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Elastic Scattering of Electrons and Positrons VI. simpozij HDZZ, Stubičke Toplice HR0500032 ELASTIC SCATTERING OF ELECTRONS AND POSITRONS Ines Krajcar Bronić Ruder Bošković Institute, Bijenička 54, HR-10000 Zagreb, Croatia e-mail: [email protected] INTRODUCTION Electrons and positrons interact with matter through several competing mechanisms, elastic and inelastic scattering being the most abundant. Elastic scattering is considered as the non-radiative interaction between the projectile electron or positron and a target atom/molecule in which the internal energy of the target is not changed. In measurements of electron scattering by molecules, pure elastic scattering cannot be resolved from low-energy vibrational or rotational excitations; and the term quasi-elastic scattering is used. Elastic scattering has a prominent influence on the transport of fast electrons and positrons in matter. In elastic collisions, these particles may undergo large deflections and, as a result, the space distribution of dose from electrons and positrons depends strongly on the elastic scattering properties of the medium. The demand for accurate cross sections of electron and positron interactions with different atoms and molecular systems has been growing rapidly in the applied science community. In particular detailed information on elastic scattering of these particles by molecules is required for Monte Carlo simulations in microdosimetry, radiation dosimetry, nuclear medicine, radiation therapy, radiation protection, atmospheric and plasma physics, various electron-spectrotroscopic techniques, etc. A similar need arises in modeling the energy deposition associated with the interaction of any form of ionising radiation with matter. REPORT COMMITTEE International Commission for Radiation Units and Measurements (ICRU), having headquarters in Bethesda, MD, USA, formed in 2000 a Report Committee that should prepare a new ICRU Report on "Elastic Scattering of Electrons and Positrons" (ESEP). The report should constitute a synthesis of the leading scientific thinking on matters of radiation quantities, units and measurements techniques and provide recommendations that represent an international consensus on these matters [1]. The ICRU sponsors for this activity are Dr. Mitio Inokuti (Argonne National Laboratory, USA, and ICRU) and Mr. Steven M. Seltzer (National Institute of Standards and Technology, USA). Dr. Francesc Salvat (Faculty of Physics, University of Barcelona, Spain) has been appointed as the Chairman of the ESEP Report Committee. The members are Dr. Martin J. Berger (Bethesda, MD, USA, U12004), Prof. Dr. Aleksander Jablonski (Institute of Physical Chemistry, 78 VI. simpozij HDZZ, Stubičke Toplice, 2005. Polish Academy of Sciences, Warszawa, Poland), Dr. Ines Krajcar Bronić (Rudjer Bošković Institute, Zagreb, Croatia), Dr. James Mitroy (Faculty of Science, Northern Territory University, Darwin, Australia), Dr. Cedric J. Powell (NIST, USA) and Dr. Leon Sanche (Faculty of Medicine, University of Sherbrooke, Canada). The first meeting of the Report Committee was held in ICRU Headquarters in Bethesda, MD, in April 2000. The objectives and scopes of the report have been elaborated and the outline of the report was discussed. Each Report Committee member received specific tasks and duties. On the second meeting in Bethesda in December 2001, the individual contributions were presented and discussed. The next meeting of the Report Committee was held in Barcelona, Spain, in June 2003. The Report has been presented in its final form, and the discussion was directed into making the report more consistent and homogeneous. OUTLINE OF THE REPORT The ESEP Report consists of the following chapters: 1. Introduction (including nomenclature, application of data to be given in the Report, and scope of the report); 2. Experimental methods (measurement techniques of differential cross sections (DCS), integral elastic (ae|) and momentum transfer (amt) cross sections; for gases, liquids and solids); 3. Theoretical background (fundamentals of scattering theory, quantum theory, approximation methods, elastic scattering by molecules, scattering in the condensed phase, positron scattering); 4. Calculations for atoms (numerical calculation methods, properties of the phase shifts, DCS for atoms, high-energy factorization) for energies above 100 eV; 5. Experimental data (comparison of theoretical with experimental data, atomic and molecular gases, condensed phases); 6. Multiple-scattering angular deflections. Two appendices contain details on the theory of relativistic kinematics and the Dirac equation. Bibliography contains more than 300 relevant references. The CD ROM with the original software for calculating DCS will be distributed with the Report. For the calculation of DCSs for free atoms the central optical model potential is used [2]. The type of the incident particle and its energy, the target atom, and the choice of the model can be chosen by the user. A program for calculation DCSs for electron or positron scattering by molecules according to the independent atom approximation will be also available [3]. EXPERIMENTAL TECHNIQUES The experimental techniques used to study electron collisions with atoms and molecules can be broadly classified into two groups: beam experiments (where 19 VI. simpozij HDZZ, Stubičke Toplice, 2005. single collisions between individual scattering partners are examined), and swarm experiments (where the derived quantities are extracted from observation of the collective motion of a large number of charged particles, electron swarms). The two techniques are complementary, although often viewed as competitive. The swarm experiments yield absolute values of the elastic momentum transfer cross section amt, while beam experiments of direct attenuation give the elastic cross section, aei, (or total cross section, at), and the crossed-beam experiments provide the elastic differential cross section, DCS or da/dQ. The beam method is applicable to a wide range of energies, except very low energies, and the measurements are straightforward to interpret. However, the problems are: preparation of electron beams with very low energy, limited angular range accessible to measurement, the need of measurements with standard gases to derive absolute data. The swarm method is experimentally easier, and is particularly reliable at low energies (<1 eV), but requires a delicate numerical analysis to derive absolute values of the sought cross sections from the measured transport parameters. DATA EXAMPLES A large part of the available experimental data pertain to atomic gases, particularly to a limited group of atoms such as hydrogen, the rare gases, the alkalis and the earth alkalis, and some metals. Only a small set of cross-section data is available for more than half of the atoms in the period table, and data for molecules are even more limited. Experimental studies of positron collision have been performed by a limited number of groups. Elastic DCS for electron collisions with argon are presented in Figure 1. Differences between the measured data from different sources [4-14] indicate the magnitude of the uncertainty of experimental data. The calculated DCS (by using the software attached to the Report) exhibit nearly the same minimum at nearly the same angles as the measured DCS. However, the static-exchange potential used in calculation (dashed curves) overestimates the DCS at intermediate and large angles (more at lower energies) because the model neglects the absorption, i.e., the loss of electrons in open inelastic channels. At small scattering angles, and especially for low-energy electrons and positrons, this model underestimates DCS, because it neglects atomic polarizability. Thus, the validity of the static-field approximation is limited to energies above about few keV. The elastic, total scattering and momentum transfer cross sections for electrons in xenon are shown in Figure 2., and compared with the total cross section for positrons. Total cross sections are approximately equal to elastic cross sections at energies below about 10 eV, where no inelastic collisions take place. The a, for positrons and electrons have different energy dependences below 100 eV, but at higher energies the two values approach each other. The crmt in xenon, as 80 VI. simpozij HDZZ, Stubičke Toplice, 2005. well as in argon and krypton, exhibit a pronounced feature below 1 eV, namely a minimum in amt known as the Ramsauer-Townsend (RT) minimum). Different sets of crmt experimental data generally agree very well at all energies, except around the RT minimum. C Ciiipta and Rocs (I 975) o--»Ar(/ IS) v Williams and Willis < I 975b) DuHoisand Rudd (1970) |M-'* /:" 300 eV •; • Janson el ul. (1976) • Vuskovk- and Kurcpa (1976) X Srivaslava ol al. (1981) CJ Wagenaar el :il. (I 986) O C'vcjanovic and Crowe ( H llroml-vri; (1 974) o-lft X Wi 11 iciin.s and Willis f 1 975 i ~- • Jansenet al.( 1976) : Ai <Z IS) 6 i i lOOoV O |, n 1 1 150 180 60 90 120 150 ISO u e (Joii) • • 1 • • 1 i i • • 1 • • i I • • c —> Ar(Z IS) •» Ar (Z IS) 1...-" /;••••••- 500 eV 800 cV Bromherg (1 974) + Urombery (1974). 700 cV 1 DuBois and Rudd (1976) A IXiRois and Rudd (1 976) \ I.,- * r • Jansenel al. ( 1976) : n ot al. (1976). 750 eV X Iga otal. (1987) I - : \ It' l7 i ^—'"'ATE II-'" i | i 1 1 t • 1 III" <M <><) I2O 150 180 60 90 120 150 ISO 0 (cleg) 9 klog) Figure 1. Differential cross sections for elastic scattering of electrons by argon. Symbols: experimental data, static-field approximation, optical model calculations. 81 VI. simpozij HDZZ,
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