Differential ionization cross sections of ethanol by electron impact: Experiment and theoretical analysis

PHYSICAL REVIEW A 112, 052816 (2025) Differential ionization cross sections of ethanol by electron impact: Experiment and theoretical analysis M. Dinger 1,2,*and W. Y. Baek 1 1Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany 2Ruprecht-Karls-Universität Heidelberg, Grabengasse 1, 69117 Heidelberg, Germany (Received 8 August 2025; accepted 20 October 2025; published 13 November 2025) Doubly differential ionization cross sections (DDCSs) of ethanol were measured for incident electron energies ranging from 60 eV to 1 keV, over an angular range of 30◦–135◦. The energies of the secondary electrons spanned from 4 eV up to approximately half of the primary electron energy. The experimental results were compared with calculations based on the distorted-wave Born approximation, including postcollision interaction between the two outgoing electrons. Overall, the experimental and theoretical data show reasonably good agreement within the experimental uncertainties. Singly differential ionization cross sections (SDCSs) were derived by integrating the DDCSs over the emission angles. These SDCSs are well reproduced by the generalized binaryencounter Bethe (GBEB) model. Total ionization cross sections (TICSs), obtained by integrating the SDCSs over the secondary electron energy, also show good agreement with the predictions of the GBEB model. DOI: 10.1103/cslk-f5l2 I. INTRODUCTION Understanding electron scattering and electron-impact ionization in matter is essential across many scientific fields, including radiation dosimetry, atmospheric physics, and plasma modeling. Low-energy electrons are released in large quantities by all forms of ionizing radiation interacting with matter, and they are primarily responsible for radiationinduced damage in the surrounding medium. Of particular interest in this context is ethanol (C2H5OH), a simple organic compound relevant to both atmospheric chemistry and radiation biology. Early investigations of electron-ethanol interactions primarily focused on total cross sections (TCS) for low-energy electron collisions. Nearly a century after the initial measurements [1], Silva et al. [2] extended the available TCS data to cover incident electron energies from 60 to 500 eV. Complementary to these efforts, differential elastic scattering cross sections (DCS) were determined by Khakoo et al. [3] for energies between 1 and 100 eV and angles from 5◦to 130◦, using both experiment and theory (Schwinger multichannel method under the static-exchange approximation). Subsequent measurements by Lee et al. [4] expanded the DCS database to higher energies (100 eV–1 keV). They also performed theoretical calculations by solving the LippmannSchwinger equation with a complex optical potential. Recently, our group measured DCS of ethanol for electron energies of 30–800 eV over the angular range between 30◦ and 150◦[5]. These measurements were supplemented by *Contact author: [email protected] Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. theoretical calculations based on the modified independent atom model [6] and the IAM-SCAR +I method [7,8]. Regarding ionization processes, several experimental studies have reported partial and total ionization cross sections (TICS) of ethanol [9–12]. Complementing these measurements, a number of theoretical studies employing semiempirical and ab initio models have been conducted to estimate TICS. However, to date, no data on differential ionization cross sections are available in the literature. Building on our previous work on the DCS of ethanol, the present study focuses on electron-impact ionization of ethanol. Specifically, we report doubly differential ionization cross sections (DDCSs) of ethanol at incident electron energies ranging from 60 to 1 keV and emission angles of 30◦–135◦. They were measured for secondary electron energies between 4 eV and approximately half the primary energy. The experimental results were compared with ab initio calculations performed using the distorted-wave Born approximation (DWBA) with single-center expanded molecular wave functions [13,14]. In addition, the applicability of a widely used semiempirical formula [15,16] to describe the angular distribution of secondary electrons is investigated. Singly differential and total ionization cross sections of ethanol were determined by integrating the DDCSs over the emission angles and additionally, over the secondary electron energies. These results are compared with available experimental data as well as with predictions from the generalized Binary-encounter Bethe (GBEB) model [17]. II. MEASUREMENT The experiment was conducted using a standard crossed-beam setup, described in detail in our previous work [13]. In brief, a monoenergetic electron beam intersected a molecular beam produced by an effusion nozzle. Secondary electrons released from the target molecules were energy analyzed using a hemispherical electron spectrometer with 2469-9926/2025/112(5)/052816(7) 052816-1 Published by the American Physical Society M. DINGER AND W. Y. BAEK PHYSICAL REVIEW A 112, 052816 (2025) a mean radius of 150 mm, equipped with five channeltron detectors. In the present setup, the five channeltrons were operated in parallel, not for an angle-resolved measurement but to increase the overall count rate. Since the channeltrons are positioned at different radii of the spectrometer, each one records electrons at a different energy. The energy resolution of the spectrometer was approximately 1.7 eV at a primary energy of 1 keV, and better than 0.7 eV for energies below 100 eV. The detection angle of electrons relative to the incident beam was adjusted by rotating the electron gun with respect to the fixed electron spectrometer, with an angular resolution of approximately 1.5◦. The electron beam current was measured using a Faraday cup, while the gas flow rate through the effusion nozzle was controlled via a capacitance manometer at the gas reservoir and an ionization gauge in the vacuum scattering chamber. Secondary electron energy spectra at each emission angle were converted into DDCSs using the relative flow technique, with nitrogen as the reference gas [5].Gasflowrateswere tuned to ensure comparable mean free paths for intermolecular collisions in both molecular beams. Gas densities were kept sufficiently low to maintain Clausing flow conditions (Knudsen number Knd>1), thereby satisfying the singlecollision condition. The overall uncertainty of the DDCS measurements was estimated to be approximately 27%. The main contributions arose from a 25% uncertainty in the reference data, statistical fluctuations of about 5% in the energy spectra, and beam current instabilities of around 10%, attributed to the influence of residual organic gas on electron emission from the electrongun filament. III. COMPUTATIONAL DETAILS Differential and total ionization cross sections were calculated using the DWBA and GBEB model, respectively. Molecular geometries, potentials, orbital energies, and electron densities were obtained from Hartree-Fock calculations with the 6-311G(d,p) basis set, using the quantum chemistry code GAUSSIAN09. The molecular wave functions and densities were then expanded around the center of mass using the SCELib3 library [18,19], allowing a single-center implementation of the DWBA for the molecular target. The outputs of the Hartree-Fock calculation, including geometry, and molecular binding and kinetic energies are provided in Table I.The theoretical models are briefly explained in the following sections. The GBEB calculations included all molecular orbitals, whereas in the DWBA calculations, the contributions from core orbitals were left out. A. Distorted-wave Born approximation Doubly differential cross sections for electron-impact ionization were obtained within the DWBA. A detailed derivation can be found in Refs. [13,14]; here we summarize the main expressions and assumptions. The direct transition Tmatrix for ionization from the ith molecular orbital (MO) is defined by Tdir (k0,kA,kB)=χ−(kA,rA)χ−(kB,rB)| ×Vee|ψi(rB)χ+(k0,rA),(1) TABLE I. Results of the quantum chemistry calculations. The binding energies Band mean kinetic energies Uof the molecular orbitals (MOs) are given in eV. The occupation is n=2 for all orbitals, and the effective molecular charges Zc,v eff are calculated according to Ref. [17]. In addition, the atomic coordinates x,y,andzare given in 10−10 m. Molecular orbital properties Atomic coordinates MO BUZ c eff Zv eff xyz 1A559.25 794.46 25 C 1.167 −0.417 0.000 2A306.78 436.06 23 C 0.000 0.548 0.000 3A305.06 435.88 21 H 1.135 −1.051 0.880 4A37.24 68.73 19 H 1.135 −1.051 −0.880 5A27.62 38.93 17 H 2.108 0.128 0.000 6A22.85 39.24 15 H 0.044 1.189 −0.880 7A19.31 43.37 7 H 0.044 1.189 0.880 1A 17.67 30.58 5 O −1.192 −0.197 0.000 8A15.63 47.76 5 H −1.935 0.380 0.000 9A14.59 32.14 3 2A 14.36 35.54 3 10A13.26 43.89 1 3A 10.48 43.37 1 where Vee is the electron-electron interaction potential, ψiis the MO wave function, and χ±are the distorted incident and outgoing electron waves. The electron momenta are denoted by k0(incoming), kA(scattered), and kB(ejected). The distorted waves are solutions to the one-electron elastic scattering Schrödinger equation, with distorting potentials taken as the sum of the spherically symmetric electrostatic term and exchange term, the latter computed using the method of Furness and McCarthy [20]. For outgoing electrons, the corresponding ionic potentials were employed. To separate angular and radial coordinates, a partial wave expansion is employed for χ±, while the molecular wave function ψi is expressed using single-center symmetry-adapted functions around the molecular center of mass: ψi(rB)=1 rB lm bi lmui lm(rB)Ylm(ˆrB),(2) with bi lm determined from the irreducible representation of the orbital (Aor A for ethanol with Cssymmetry). The angular part is described by spherical harmonics Ylm, and ui lm gives the radial contribution. For comparison with experimental cross sections of randomly oriented molecules in the gas beam, a full orientation average of the Tmatrix is performed. This approach provides higher accuracy than the orientation-averaged molecular orbital (OAMO) method, where only ψiis averaged. The DDCS is obtained by numerically integrating the triply differential cross section expressed in terms of the squared, orientation-averaged Tmatrix: d2σi dBdEB =(2π)4nikAkB k0dA|Ce,−e|2|T|2,(3) where niis the electron occupancy of orbital i, and |Ce,−e|2 is the postcollision interaction (PCI) correction between the outgoing electrons, for which we adopt the formula of Ward 052816-2 DIFFERENTIAL IONIZATION CROSS SECTIONS … PHYSICAL REVIEW A 112, 052816 (2025) and Macek [21]. Finally, exchange effects between the two outgoing electrons are included by interchanging the coordinates of the scattered and ejected electrons. The full squared Tmatrix is then given by |T|2=|Tdir|2+|Tex|2−Re(T∗ dirTex ),(4) where Tex denotes the exchange term. B. Generalized Binary-encounter Bethe model The binary-encounter Bethe (BEB) model is widely used to compute TICS and singly differential (SDCS) ionization cross sections. In this framework, the cross sections depend on the binding energy Bi, mean kinetic energy Ui, occupation number niof the molecular orbital, and the incident electron energy T. For a specific orbital i, the total cross section is given by σ= i Si ti+(ui+1)/νiln ti 21−1 t2 i+1−1 ti −ln ti ti+1, (5) with the scaling factor Si=4πa2 0ni(R/Bi)2. Here, a0is the Bohr radius, Ris the Rydberg constant, and νiis a correction factor. The lowercase variables ti,ui, and iare dimensionless forms of the corresponding energies, each normalized to the binding energy Bi(e.g., ti=T/Bi). Similarly, the SDCS is given by dσ d(,t)= i Si ti+(ui+1)/νi 3  k=1 Fk(ti) ×[(i+1)−k+(ti−i)−k],(6) where F1=−(ti+1)−1,F2=1,F3=ln(ti).(7) The correction factor νiaccounts for electron acceleration in the field of the residual ion. In the GBEB model [17], νiis expressed in terms of effective molecular charges Zc,v eff experienced by the incident electron, where cand vlabel core and valence orbitals, respectively. We adopt the description of Ref. [17], where the “core” category includes both deep core and inner valence orbitals, while “valence” refers only to the outermost valence orbitals. The procedure for obtaining Zc,v eff is detailed in Ref. [17], and the parameter values used in the present calculations are listed in Table I. IV. RESULTS AND DISCUSSION The experimental results are summarized in Table II and illustrated in Fig. 1, alongside theoretical predictions obtained using the DWBA. The theoretical methods are described in detail in our previous works [13,14]. In Fig. 1solid lines represent DWBA calculations that include PCI, while dashed lines correspond to those without PCI. Under the assumption that the PCI does not change the total number of electrons emitted at a given energy, the PCI-included DDCSs were rescaled so that their angular integral matches that of the DDCSs without PCI. As evident in Fig. 1, the theoretical predictions that account for PCI exhibit overall good agreement with the experimental data within the experimental uncertainties. As expected, the level of agreement deteriorates with decreasing primary electron energy. Figure 1clearly indicates that PCI becomes a significant factor when the energy of the scattered primary electron approaches that of the secondary electron. In this energy regime, the experimental angular distribution of secondary electrons can only be accurately reproduced when PCI is included in the theoretical model. Figure 1also demonstrates that low-energy secondary electrons, primarily generated in collisions with large impact parameters, are emitted more isotropically, whereas higher-energy secondary electrons exhibit a stronger binary collision character, marked by pronounced angular peaks. It is also noteworthy that electron emission in the forward direction increases significantly when the energies of the two outgoing electrons become nearly equal. This effect is clearly observed, for example, at a secondary electron energy of E=30 eV and a primary energy of T=80 eV. Depending on the ionized molecular orbital, the energy of the primary scattered electron in this case ranges from approximately 12.5 to 39.5 eV, comparable to the secondary electron energy. A similar enhancement at small emission angles has been observed in other molecules, such as propane [16]. As shown in Fig. 2, this behavior can be attributed to the exchange effect, which becomes more pronounced when both electrons move in the same direction with similar velocities. In the absence of the exchange effect, a broad peak appears in the angular distribution of the ejected electrons. The experimental DDCSs are fitted using a semiempirical formula to allow extrapolation beyond the measured angular range, i.e., below 30◦and above 135◦. This formula is based on two Lorentzian functions that describe the binary collision peak ( fBE) and backward electron emission ( fb)[15,16]: dσ2 dεdθ=A1[fBE(ε,t,θ)+A2fb(ε,t,θ)],(8) where the dimensionless variables are defined as t=T/I and ε=E/I, with Ibeing the ionization potential of ethanol (10.48 eV [22]). The coefficients A1and A2are energydependent fit parameters, and fBE and fbare given by fBE(ε,t,θ)=1 1+[(cos θ−cos θ0)/(b1sin2θ0/ε)]2 (9) and fb(ε,t,θ)=1 1+[(cos θ+1)/b2]2,(10) where cos θ0is given by cos θ0≈ε+1 t.(11) The parameters b1and b2are related to the peak widths. Figure 3presents examples of the best fits of Eq. (8)tothe experimental data. As evident from Fig. 3, the experimental DDCSs are well described by Eq. (8), except at secondary electron energies near half of the primary electron energy, where deviations become apparent due to the exchange effect. 052816-3 M. DINGER AND W. Y. BAEK PHYSICAL REVIEW A 112, 052816 (2025) FIG. 1. Experimental results for the DDCSs of ethanol as a function of emission angle θ, shown for various secondary electron energies E as indicated in the legend. The primary energies Tare ranging from 60 eV to 1 keV. Theoretical DWBA calculations are depicted by dashed lines and DWBA calculations including PCI are depicted by solid lines. FIG. 2. Influence of the exchange effect on the angular distribution of secondary electrons, illustrated using the theoretical DDCS at 80 eV (DWBA with PCI). The inclusion and omission of the exchange effect in the DWBA is indicated by solid and dashed lines, respectively. A pronounced enhancement of forward emission due to the exchange effect is evident at E=30 eV. The extrapolated data were subsequently integrated over the emission angles to obtain the SDCSs dσ/dEof ethanol. Figure 4shows the resulting SDCSs in comparison with predictions from the GBEB model [17]. As evident from Fig. 4, the experimental SDCSs are generally well reproduced by the GBEB model within the experimental uncertainties, except for deviations at secondary electron energies near half of the kinetic energy of incident electrons. This discrepancy is expected, as the Lorentzian functions used in the semiempirical formula do not adequately capture the enhancement of the forward electron emission due to the exchange effect. To obtain the TICS, σ, the SDCSs were integrated over the secondary electron energy E, where values below E⩽4eV were extrapolated using the GBEB formula. Figure 5shows the resulting TICS, compared with literature data and predictions from the GBEB model. It is worth noting that the literature values for TICS were derived from measurements of the count rates of ionic fragments produced by electron impact on ethanol. As shown in Fig. 5, the present results are generally higher than the literature data but are well reproduced by the GBEB model within the experimental uncertainties. The observed overestimation may arise from inaccuracies in extrapolating the present experimental data outside the 052816-4 DIFFERENTIAL IONIZATION CROSS SECTIONS … PHYSICAL REVIEW A 112, 052816 (2025) FIG. 3. Results of the best fits of Eq. (8) to the experimental DDCSs, illustrated for the representative cases T=100 eV and T=400 eV. The symbols denote the same secondary electron energies Eas in Fig. 1. measured angular range and for secondary energies below E⩽4 eV. However, these effects are taken into account within the quoted uncertainties. V. CONCLUSION The experimental DDCSs of ethanol measured in this study show overall good agreement with DWBA predictions within the experimental uncertainties, when PCI is taken into account. The DWBA calculations indicate that PCI has a significant impact on the angular distribution of secondary electrons at incident electron energies below 400 eV, especially when FIG. 4. Experimental singly differential ionization cross sections of ethanol as a function of secondary electron energy E,for different primary energies Tas indicated in the legend. The experimental data is compared with the predictions of the GBEB model (lines of various styles, see legend). the two outgoing electrons have comparable energies. In this energy range, electron emission in the forward direction is notably enhanced. The DWBA results suggest that this enhancement is primarily due to the exchange effect. The SDCSs, obtained by integrating the experimental DDCSs over emission angles, exhibit good agreement with the predictions of the GBEB model, except near secondary electron energies corresponding to approximately half the initial kinetic energy. This discrepancy is likely due to the enhanced forward emission caused by the exchange effect, which is underestimated in the extrapolation, as discussed above. The FIG. 5. Present results () for the TICS of ethanol in comparison with the predictions of the GBEB model (solid line), and literature data: Đuri´ cet al. [9](×), Rejoub et al. [10](), Hudson et al. [11] (), Nixon et al. [12](◦). 052816-5 M. DINGER AND W. Y. BAEK PHYSICAL REVIEW A 112, 052816 (2025) TABLE II. Present experimental ionization cross sections of ethanol. The DDCSs are given in units of 10−18 cm2eV−1sr−1,theSDCSsare given in units of 10−18 cm2eV−1, and the TICSs are presented in units of 10−16 cm2. Experimental uncertainties amount to 27% for the DDCS and 30% for the SDCSs and TICSs. T=60 eV DDCS E/θ 30◦45◦60◦75◦90◦105◦120◦135◦SDCS 5 eV 5.3803 4.2014 4.7016 4.6082 4.7022 5.0089 4.3535 4.4492 58.6 10 eV 3.8398 3.1378 2.9483 2.9258 2.7903 2.6976 2.4771 2.6701 35.8 20 eV 4.6765 2.8016 1.9741 1.6591 1.3304 1.1899 1.0913 1.2338 22.6 TICS 10.5 T=80 eV DDCS E/θ 30◦45◦60◦75◦90◦105◦120◦135◦SDCS 5 eV 6.2577 4.4084 5.1893 4.6375 4.7419 4.4638 4.1120 4.2435 58.9 10 eV 2.9237 2.5511 3.0780 2.7111 2.6863 2.4647 2.1915 2.2129 32 20 eV 1.6163 1.3869 1.6275 1.2693 1.1247 0.9240 0.7931 0.8058 14.3 30 eV 2.1517 1.4781 1.3150 0.8221 0.6342 0.4899 0.4418 0.4667 11.1 TICS 10.6 T=100 eV DDCS E/θ 30◦45◦60◦75◦90◦105◦120◦135◦SDCS 5 eV 4.3335 4.3659 4.9591 4.8098 5.2117 4.7082 4.5401 4.1914 57.7 10 eV 2.7217 2.6068 2.7986 2.9080 2.9534 2.5564 2.2688 2.2823 32.5 20 eV 1.2228 1.1037 1.2337 1.2593 1.1583 0.8949 0.7728 0.7220 12.6 40 eV 1.5764 1.1573 0.8019 0.5999 0.4199 0.3121 0.2504 0.2722 7.55 TICS 10.6 T=200 eV DDCS E/θ 30◦45◦60◦75◦90◦105◦120◦135◦SDCS 5 eV 3.3756 3.3522 4.3038 3.5535 3.2882 3.3720 2.9737 2.1048 40 10 eV 2.0963 1.7717 2.0294 2.1204 1.8678 1.8334 1.5930 1.2496 22.6 20 eV 0.9538 0.7205 0.8073 0.8247 0.7467 0.6526 0.5953 0.4075 8.37 40 eV 0.2553 0.2028 0.2817 0.2547 0.2049 0.1481 0.1309 0.0947 2.36 60 eV 0.2104 0.1662 0.2004 0.1673 0.0915 0.0708 0.0521 0.0410 1.43 80 eV 0.2990 0.2015 0.1887 0.1021 0.0585 0.0384 0.0340 0.0276 1.18 TICS 7.63 T=400 eV DDCS E/θ 30◦45◦60◦75◦90◦105◦120◦135◦SDCS 5 eV 2.2338 2.4506 2.4615 2.1177 2.0805 2.3887 1.7921 1.1748 27.8 10 eV 1.1458 1.2036 1.1656 1.0741 1.0673 1.2773 0.8178 0.6312 12.6 20 eV 0.4310 0.4567 0.5017 0.4567 0.3976 0.4533 0.2617 0.1869 5.05 50 eV 0.0688 0.0931 0.1144 0.1091 0.0728 0.0575 0.0359 0.0260 0.86 100 eV 0.0235 0.0464 0.0452 0.0283 0.0129 0.0082 0.0078 0.0047 0.234 150 eV 0.0236 0.0357 0.0230 0.0088 0.0043 0.0030 0.0023 0.0019 0.133 TICS 4.95 T=1000 eV DDCS E/θ 30◦45◦60◦75◦90◦105◦120◦135◦SDCS 5 eV 0.9231 0.8147 0.6071 0.8983 1.5443 1.2965 1.1031 0.7652 13.000 10 eV 0.6121 0.5033 0.3696 0.5014 0.7598 0.6615 0.5543 0.4428 7.190 20 eV 0.1930 0.1821 0.1598 0.2173 0.3257 0.2620 0.1869 0.1298 2.470 50 eV 0.0253 0.0307 0.0347 0.0591 0.0739 0.0417 0.0262 0.0170 0.424 100 eV 0.0054 0.0085 0.0121 0.0168 0.0153 0.0070 0.0041 0.0025 0.101 200 eV 0.0018 0.0036 0.0058 0.0047 0.0021 0.0010 0.0009 0.0007 0.030 TICS 2.41 052816-6 DIFFERENTIAL IONIZATION CROSS SECTIONS … PHYSICAL REVIEW A 112, 052816 (2025) TICSs, determined by integrating the SDCSs over secondary electron energies, also show good agreement with the GBEB model within experimental uncertainties. However, they tend to be systematically higher than experimental values reported in the literature, likely due to overestimation of the used extrapolation techniques. ACKNOWLEDGMENTS This research was supported by the joint research project BIOSPHERE. The Project No. 21GRD02 BIOSPHERE has received funding from the European Partnership on Metrology, cofinanced by the European Union’s Horizon Europe Research and Innovation Programme and by the participating states. The authors express their thanks to Heike Nittmann and Andreas Pausewang for their assistance and technical support during the measurements. DATA AVAILABILITY The data that support the findings of this article are openly available [23]. APPENDIX: DOUBLY DIFFERENTIAL IONIZATION CROSS SECTIONS OF ETHANOL Table II summarizes the experimental results of the current work, including experimental datasets of the DDCS, SDCS, and TICS of ethanol. [1] F. Schmieder, Neue wirkungsquerschnittsmessungen an gasen und dämpfen, Z. Elektrochem. Angew. Phys. Chem. 36, 700 (1930). [2] D. G. Silva, T. Tejo, J. Muse, D. Romero, M. A. Khakoo, and M. C. Lopes, Total electron scattering cross sections for methanol and ethanol at intermediate energies, J. Phys. B 43, 015201 (2010). [3] M. A. Khakoo, J. Muse, C. Campbell, M. C. A. Lopes, H. Silva, C. Winstead, and V. McKoy, Low energy electron scattering from polyatomic targets, J. Phys.: Conf. Ser. 194, 012027 (2009). [4] M. T. Lee, G. L. De Souza, L. E. MacHado, L. M. Brescansin, A. S. Dos Santos, R. R. Lucchese, R. T. Sugohara, M. G. Homem, I. P. Sanches, and I. Iga, Electron scattering by methanol and ethanol: A joint theoretical-experimental investigation, J. Chem. Phys. 136, 114311 (2012). [5] M. Dinger, Y. Park, P. Hepperle, and W. Y. Baek, Combined experimental and theoretical study on the elastic electron scattering cross sections of ethanol, Eur. Phys. J. D 77,52 (2023). [6] S. Hayashi and K. Kuchitsu, Elastic scattering of electrons by molecules at intermediate energies. I. General theory, J. Phys. Soc. Jpn. 41, 1724 (1976). [7] F. Blanco and G. García, Screening corrections for calculation of electron scattering differential cross sections from polyatomic molecules, Phys. Lett. A 330, 230 (2004). [8] F. Blanco and G. García, Interference effects in the electron and positron scattering from molecules at intermediate and high energies, Chem. Phys. Lett. 635, 321 (2015). [9] N. Đuri´ c, I. ˇ Cadež, and M. Kurepa, Total electron impact ionization cross sections of methanol, ethanol and n-propanol molecules, Fizika 21, 339 (1989). [10] R. Rejoub, C. D. Morton, B. G. Lindsay, and R. F. Stebbings, Electron-impact ionization of the simple alcohols, J. Chem. Phys. 118, 1756 (2003). [11] J. E. Hudson, M. L. Hamilton, C. Vallance, and P. W. Harland, Absolute electron impact ionization cross-sections for the C1to C4alcohols, Phys. Chem. Chem. Phys. 5, 3162 (2003). [12] K. L. Nixon, W. A. Pires, R. F. Neves, H. V. Duque, D. B. Jones, M. J. Brunger, and M. C. Lopes, Electron impact ionisation and fragmentation of methanol and ethanol, Int. J. Mass. Spectrom. 404, 48 (2016). [13] M. Dinger, W. Y. Baek, and H. Rabus, Comparative experimental and theoretical study on doubly differential electron-impact ionization cross sections of pyrimidine, Phys. Rev. A 109, 062813 (2024). [14] M. Dinger and W. Y. Baek, Electron-impact total, multipledifferential elastic, and ionization cross sections of ammonia: A joint theoretical and experimental study, Phys. Rev. A 112, 042801 (2025). [15] M. E. Rudd, Differential and total cross sections for ionization of helium and hydrogen by electrons, Phys. Rev. A 44, 1644 (1991). [16] W. Y. Baek, M. U. Bug, H. Nettelbeck, and H. Rabus, Doubly differential cross sections for electron-impact ionization of propane in the energy range from 30 eV to 1 keV, Eur. Phys. J. D73, 61 (2019). [17] Y. C. Wang, G. Visentin, L. G. Jiao, and S. Fritzsche, Acceleration correction to the binary-encounter Bethe model for the electron-impact ionization of molecules, Phys. Rev. A 109, 022804 (2024). [18] N. Sanna and F. A. Gianturco, SCELib: A parallel computational library of molecular properties in the single center approach, Comput. Phys. Commun. 128, 139 (2000). [19] N. Sanna, I. Baccarelli, and G. Morelli, SCELib3.0: The new revision of SCILib, the parallel computational library of molecular properties in the single center approach, Comput. Phys. Commun. 180, 2544 (2009). [20] J. B. Furness and I. E. McCarthy, Semiphenomenological optical model for electron scattering on atoms, J. Phys. B 6, 2280 (1973). [21] S. J. Ward and J. H. Macek, Wave functions for continuum states of charged fragments, Phys.Rev.A49, 1049 (1994). [22] S. G. Lias and W. G. Mallard, NIST Chemistry Webbook, NIST Standard Reference Database Number 69, https://webbook. nist.gov/cgi/cbook.cgi?ID=C64175&Mask=20#Ion-Energetics (2024), Ionization energy of ethanol, evaluated by S. G. Lias. [23] M. Dinger and W. Y. Baek, Differential ionization cross sections of ethanol by electron impact: Experiment and theoretical analysis - Datasets, Zenodo (2025), https://doi.org/10.5281/zenodo. 17432475. 052816-7