APPLICATION OF THE LAMBERT W-FUNCTION TO THE CALCULATION OF THE ELECTRON TRANSMISSION COEFFICIENT AND THE YIELD OF BREMSSTRAHLUNG FROM THE BETHE-HEITLER THEORY
https://doi.org/10.56304/S2079562925060090
EDN: PGYJKB
Abstract
Based on the theory of the interaction of electrons with matter (Bethe, Heitler, Bloch) during their multiple scattering (Goudsmit, Saunderson), analytical expressions were obtained for the electron transmission coefficient and the energy yield of bremsstrahlung. These expressions depend on the material and thickness of the target and the initial kinetic energy of the electron. An analytical expression for the electron range was also obtained with insignificant simplifications, using the Lambert-function.
References
1. Corless R.M., Gonnet G.H., Hare D.E.G., Jeffrey D.J., Knuth D.E. // Adv. Comput. Math. 1996. V. 5 (1). P. 329.
2. Mezo I. // J. Math. Anal. Appl. 2017. V. 455 (1). P. 538.
3. Mezo I., Baricz A. // Transact. Amer. Math. Soc. 2017. V. 369 (11). P. 7917.
4. Дубинов А.Е., Дубинова И.Д., Сайков С.К. W-функция Ламберта и ее применение в математических задачах физики: Учеб. пособ. для вузов. 2006. Саров: ФГУП “РФЯЦ-ВНИИЭФ”.
5. Стародубцев С.В., Романов А.М. Прохождение заряженных частиц через вещество. 1962. Ташкент: Акад. наук УзССР.
6. Attix F.H. Introduction to radiological physics and radiation dosimetry. 2004. Weinheim: WILEY-VCH Verlag GmbH & Co.
7. Gradshteyn I.S., Ryzhik I.M. Table of integrals, series, and products. 2007. Academic Press.
8. https://physics.nist.gov/PhysRefData/Star/Text/ESTAR.html.
9. Королюк В.Н., Усова Л.В. // Аналитика и контроль. 2002. Т. 6 (4). С. 353.
10. Goudsmit S., Saunderson J.L. // Phys. Rev. 1940. V. 57 (1). P. 24.
11. Lazurik V., Moskvin V., Tabata T. // IEEE Trans. Nucl. Sci. 1998. V. 45 (3). P. 626.
12. Belyshev S.S., Dzhilavyan L.Z., Stopani K.A. // Bull. Russ. Acad. Sci.: Phys. 2019. V. 83 (4). P. 458.
13. https://physics.nist.gov/PhysRefData/XrayMassCoef/tab3.html.
14. Isaev V.I., Kovalev V.P. // At. Energy. 1984. V. 56 (6). P. 425.
15. Scott T., Mann R., Martinez II.R. // Appl. Algebra Eng. Commun. Comput. 2006. V. 17 (1). P. 41.
Review
For citations:
Ivanov I.A. APPLICATION OF THE LAMBERT W-FUNCTION TO THE CALCULATION OF THE ELECTRON TRANSMISSION COEFFICIENT AND THE YIELD OF BREMSSTRAHLUNG FROM THE BETHE-HEITLER THEORY. Nuclear Physics and Engineering. 2025;16(6):823-830. (In Russ.) https://doi.org/10.56304/S2079562925060090. EDN: PGYJKB
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