Evaluation report for the inelastic differential cross section


Lin-Fan Zhu


All of the inelastic differential cross sections (IDCS’s) have been measured by the traditional electron energy loss spectrometer, and most of them were normalized to their absolute elastic differential cross sections. The IDCS includes the ones for the vibrational excitations and the electronic excitations. This time we have collected the IDCS’s for 7 molecules, I will give this evaluation report according to different molecules.


I. IDCS’s for CO

The very early experimental study of the IDCS’s for the electronic excitations of CO was carried out by Tramjar et al. [1]. Subsequent to this work, Zetner and Trajmar [2] reported a preliminary series of low-energy measurements (12.5 and 15 eV) for , ,  and  electronic states. This data has been recently updated by Zetner et al. [3]. The most comprehensive experimental study to date for the electronic excitations of CO is due to Middleton et al. [4]. In this work, IDCS’s for ,, , , , , ,  andelectronic states were reported at incident electron energies of 20, 30, 40 and 50 eV. These IDCS’s in 10°–90° were obtained by a deconvolution technique. For the higher incident electron energies, the IDCS’s in the angular range of 5–120° for the,  and  states were measured by Kanik et al. [5] at 100 eV. The IDCS’s for theelectronic state were measured by Zobel et al. [6] with near threshold excitation function. This preliminary study of Zobel et al. [6] has been extended [7, 8] to other electronic states, i.e., , , , , ,  and . This work was carried out at incident energies of 6.5–15.2 eV and for the scattered angles between 20° and 140°.

From a theoretical perspective, the complicated nature of the electron–target interaction potential has prevented rapid progress. Lee and McKoy [9] employed a distorted-wave model to calculate IDCS’s for the, , ,  and  excitations at the incident energies of 20–50 eV. Weatherford and Huo [10] have applied a Schwinger multichannel (SMC) formulation to calculate IDCS’s for  at incident energies of 10–20 eV. Sun et al. [11] have employed Schwinger multichannel variational method to calculate IDCS’s for , , , , ,  and  at incident energies of 6.5–30 eV. An extensive series of distorted-wave calculations for electron impact excitation of ,, and were carried out by Lee et al. [12], the incident electron energies were 20–100 eV.

The experimental IDCS’s of Zetner et al. [3], Middleton et al. [4], Kanik et al. [5] and Zobel et al. [7,8] for , , ,  , , , ,,  and  are recommended.

The IDCS’s for the first vibrational excitation () have been reported by Chutjian and Tanaka [13] at incident energies of 3–100 eV and by Middleton et al. [4] and Gibson et al. [14] at incident energies between 1 and 50 eV. At 20 eV where the well-known COresonance exists, the data of Middleton et al. [4] are subject to a mismatch effect in the incident energies, while such an effect is minimized by Gibson et al. [14]. Moreover, in a region away from theshape resonance the data of Gibson et al. [14] and Middleton et al.[4] are in good agreement, while the data of Chutjian and Tanaka[13] underestimates the magnitude of the IDCS’s across the entire angular range. So for the same incident electron energies the more recently experimental data of Gibson et al. [14] are recommended.


Ⅱ. IDCS’s for CO2

There are two experimental IDCS’s of CO2. One is made by Sophia University group in Japan for the differential cross sections of the vibrational excitations of carbon dioxide [15]. The absolute values were obtained by normalizing the inelastic cross sections to the elastic ones measured in Ref. [16], their experimental errors are estimated to be 30% including the errors in deconvolving the intensity of the individual vibrational modes from the energy-loss spectra (5%). The other is made by the Flinders University group in Australia group and the Sophia University group independently [17]. The accuracy of their experimental methods was established independently by using several different normalization techniques at both Sophia and Flinders Universities.


III. IDCS’s for H2O

The experimental IDCS’s of the vibrational excitations for H2O have been reported by Seng and Linder [18,19], Trajmar et al. [20], Shyn et al. [21], Furlan et al. [22] and El-Zein et al. [23,24]. Seng and Linder [19] reported the cross sections for the vibrational excitations of the bending (010) and unresolved stretching (100 + 001) modes for the incident energy range 0.35–8 eV. Trajmar et al. [20] measured the relative IDCS’s for the vibrational excitations of the (100,001) modes at impact energies of 15 and 53 eV. Shyn et al. [21] reported IDCSs in 30°-150° for the bending (010) and unresolved stretching (100 + 001) modes at seven energies in the range of 2.2–20 eV. Furlan et al. [22] reported the IDCS’s in 10°-60° for the two vibrational modes at incident energies of 30 and 50 eV. El-Zein et al. [23] determined the IDCSs for the same vibrational modes at the single energy 7.5 eV. The work [23] is extended to eight energies in the range 6-20 eV and angular range 10°-135° by El-Zein et al. [24]. Among these mentioned works, only the data of Shyn et al. [21] and El-Zein et al. [23,24] are given in tables. In addition, the work of El-Zein et al. [24] is recent and comprehensive. So the data of Shyn et al. [21] and El-Zein et al. [24] are recommended.


Ⅳ. IDCS’s for CH4

Only three experimental groups have reported the absolute IDCS’s of CH4 [25-27], which have been normalized to the absolute elastic DCS’s [28]. Both Curry et al. [25] and Tanaka et al. [27] investigated the IDCS’s for the vibrational excitations to  and  of CH4 respectively, while there are slight diferences in the incident energies and scattering angles between them. Vuskovic and Trajmar[26] divided the inelastic region from 7.5eV to 15eV into five ranges at impact energies of 20, 30 and 200eV, and their IDCS’s have been determined. However, the five ranges can not give the definite assignments. So we recommend the experimental IDCS’s of Refs. [25,27].


Ⅴ. IDCS’s for C2H4

The IDCS’s of C2H4 have been measured by Mapstone et al. [29], Asmis and Allan [30], and Walker et al. [31]. However, only the work of Mapstone et al. [29] has data tables. So we recommend the experimental data of Mapstone et al. [29].


Ⅵ. IDCS’s for C6H6

   Up to 2005, the experimental IDCS’s for the 1E1u+1 B1u 1Ag transition were only reported at 1 keV impact energy by Ref. [32]. IDCS’s were determined from the GOS values which was normalized to the known OOS. So this work is recommended.


. IDCS’s for C4F8

   To the best of our knowledge, up to 2005, the experimental IDCS’s for the excitation at 0.16 eV were only reported with the incident energies from 1.5 to 7.5eV by the relative flow technique [33]. So this work is recommended.



[1]      S. Trajmar, W. Williams and D. C. Cartwright, Proceedings VII ICPEAC, North Holland, Amsterdam, 1971, p1066

[2]      P. Zetner and S. Trajmar,  in J. Geddes et al.(Eds.), Proceeding of the XV ICPEAC, Brighton, England, 1987, p307

[3]      P. W. Zetner, I. Kanik and S. Trajmar, J. Phys. B 31, 2395(1998)

[4]      A .G. Middleton, M. J. Brunger and P. J. O. Teubner, J. Phys. B 26, 1743(1993)

[5]      I. Kanik, M. Ratliff and S. Trajmar, Chem. Phys. Lett. 208, 341(1993)

[6]      J. Zobel, U. May, K. Jung, D. N. Tripathi, D. K .Rai, H. Ehrhardt, in: H. Ehrhardt, L. A. Morgan (Eds.), Electron Collisions with Molecules, Clusters, Surfaces, Plenum Press, New York, 1994, p31.

[7]      J. Zobel, U. Mayer, K. Jung and H. Ehrhardt, J. Phys. B29, 813(1996)

[8]      J. Zobel, U. Mayer, K. Jung, H. Ehrhardt, H. Pritchard, C. Winstead and V. McKoy, J. Phys. B 29, 839(1996)

[9]      M.-T. Lee and V. McKoy, J. Phys. B 15, 3971(1982)

[10]  C. A. Weatherford and W. M. Huo, Phys. Rev. A 41, 186(1990)

[11]  Q. Sun, C. Winstead and V. McKoy, Phys. Rev. A 46, 6987 (1992)

[12]  M.-T. Lee, A. M. Machado, M. M. Fujimoto, L. E. Machado and L. M. Brescansin, J. Phys. B 29, 4285 (1996)

[13]  A. Chutjian and H. Tanaka, J. Phys. B 13, 1901(1980)

[14]  J. Gibson, L. A. Morgan, R. J. Gulley, M. J. Brunger and S. J. Buckman, J. Phys. B 29, 3197(1996)

[15]  M. Kitajima, S. Watanabe, H. Tanaka et al., J. Phys. B 34, 1929(2001)

[16]  H. Tanaka, T. Ishikawa, T. Masai et al., Phys. Rev. A 57, 1798(1998)

[17]  M. A. Green, P. J. O. Teubner, L. Campbell et al., J. Phys. B35,567 (2002)

[18]  G. Seng and F. Linder, J. Phys. B 7, L509(1974)

[19]  G. Seng and F. Linder, J. Phys. B 9, 2539(1976)

[20]  S. Trajmar, W. Williams and A. Kuppermann, J. Chem. Phys. 58, 2521(1973)

[21]  T. W. Shyn, S. Y. Cho, and T. E. Cravens, Phys. Rev. A 38, 678(1988)

[22]  M. Furlan, M. J. Hubin-Franskin, J. Delwiche and J. E. Collin, J. Chem. Phys. 95, 1671(1991)

[23]  A. El-Zein, M. J. Brunger and W. R. Newell, Chem. Phys. Lett. 319, 701(2000)

[24]  A. El-Zein, M. J. Brunger and W. R. Newell, J. Phys. B 33, 5033(2000)

[25]  P. J. Curry, W. R. Newell and A. C. H. Smith, J. Phys. B18, 2303(1985)

[26]  L.Vuskovic and S.Trajmar, J. Chem. Phys 78, 4947(1983)

[27]  H. Tanaka, M. Kubo, N. Onodera and A. Suzuki, J. Phys. B16,2861(1983)

[28]  H. Tanaka, T. Okada, L. Boesten, T. Suzuki, T. Yamamoto and M. Kubo, J. Phys. B15, 3305 (1982)

[29]  B. Mapstone, M. J. Brunger and W. R. Newell, J. Phys. B33, 23(2003)

[30]  K. R. Asmis and M. Allan, J. Chem. Phys. 106, 7044(1997)

[31]  I. C. Walker, A. Stamatovic and S. F. Wong, J. Chem. Phys. 69, 5532(1978)

[32]  H. M. Boechat Roberty, M. L. M. Rocco, C. A. Lucas and G. G. B. de SouzaJ. Phys. B37,1467(2004)

[33]  M. Jelisavcic, R. Panajotovic, M. Kitajima, M. Hoshino, H. Tanaka and S. J. Buckman, J. Chem. Phys.121, 5272(2004)