38 0.15

30 46.2 26.2 3.67 0.888 5.56 8.37 1.502

40 43.2 21.9 2.829 0.515 5.50 10.6 1.846

50 41.0 19.0 2.296 0.338 4.85 11.2 3.305

70 36.5 15.4 1.691 0.178 1.98 12.0 5.316

100 31.4 12.3 1.210 0.091 0.948 12.5 4.354

150 26.3 9.53 0.836 0.042 0.411 12.0 3.481

200 22.0 7.90 0.641 0.024 0.227 9.89 3.318

300 16.6 6.19 0.445 0.011 0.099 7.90 1.955

400 13.7 5.15 0.338 0.007 0.055 6.57 1.581

500 11.8 4.45 0.267 0.004 0.034 5.64 1.404

700 9.08 3.53 0.196 0 0.017 4.37 0.964

1000 6.96 2.70 0.142 0 0.008 3.39 0.719

1500 5.11 1.95 0.098 0 0.004 2.49 0.568

2000 3.90 1.54 0.075 0 0 1.99 0.295

3000 2.84 1.09 0.052 0 0 1.46 0.238

4000 2.17 0.851 0.040 0 0 1.16 0.119

5000 1.78 0.700 0.032 0 0 0.978 0.070

7000 1.327 0.518 0.024 0 0 0.750 0.035

10 000 0.958 0.378 0.016 0 0 0.563 0.001

LEPTS data collection and is supplied in numerical formin Tables 1 and S4∗∗.

This work is partially supported by MINECO (FIS2012-31230), COST (MP1002, CM1301) and ARC (DP140102854).

References

1. B. Boudaiffa, P. Cloutier, D. Hunting, M.A. Huels, L.Sanche, Science 287, 1658 (2000)

2. B. Boudaiffa, P. Cloutier, D. Hunting, M.A. Huels, L.Sanche, Radiat. Res. 157, 227 (2002)

3. M.A. Huels, B. Boudaiffa, P. Cloutier, D. Hunting, L.Sanche, J. Am. Chem. Soc. 125, 4467 (2003)

4. E. Alizadeh, A.G. Sanz, G. Garcıa, L. Sanche, J. Phys.Chem. Lett. 4, 820 (2013)

5. A. Munoz, F. Blanco, G. Garcia, P.A. Thorn, M.J.Brunger, J.P. Sullivan, S.J. Buckman, Int. J. MassSpectrom. 277, 300 (2008)

6. J. Tennyson, Phys. Rep. 491, 29 (2010)

7. A.G. Sanz, M. Fuss, F. Blanco, F. Sebastanelli, F. Blanco,F. Gianturco, G. Garcıa, J. Chem. Phys. 137, 124103(2012)

8. C. Winstead, V. McKoy, in Radiation Damage inBiomolecular Systems, edited by G. Garcia Gomez-Tejedor, M.C. Fuss (Springer Sciences, Dordrecht, 2012)

9. A. Zecca, C. Perazzolli, M. Brunger, J. Phys. B 38, 2079(2005)

10. P. Mozejko, E. Ptasinska-Denga, A. Domaracka, C.Szmytkowski, Phys. Rev. A 74, 012708 (2006)

11. M. Fuss, A. Munoz, J.C. Oller, F. Blanco, D. Almeida, P.Limao-Vieira, T.P.D. Do, M.J. Brunger, G. Garcıa, Phys.Rev. A 80, 052709 (2009)

12. W.Y. Baek, M. Bug, H. Rabus, E. Gargoni, B. Grosswendt,Phys. Rev. A 86, 032702 (2012)

13. M. Dampc, E. Szymanska, B. Mielewska, M. Zubek, J.Phys. B 44, 055206 (2011)

14. A.R. Milosavljevic, A. Giuliani, D. Sevic, M.-J. Hubin-Franskin, B.P. Marinkovic, Eur. Phys. J. D 35, 411 (2005)

15. C.J. Colyer, V. Vizcaino, J.P. Sullivan, M.J. Brunger, S.J.Buckman, New J. Phys. 9, 41 (2007)

Page 8 of 8 Eur. Phys. J. D (2014) 68: 161

16. M. Allan, J. Phys. B 40, 3531 (2007)17. M. Dampc, A.R. Milosavljevic, I. Linert, B.P. Marinkovic,

M. Zubek, Phys. Rev. A 75, 042710 (2007)18. M.G.P. Homem, R.T. Sugohara, I.P. Sanches, M.T. Lee, I.

Iga, Phys. Rev. A 80, 032705 (2009)19. A. Gauf, L.R. Hargreaves, A. Jo, J. Tanner, T. Walls, C.

Winstead, V. McKoy, Phys. Rev. A 85, 052717 (2012)20. T.P.T. Do, M. Leung, M. Fuss, G. Garcia, F. Blanco, K.

Ratnavelu, M.J. Brunger, J. Chem. Phys. 134, 144302(2011)

21. D. Bouchiha, J.D. Gorfinkiel, L.G. Caron, L. Sanche, J.Phys. B 39, 975 (2006)

22. C. Winstead, V. McKoy, J. Chem. Phys. 125, 074302(2006)

23. C.S. Trevisan, A.E. Orel, T.N. Rescigno, J. Phys. B 39,L255 (2006)

24. P. Mozejko, L. Sanche, Radiat. Phys. Chem. 73, 77 (2005)25. C. Champion, J. Chem. Phys., in press26. L. Chiari, E. Anderson, W. Tattersall, J.R. Machacek, P.

Palihawadana, C. Makochekanwa, J.P. Sullivan, G. Garcıa,F. Blanco, R.P. McEachran, M.J. Brunger, S. Buckman,J. Chem. Phys. 138, 074301 (2013)

27. M.C. Fuss, R. Colmenares, A.G. Sanz, A. Munoz, J.C.Oller, F. Blanco, T.P.T. Do, M.J. Brunger, D. Almeida, P.Limao-Vieira, G. Garcıa, J. Phys.: Conf. Ser. 373, 012010(2012)

28. F. Blanco, A. Munoz, D. Almeida, F. Ferreira da Silva, P.Limao-Vieira, M. Fuss, A.G. Sanz, G. Garcıa, Eur. Phys.J. D, submitted for publication

29. F. Blanco, G. Garcia, Phys. Lett. A 295, 178 (2002)30. F. Blanco, G. Garcıa, Phys. Rev. A 67, 022701 (2003)31. F. Blanco, G. Garcia, Phys. Lett. A 317, 458 (2003)32. F. Blanco, G. Garcia, Phys. Lett. A 330, 230 (2004)33. R.D. Cowan, The Theory of Atomic Structure and Spectra

(University of California Press, London, 1981)34. M.E. Riley, D.G. Truhlar, J. Chem. Phys. 63, 2182 (1975)35. X.Z. Zhang, J.F. Sun, Y.F. Liu, J. Phys. B 25, 1893 (1992)36. G. Staszewska, D.W. Schwenke, D. Thirumalai, D.G.

Truhlar, Phys. Rev. A 28, 2740 (1983)37. O. Zatsarinny, K. Bartschat, G. Garcia, F. Blanco, L.R.

Hargreaves, D.B. Jones, R. Murrie, J.R. Brunton, M.J.Brunger, M. Hoshino, S.J. Buckman, Phys. Rev. A 83,042702 (2011)

38. J.B. Maljkovic, A.R. Milosavljevic, F. Blanco, D. Sevic, G.Garcıa, B.P. Marinkovic, Phys. Rev. A 79, 052706 (2009)

39. F. Blanco, G. Garcıa, Phys. Lett. A 360, 707 (2007)40. A. Jain, J. Phys. B 21, 905 (1988)41. A. Munoz, J.C. Oller, F. Blanco, J.D. Gorfinkiel, P. Limao-

Vieira, G. Garcıa, Phys. Rev. A 76, 052707 (2007)42. A.G. Sanz, M. Fuss, F. Blanco, F. Sebastanelli, F. Blanco,

F. Gianturco, G. Garcıa, J. Chem. Phys. 137, 124103(2012)

43. Cz. Szmytkowski, A. Domaracka, P. Mozejko, E.Ptasinska-Denga, J. Chem. Phys. 130, 134316 (2009)

44. A. Giuliani, P. Limao-Vieira, D. Duflot, A.R.Milosavljevic, B.P. Marinkovic, S.V. Hoffmann, N.Mason, J. Delwiche, M.-J. Hubin-Franskin, Eur. Phys. J.D 51, 97 (2009)