Ядерна фізика та енергетика Nuclear Physics and Atomic Energy   ISSN: 1818-331X (Print), 2074-0565 (Online)   Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine   Languages: Ukrainian, English   Periodicity: 4 times per year   Open access peer reviewed journal

Full text (en)

V. N. Maslov¹, Yu. P. Stepanovsky<sup>2

1</sup>Theoretical Physics Department, V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
²National Science Center "Kharkiv Institute of Physics and Technology", National Academy of Sciences of Ukraine, Kharkiv, Ukraine

Abstract: Elastic scattering of the ultra relativistic polarized electrons on atomic nucleus with arbitrary spin is considered. The covariant parameterization of the electromagnetic current for a particle with arbitrary spin is used. This parameterization is based on the Bargman - Wigner formalism for the description of arbitrary spin particles (atomic nuclei) with using Tchebichef polynomials of a discrete variable for determination of the "physical" electromagnetic form factors that are electric and magnetic multipole momenta in the Breit reference frame. The generalized Rosenbluth formula is obtained for the cross section of the ultra relativistic electron scattering in a laboratory system in terms of the "physical" electromagnetic form factors as well as the initial and final polarization characteristics of the electron.

Keywords: elastic scattering, relativistic energy, polarized electrons, electromagnetic form factors, Bargman - Wigner formalism, Tchebichef polynomials, Rosenbluth formula.

1. Meckler A. On the algebra of angular momentum. Supplemento al Nuovo Cim. 12 (1959) 40. https://doi.org/10.1007/BF02726533

2. Hofstadter R. Electron Scattering and Nuclear Structure. Rev. Mod. Phys. 28 (1956) 215. https://doi.org/10.1103/RevModPhys.28.214

3. Hofstadter R. Structure of Nuclei and Nucleons (Nobel Lecture, 1961). Science 136 (1962) 1013. https://doi.org/10.1126/science.136.3521.1013

4. Gourdin M. Electromagnetic form factors. Nuovo Cim. 36 (1965) 129. https://doi.org/10.1007/BF02750666

5. Gourdin M., Micheli J. Electromagnetic form factors. - II. Nuovo Cim. A 40 (1965) 225. https://doi.org/10.1007/BF02832921

6. Kirichenko I. K., Stepanovsky Yu.P. "Physical" form factors and covariant parameterization of electromagnetic current for particle with arbitrary spin. Phys. Atom. Nucl. 20 (1974) 554.

7. Tchebicheff P. L. Sur une nouvelle série. Bull. de la Classe phys.-mathém. de l’Acad. Imp. de sciences de St.-Pétersbourg (1859) Vol. 17, p. 257.

8. Bateman H. Higher Transcendental Functions Vol. 2, Ch. 10 (New York - Toronto - London: McGraw-Hill Book Company, Inc., 1953) 356 p.

9. Akhiezer A. I., Berestecky V. B. Quantum Electrodynamics. 4-th ed. Ch. 1 (Moscow: Nauka, 1981) 432 p.

10. Bargman V., Wigner E. P. Group Theoretical Discussion of Relativistic Wave Equations. Proc. Nat. Acad. Sci. USA 34 (1948) 211. https://doi.org/10.1073/pnas.34.5.211

11. Rekalo M. P., Tomasi-Gustafsson E. Polarization effects in elastic electron-proton scattering (Lecture notes). nucl-th/0202025.

12. Dogyust I. V., Stepanovsky Yu. P. On calculation of probabilities of scattering processes with polarized spin 1/2 particles. Phys. Atom. Nucl. 8 (1968) 382.

13. Mott N. F. The Scattering of Fast Electrons by Atomic Nuclei. Proc. R. Soc. Lond. A 124 (1929) 425. https://doi.org/10.1098/rspa.1929.0127

14. Rosenbluth M. N. High Energy Elastic Scattering of Electrons on Protons. Phys. Rev. 79 (1950) 615. https://doi.org/10.1103/PhysRev.79.615