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Elastic electron scattering from formamide molecule
Nuclear Instruments and Methods in Physics Research B 279 (2012) 124–127
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Elastic electron scattering from formamide molecule J.B. Maljkovic´ a, F. Blanco b, G. García c, B.P. Marinkovic´ a, A.R. Milosavljevic´ a,⇑ a
Laboratory for Atomic Collision Processes, Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia Departamento de Física Atómica Molecular y Nuclear, Facultad de Ciencias Físicas, Universidad Complutense, Avda. Complutense s/n, E-28040 Madrid, Spain c Instituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 121, 28006 Madrid, Spain b
a r t i c l e
i n f o
Article history: Received 13 July 2011 Received in revised form 8 September 2011 Available online 17 November 2011 Keywords: Formamide Elastic electron scattering Differential cross sections Relative flow method
a b s t r a c t Elastic electron scattering from gaseous formamide (H2NCHO) has been investigated. Absolute elastic differential cross sections (DCSs) were determined both experimentally and theoretically. The measurements were performed using a cross beam technique, for the incident energies of 100, 150 and 300 eV and scattering angles from 20° to 110°. Relative elastic DCSs were measured as a function of the angle and the absolute DCSs were determined using the relative flow method. The calculations of electron interaction cross sections are based on a corrected form of the independent-atom method, known as the SCAR (screen corrected additivity rule) procedure and using an improved quasifree absorption model. Calculated results agree very well with the experiment. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Formamide (H2NCHO) represents the smallest molecular system containing the peptide bond (see Fig. 1). Therefore, the investigation on electron interaction with formamide can be useful to understand processes of electron–protein interactions and modeling of energy deposition upon high-energy irradiation of bio-material. Investigation of electron interaction with small biomolecules representing building blocks of large bio-systems (RNA, DNA, proteins) has been mainly motivated in recent years by radiation damage research [1]. With this respect, our previous work includes measurements of absolute differential cross sections for electron scattering from several different molecules representing backbone sugar and nucleobasis sub-units of DNA [2,3]. However, to our knowledge, there are no published absolute differential cross sections for electron interaction by formamide molecule, which may be used as a basic sub-unit of the protein chain. Most recently, integral and momentum transfer cross sections for elastic scattering of low energy electrons (1–12 eV) by formamide [4], using Schwinger multichannel method have been reported. On the other hand, the formamide, which is considered as a prebiotic molecule has been attracting considerable attention in recent years in the astrobiological research, since it has been identified in the interstellar regions [5]. Within this context, some of the recent results include the laboratory studies either on production of formamide in interstellar ice analogs [6] or chemical evolution of formamide under ion irradiation at low temperature (simulated ⇑ Corresponding author. E-mail address: [email protected] (A.R. Milosavljevic´). 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2011.10.029
astrophysical conditions) [7]. Furthermore, recent photoionization mass spectrometric study of formamide have been carried out using synchrotron radiation over the photon energy range 10–20 eV [8]. Finally, Hamann et al. [9] have been investigating dissociative electron attachment to gas phase formamide, using cross electron/molecule beam technique. In the present study, we report differential cross sections (DCSs) for elastic electron–formamide scattering at 100, 150 and 300 eV incident energies, obtained using a crossed beam spectrometer. Absolute DCSs were determined according to relative flow technique [10,11]. These absolute values were then used to normalize relative DCSs. The experimental procedure has been checked according to DCS measurements for Ar [12].
2. Experimental set-up The experimental set-up is described previously [13]. Briefly, an electron gun produces the electron beam that is crossed perpendicularly by molecular beam, obtained by nonmagnetic stainless steel needle. The scattered electrons are retarded and focused into the double mirror cylindrical energy analyzer DCMA, followed by a three-element lens to further focus transmitted beam into the channel multiplier. The electron gun can be rotated around the needle in the angular range from about 40° to 120°. The base pressure was about 4 10 7 mbar. The working pressure was usually in the range (2–5) 10 6 mbar. The best energy resolution is limited by a thermal spread of primary electrons to about 0.5 eV. Formamide, with declared purity better than 99%, was used after several freeze–thaw cycles under vacuum. Gaseous formamide was introduced into the scattering region from a glass container via a
J.B. Maljkovic´ et al. / Nuclear Instruments and Methods in Physics Research B 279 (2012) 124–127
Fig. 1. Schematic drawing of formamide molecule and peptide bond linking two amino acids.
gas line system, which was heated to provide stable experimental conditions and to improve the signal. The influence of formamide dimerization to the measured scattered electron current was presumed to be negligible for the used experimental conditions (low pressure and increased temperature, see below details) due to a very low dimer/monomer proportion [14,15]. At a given electron energy, the relative cross section has been derived as a function of scattering angle, from 20° to 110° (in 10° steps), by measuring the elastic scattering intensity. The background contributions which were typically below 15% of the elastic electron intensities have been subtracted from the measured electron yields. The calibration of both angular scale and true zero angular position, as well as reliability of DCS shapes, have been tested according to DCSs for elastic electron–Ar scattering. The latter were obtained under the same experimental conditions, and showed very good agreement with previous results. The relative cross sections were next normalized to the absolute values obtained at several scattering angles (40°, 80° or 90°) using the relative flow technique [10,11] and procedure described in [3], and Ar as a reference gas [12]. In the relative flow method, the DCS for scattering of the unknown gas is determined by comparing scattered electron intensities from a standard target (here Ar), with its known differential cross sections, at a given incident electron energy (E0) and a scattering angle (h), and applying measured relative flow-rates (FRs) of both gases, as well as their known
125
molecular weights (see the formula in, e.g. [3]). Here, identical collision region geometry conditions are assumed. The scheme of the present gas system which allows efficient relative flow measurement procedure and background subtraction is shown in Fig. 2. To obtain the same profiles for both gas beams, the gases should be operated at pressures behind the needle so that their mean-free paths are the same. The pressure of formamide behind the tube forming the molecular beam was maintained below 0.2 mbar. The ratio of the pressures behind the tube for formamide to that of Ar was adjusted to be about 1.4, according to gas kinetic diameters [16]. However, during the measurements it has been proved by varying the ratio of the Ar and formamide pressures that absolute values of the cross sections do not depend crucially on the pressure ratio to within uncertainties in the measured cross sections. Actually, the experimental challenge in the work with formamide is to obtain stable conditions, such as pressure behind the gas needle. Note that it has been shown recently that the relative flow method may be performed without a need to know the molecular diameters of used gases, with an appropriate molecular source [17,18]. On the other hand, Homem et al. have argued in the most recent report [19] that in fact, the effect of vapor adsorption on surfaces may significantly affect the relative FR determination and thus the measured absolute DCS. In the present experiment, the relative FR were determined using the method of pressure-increase (MPI), as defined in [19], by closing the capillary valve (CV) and recording the MKS pressure increase versus time (see Fig. 2). Since the whole gas handling system (including capillary) was heated to about 60 °C, the influence of adsorption effect should be reduced to within stated experimental uncertainty. It should be noted, however, that we did see a difference in the measured FRs when operating experiment at lower, ambient temperatures, which is in line with the study in Ref. [19]. The errors for the relative DCSs measured as a function of the scattering angle include statistical errors (0.2–5%) according to Poisson’s distribution and short term stability errors (0.3–7.5%) according to discrepancy of repeated measurements at the same incident energy and scattering angle. The error of the relative angle-differential DCSs could be somewhat enlarged (up to 10–15%) at small scattering angles (below 35°) due to corrections to the effective scattering volume, which were obtained according to benchmark DCSs measured for Ar. The errors for absolute DCSs, obtained by relative flow technique is dominantly defined by the error of reference absolute DCSs for Ar, which we assume to be about 20%. The later thus defines a minimal uncertainty of our results, while the overall error of the present absolute elastic DCSs for formamide is estimated to be up to 25%. 3. Calculations
Fig. 2. Schematic drawing of the gas system for relative flow measurements.
The calculations of absolute DCSs are performed by applying a corrected form of the independent atom method (IAM), known as the screen corrected additivity rule (SCAR) procedure, and using an improved quasifree absorption model, which includes relativistic and many-body effects, as well as inelastic processes. The advantage of the SCAR procedure is that accounts for the overlapping of atomic cross sections inside the molecule, thus correcting (reducing) cross sections obtained by the IAM. A detailed description of the theoretical procedure applied in the present work can be found elsewhere [20]. Finally, it should be noted that the present method for DCS calculations gave a very good agreement with experimental results in our previous investigation of electron interaction with different molecules representing DNA sub-units (see [2,3] and references therein).
126
J.B. Maljkovic´ et al. / Nuclear Instruments and Methods in Physics Research B 279 (2012) 124–127
4. Results The absolute DCSs for elastic scattering of electrons from formamide molecule at incident energies of 100, 150 and 300 eV are shown in Fig. 3. One can see a very good agreement between experimental and theoretical data, both in DCSs shape and on the absolute scale. A small disagreement, out of error bars can be seen only at the lowest angles but it is difficult to determine which data set (experimental or theoretical) is more accurate in this region. The SCAR theoretical procedure can suffer from an overestimation of DCSs at small angles, as discussed previously [3]. On the other hand, measurement of the DCSs at small scattering angles is less accurate due to an influence of the primary electron beam and higher uncertainty of the effective scattering volume. Generally, the angle dependent DCSs for elastic electron/formamide scattering at higher incident energies show strong forward peaking without sharp structures. A shallow minimum at about 90° disappears with increasing the energy, similarly to previously reported results for biomolecules [2,3]. The relative experimental DCSs measured as a function of angle are normalized according to relative flow measurements at specific incident energies and scattering angles, which are also shown. The independently measured absolute values are also in good
Table 1 Experimentally obtained DCSs for elastic electron scattering from formamide in units of 10 20 m2 sr 1 as a function of scattering angle (h) and incident energy (E0). The absolute errors of relative cross sections (statistical, short-term stability and uncertainty of the effective scattering volume) are up to 15%. The errors of the absolute cross sections are estimated to be up to 25% (see Section 2 for detailed error discussion). h (°)
20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110
E0 (eV) 100
150
300
– – – 0.841 0.602 0.431 0.319 0.221 0.182 0.135 0.120 0.106 0.105 0.102 0.0968 0.101 0.108 0.115 0.123
1.70 1.33 0.933 0.501 0.327 0.245 0.185 0.128 0.102 0.0898 0.0809 0.0769 0.0684 0.0672 0.0690 0.0661 0.0685 0.0670 0.0685
0.971 0.616 0.464 0.283 0.220 0.144 0.107 0.0866 0.0705 0.0584 0.0525 0.0453 0.0381 0.0333 0.0291 0.0279 0.0261 0.0264 0.0253
Fig. 4. Energy dependence of absolute DCS for elastic electron scattering from formamide at the scattering angles of 60°. Extracted absolute experimental results (circles) are compared with the calculated curve (line).
accordance with the DCS shape. The experimental absolute DCSs are tabulated in Table 1. Fig. 4 shows the energy dependence of the DCS at one fixed scattering angle. The decreasing of the DCS as a function of the incident energy is similar as for previously measured molecules, e.g. [2,3]. It should be noted a good agreement between calculated results and data extracted from experimentally obtained absolute DCS in Table 1. According to our knowledge, there is no existing DCS data for formamide to compare with the present results. However, it should be pointed out that the present calculation of the integral elastic cross section at 10 eV of 24.5 [10 20 m2] agrees very well with the recent result obtained by Schwinger multichannel method [4]. Acknowledgments Fig. 3. Angular dependence of absolute DCSs for elastic electron scattering from formamide molecule at different incident energies. The final experimental results (circles) are presented together with the values obtained directly by relative-flow measurements (stars). The calculated absolute DCSs are presented obtained by full line.
The work was supported by the Ministry of Education and Science of Republic of Serbia (Project No. 181020) and Spanish Ministerio de Ciencia e Innovación Project FIS2009-10245, and motivated by COST projects ECCL (CM0601) and Nano-IBCT
J.B. Maljkovic´ et al. / Nuclear Instruments and Methods in Physics Research B 279 (2012) 124–127
(MP1002). We are also grateful to Dr. A. Giuliani from SOLEIL for discussion that initiated this work. References [1] B. Boudaiffa, P. Cloutier, D. Hunting, M.A. Huels, L. Sanche, Science 287 (2000) 1658. [2] J.B. Maljkovic´, A.R. Milosavljevic´, F. Blanco, D. Ševic´, G. García, B.P. Marinkovic´, Phys. Rev. A 79 (2009) 052706. [3] A.R. Milosavljevic´, F. Blanco, J.B. Maljkovic´, D. Ševic´, G. García, B.P. Marinkovic´, New J. Phys. 10 (2008) 103005. [4] M. Bettega, Phys. Rev. A 81 (2010) 062718. [5] J.M. Hollis, F.J. Lovas, A. Remijan, P.R. Jewell, V. Ilushin, I. Kleiner, Astophys. J. 643 (2006) L25. [6] B.M. Jones, C.J. Bennett, R.I. Kaiser, Astophys. J. 734 (2011) 78. [7] J.R. Brucato, G.A. Baratta, G. Strazzulla, Astron. Astrophys. 455 (2006) 395–399. [8] S. Leach, H.W. Jochims, H. Baumgärtel, J. Phys. Chem. A 114 (2010) 4847–4856.
127
[9] T. Hamann, A. Edtbauer, F. Ferreira, S. da Silva, P. Denifl, P. Scheier, P. Swiderek, Phys. Chem. Chem. Phys. 13 (2011) 12305. [10] S.K. Srivastava, A. Chutjian, S.J. Trajmar, Chem. Phys. 63 (1975) 2659. [11] J.C. Nickel, P.V. Zetner, G. Shen, S. Trajmar, J. Phys. E Sci. Instrum. 22 (1989) 730. [12] J.F. Williams, A.J. Crowe, J. Phys. B: At. Mol. Opt. Phys. 8 (1975) 2233. ˇ adezˇ, B.P. Marinkovic´, J. Phys. B: [13] A.R. Milosavljevic´, S. Mandzˇukov, D. Ševic, I. C At. Mol. Opt. Phys. 39 (2006) 609. [14] G.C.G. Waschewsky, R. Horansky, V. Vaida, J. Phys. Chem. 100 (1996) 11559. [15] C. Colominas, F. Javier Luque, M. Orozco, J. Phys. Chem. A 103 (1999) 6200. [16] Z. Brnstein und Bd I. Funktionen., Atom und Molekularphysik 1. Atome und Ionen, Springer, Berlin, 1950. [17] M.A. Khakoo et al., J. Phys. B: At. Mol. Opt. Phys. 40 (2007) 3601. [18] H. Silva, J. Muse, M.C.A. Lopes, M.A. Khakoo, Phys. Rev. Lett. 101 (2008) 033201. [19] M.G.P. Homem, I. Iga, R.T. Sugohara, I.P. Sanches, M.T. Lee, Rev. Sci. Instrum. 82 (2011) 013109. [20] F. Blanco, G. García, Phys. Lett. A 360 (2007) 707.
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Elastic electron scattering from formamide molecule J.B. Maljkovic´ a, F. Blanco b, G. García c, B.P. Marinkovic´ a, A.R. Milosavljevic´ a,⇑ a
Laboratory for Atomic Collision Processes, Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia Departamento de Física Atómica Molecular y Nuclear, Facultad de Ciencias Físicas, Universidad Complutense, Avda. Complutense s/n, E-28040 Madrid, Spain c Instituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 121, 28006 Madrid, Spain b
a r t i c l e
i n f o
Article history: Received 13 July 2011 Received in revised form 8 September 2011 Available online 17 November 2011 Keywords: Formamide Elastic electron scattering Differential cross sections Relative flow method
a b s t r a c t Elastic electron scattering from gaseous formamide (H2NCHO) has been investigated. Absolute elastic differential cross sections (DCSs) were determined both experimentally and theoretically. The measurements were performed using a cross beam technique, for the incident energies of 100, 150 and 300 eV and scattering angles from 20° to 110°. Relative elastic DCSs were measured as a function of the angle and the absolute DCSs were determined using the relative flow method. The calculations of electron interaction cross sections are based on a corrected form of the independent-atom method, known as the SCAR (screen corrected additivity rule) procedure and using an improved quasifree absorption model. Calculated results agree very well with the experiment. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Formamide (H2NCHO) represents the smallest molecular system containing the peptide bond (see Fig. 1). Therefore, the investigation on electron interaction with formamide can be useful to understand processes of electron–protein interactions and modeling of energy deposition upon high-energy irradiation of bio-material. Investigation of electron interaction with small biomolecules representing building blocks of large bio-systems (RNA, DNA, proteins) has been mainly motivated in recent years by radiation damage research [1]. With this respect, our previous work includes measurements of absolute differential cross sections for electron scattering from several different molecules representing backbone sugar and nucleobasis sub-units of DNA [2,3]. However, to our knowledge, there are no published absolute differential cross sections for electron interaction by formamide molecule, which may be used as a basic sub-unit of the protein chain. Most recently, integral and momentum transfer cross sections for elastic scattering of low energy electrons (1–12 eV) by formamide [4], using Schwinger multichannel method have been reported. On the other hand, the formamide, which is considered as a prebiotic molecule has been attracting considerable attention in recent years in the astrobiological research, since it has been identified in the interstellar regions [5]. Within this context, some of the recent results include the laboratory studies either on production of formamide in interstellar ice analogs [6] or chemical evolution of formamide under ion irradiation at low temperature (simulated ⇑ Corresponding author. E-mail address: [email protected] (A.R. Milosavljevic´). 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2011.10.029
astrophysical conditions) [7]. Furthermore, recent photoionization mass spectrometric study of formamide have been carried out using synchrotron radiation over the photon energy range 10–20 eV [8]. Finally, Hamann et al. [9] have been investigating dissociative electron attachment to gas phase formamide, using cross electron/molecule beam technique. In the present study, we report differential cross sections (DCSs) for elastic electron–formamide scattering at 100, 150 and 300 eV incident energies, obtained using a crossed beam spectrometer. Absolute DCSs were determined according to relative flow technique [10,11]. These absolute values were then used to normalize relative DCSs. The experimental procedure has been checked according to DCS measurements for Ar [12].
2. Experimental set-up The experimental set-up is described previously [13]. Briefly, an electron gun produces the electron beam that is crossed perpendicularly by molecular beam, obtained by nonmagnetic stainless steel needle. The scattered electrons are retarded and focused into the double mirror cylindrical energy analyzer DCMA, followed by a three-element lens to further focus transmitted beam into the channel multiplier. The electron gun can be rotated around the needle in the angular range from about 40° to 120°. The base pressure was about 4 10 7 mbar. The working pressure was usually in the range (2–5) 10 6 mbar. The best energy resolution is limited by a thermal spread of primary electrons to about 0.5 eV. Formamide, with declared purity better than 99%, was used after several freeze–thaw cycles under vacuum. Gaseous formamide was introduced into the scattering region from a glass container via a
J.B. Maljkovic´ et al. / Nuclear Instruments and Methods in Physics Research B 279 (2012) 124–127
Fig. 1. Schematic drawing of formamide molecule and peptide bond linking two amino acids.
gas line system, which was heated to provide stable experimental conditions and to improve the signal. The influence of formamide dimerization to the measured scattered electron current was presumed to be negligible for the used experimental conditions (low pressure and increased temperature, see below details) due to a very low dimer/monomer proportion [14,15]. At a given electron energy, the relative cross section has been derived as a function of scattering angle, from 20° to 110° (in 10° steps), by measuring the elastic scattering intensity. The background contributions which were typically below 15% of the elastic electron intensities have been subtracted from the measured electron yields. The calibration of both angular scale and true zero angular position, as well as reliability of DCS shapes, have been tested according to DCSs for elastic electron–Ar scattering. The latter were obtained under the same experimental conditions, and showed very good agreement with previous results. The relative cross sections were next normalized to the absolute values obtained at several scattering angles (40°, 80° or 90°) using the relative flow technique [10,11] and procedure described in [3], and Ar as a reference gas [12]. In the relative flow method, the DCS for scattering of the unknown gas is determined by comparing scattered electron intensities from a standard target (here Ar), with its known differential cross sections, at a given incident electron energy (E0) and a scattering angle (h), and applying measured relative flow-rates (FRs) of both gases, as well as their known
125
molecular weights (see the formula in, e.g. [3]). Here, identical collision region geometry conditions are assumed. The scheme of the present gas system which allows efficient relative flow measurement procedure and background subtraction is shown in Fig. 2. To obtain the same profiles for both gas beams, the gases should be operated at pressures behind the needle so that their mean-free paths are the same. The pressure of formamide behind the tube forming the molecular beam was maintained below 0.2 mbar. The ratio of the pressures behind the tube for formamide to that of Ar was adjusted to be about 1.4, according to gas kinetic diameters [16]. However, during the measurements it has been proved by varying the ratio of the Ar and formamide pressures that absolute values of the cross sections do not depend crucially on the pressure ratio to within uncertainties in the measured cross sections. Actually, the experimental challenge in the work with formamide is to obtain stable conditions, such as pressure behind the gas needle. Note that it has been shown recently that the relative flow method may be performed without a need to know the molecular diameters of used gases, with an appropriate molecular source [17,18]. On the other hand, Homem et al. have argued in the most recent report [19] that in fact, the effect of vapor adsorption on surfaces may significantly affect the relative FR determination and thus the measured absolute DCS. In the present experiment, the relative FR were determined using the method of pressure-increase (MPI), as defined in [19], by closing the capillary valve (CV) and recording the MKS pressure increase versus time (see Fig. 2). Since the whole gas handling system (including capillary) was heated to about 60 °C, the influence of adsorption effect should be reduced to within stated experimental uncertainty. It should be noted, however, that we did see a difference in the measured FRs when operating experiment at lower, ambient temperatures, which is in line with the study in Ref. [19]. The errors for the relative DCSs measured as a function of the scattering angle include statistical errors (0.2–5%) according to Poisson’s distribution and short term stability errors (0.3–7.5%) according to discrepancy of repeated measurements at the same incident energy and scattering angle. The error of the relative angle-differential DCSs could be somewhat enlarged (up to 10–15%) at small scattering angles (below 35°) due to corrections to the effective scattering volume, which were obtained according to benchmark DCSs measured for Ar. The errors for absolute DCSs, obtained by relative flow technique is dominantly defined by the error of reference absolute DCSs for Ar, which we assume to be about 20%. The later thus defines a minimal uncertainty of our results, while the overall error of the present absolute elastic DCSs for formamide is estimated to be up to 25%. 3. Calculations
Fig. 2. Schematic drawing of the gas system for relative flow measurements.
The calculations of absolute DCSs are performed by applying a corrected form of the independent atom method (IAM), known as the screen corrected additivity rule (SCAR) procedure, and using an improved quasifree absorption model, which includes relativistic and many-body effects, as well as inelastic processes. The advantage of the SCAR procedure is that accounts for the overlapping of atomic cross sections inside the molecule, thus correcting (reducing) cross sections obtained by the IAM. A detailed description of the theoretical procedure applied in the present work can be found elsewhere [20]. Finally, it should be noted that the present method for DCS calculations gave a very good agreement with experimental results in our previous investigation of electron interaction with different molecules representing DNA sub-units (see [2,3] and references therein).
126
J.B. Maljkovic´ et al. / Nuclear Instruments and Methods in Physics Research B 279 (2012) 124–127
4. Results The absolute DCSs for elastic scattering of electrons from formamide molecule at incident energies of 100, 150 and 300 eV are shown in Fig. 3. One can see a very good agreement between experimental and theoretical data, both in DCSs shape and on the absolute scale. A small disagreement, out of error bars can be seen only at the lowest angles but it is difficult to determine which data set (experimental or theoretical) is more accurate in this region. The SCAR theoretical procedure can suffer from an overestimation of DCSs at small angles, as discussed previously [3]. On the other hand, measurement of the DCSs at small scattering angles is less accurate due to an influence of the primary electron beam and higher uncertainty of the effective scattering volume. Generally, the angle dependent DCSs for elastic electron/formamide scattering at higher incident energies show strong forward peaking without sharp structures. A shallow minimum at about 90° disappears with increasing the energy, similarly to previously reported results for biomolecules [2,3]. The relative experimental DCSs measured as a function of angle are normalized according to relative flow measurements at specific incident energies and scattering angles, which are also shown. The independently measured absolute values are also in good
Table 1 Experimentally obtained DCSs for elastic electron scattering from formamide in units of 10 20 m2 sr 1 as a function of scattering angle (h) and incident energy (E0). The absolute errors of relative cross sections (statistical, short-term stability and uncertainty of the effective scattering volume) are up to 15%. The errors of the absolute cross sections are estimated to be up to 25% (see Section 2 for detailed error discussion). h (°)
20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110
E0 (eV) 100
150
300
– – – 0.841 0.602 0.431 0.319 0.221 0.182 0.135 0.120 0.106 0.105 0.102 0.0968 0.101 0.108 0.115 0.123
1.70 1.33 0.933 0.501 0.327 0.245 0.185 0.128 0.102 0.0898 0.0809 0.0769 0.0684 0.0672 0.0690 0.0661 0.0685 0.0670 0.0685
0.971 0.616 0.464 0.283 0.220 0.144 0.107 0.0866 0.0705 0.0584 0.0525 0.0453 0.0381 0.0333 0.0291 0.0279 0.0261 0.0264 0.0253
Fig. 4. Energy dependence of absolute DCS for elastic electron scattering from formamide at the scattering angles of 60°. Extracted absolute experimental results (circles) are compared with the calculated curve (line).
accordance with the DCS shape. The experimental absolute DCSs are tabulated in Table 1. Fig. 4 shows the energy dependence of the DCS at one fixed scattering angle. The decreasing of the DCS as a function of the incident energy is similar as for previously measured molecules, e.g. [2,3]. It should be noted a good agreement between calculated results and data extracted from experimentally obtained absolute DCS in Table 1. According to our knowledge, there is no existing DCS data for formamide to compare with the present results. However, it should be pointed out that the present calculation of the integral elastic cross section at 10 eV of 24.5 [10 20 m2] agrees very well with the recent result obtained by Schwinger multichannel method [4]. Acknowledgments Fig. 3. Angular dependence of absolute DCSs for elastic electron scattering from formamide molecule at different incident energies. The final experimental results (circles) are presented together with the values obtained directly by relative-flow measurements (stars). The calculated absolute DCSs are presented obtained by full line.
The work was supported by the Ministry of Education and Science of Republic of Serbia (Project No. 181020) and Spanish Ministerio de Ciencia e Innovación Project FIS2009-10245, and motivated by COST projects ECCL (CM0601) and Nano-IBCT
J.B. Maljkovic´ et al. / Nuclear Instruments and Methods in Physics Research B 279 (2012) 124–127
(MP1002). We are also grateful to Dr. A. Giuliani from SOLEIL for discussion that initiated this work. References [1] B. Boudaiffa, P. Cloutier, D. Hunting, M.A. Huels, L. Sanche, Science 287 (2000) 1658. [2] J.B. Maljkovic´, A.R. Milosavljevic´, F. Blanco, D. Ševic´, G. García, B.P. Marinkovic´, Phys. Rev. A 79 (2009) 052706. [3] A.R. Milosavljevic´, F. Blanco, J.B. Maljkovic´, D. Ševic´, G. García, B.P. Marinkovic´, New J. Phys. 10 (2008) 103005. [4] M. Bettega, Phys. Rev. A 81 (2010) 062718. [5] J.M. Hollis, F.J. Lovas, A. Remijan, P.R. Jewell, V. Ilushin, I. Kleiner, Astophys. J. 643 (2006) L25. [6] B.M. Jones, C.J. Bennett, R.I. Kaiser, Astophys. J. 734 (2011) 78. [7] J.R. Brucato, G.A. Baratta, G. Strazzulla, Astron. Astrophys. 455 (2006) 395–399. [8] S. Leach, H.W. Jochims, H. Baumgärtel, J. Phys. Chem. A 114 (2010) 4847–4856.
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