Z. Phys. D 32, 93-100 (1994) ZEITSCHRIFT FORPHYSIK D ~) Springer-Verlag 1994 Phenomenology and scaling of electron scattering cross sections from "almost spherical" molecules over a wide energy range Norman H. March t, Antonio Zecca 2, Grzegorz P. Karwasz 2 Theoretical ChemistryDepartment, Universityof Oxford, 5 South Parks Road, Oxford OX1 3UB, UK 2Dipartimento di Fisica, Universitfidegli Studi di Trento, 1-38050 Povo (Trento), Italy (Fax: +39-461/881696) Received: 18 May 1994 / Final version: 18 July 1994 Abstract. Total cross sections for electron scattering on "quasi spherical" (CH4, SiH4, GeH4)molecules have been analyzed phenomenologically over a wide energy range. Regions, at low and high energies can be usefully repre- sented by simple analytical formulae. Regularities associ- ated with characteristic points such as the Ramsauer minima have been exposed. Comparison with other sim- ple hydrides (NH3, H20, H2S) allows the demonstration of a possible correlation between the maximum value of the total cross section and the bond length. Some points of contact with first-principles theory are noted and in particular the energy at which the maximum cross sec- tion occurs, is related to the occurrence of a partial wave resonance. In the absence of complete data for GeH4, prediction of characteristic points in the low energy cross section proves possible via the phenomenological analy- sis. Similarly, in the high energy regime, predictions of the cross section for SnH 4 is made from data on the lighter molecules of the series, using non-relativistic Thomas- Fermi self consistent field scaling. PACS: 34.80.Bm; 34.80.Gs I. Introduction In recent years numerous careful prepared experiments have yielded measurements of total cross sections for elec- tron-atom scattering. However, in spite of such efforts, quite large discrepancies (up to 50%) remain in the de- termination of characteristic features of the cr (E) curves. Relatively fewer data exist when one turns to the case of molecular targets, in spite of their practical impor- tance. Methane is the most extensively studied molecule experimentally (see [ 1] for the recent review of total cross sections between 1 and 4000 eV). The Ramsauer mini- mum for this molecule, for example, has been determined in independent experiments [2, 3] with better accuracy than for Kr and Xe [4-6]. A similar minimum in the total elastic cross section has been observed for CF 4 [7]. Swarm data [8-10] suggest the existence of a Ramsauer minimum also for Sill 4. The existence of the above data for certain "almost spherical" molecules, typified by CH4, Sill 4 and GeH 4 especially, has prompted us to attempt a comparative analysis of existing measurements. The approach adopted is to consider cross section data over a wide energy range, and to employ phenomenotogical, and also scaling ar- guments. As further background to the present study, it is rele- vant to note that analyzing the total cross section cr (E) for electron scattering from rare gases and CH 4 for energy E less than the energy coresponding to the Ramsauer minimum, ER say, Freeman and March [ 11 ]) proposed as "independent variable" the quantity {Ea (E)} 1/~ "~(k2o') 1/2, with E=h2k2/2m. They found Ea = const: E c < E < E R (1.1) down to some (not, as yet, sharply defined) energy Ec, below which ao = 4 rta 2 , E < E c (1.2) where a is the scattering length. A similar relation to that in Eq. (1.1), namely Ea = B, was earlier found by Zecca et al. [12] for electron scattering from simple hydrides (CH 4, Sill 4, NH 3, H20, HzS) at high energies, beyond some "asymptotic energy", E z say. In that approximation a (E) tends to a constant value o'z for E~ E z. The purpose of the present work, apart from providing a phenomenological analysis of the total cross sections for a set of light molecules over a wide energy range, is to forge links between the two "asymptotic" regimes de- tailed above. Lack of complete data for low energy scat- tering from Sill 4 and GeH 4 has motivated the examina- tion of other simple targets, like NH3, HzO, HzS which, although not being spherical, can be also treated in a one- center expansion [13]. We felt it of interest to include also CF4: though evidently less spherical because of core electrons on the outer atoms (compare [ 14] for utility of one-center expansion).