Path integral approach to electron scattering in classical electromagnetic potential

doi:10.1088/1674-1056/25/5/050303

中国物理B ›› 2016, Vol. 25 ›› Issue (5): 50303-050303.doi: 10.1088/1674-1056/25/5/050303

Path integral approach to electron scattering in classical electromagnetic potential

Chuang Xu(许闯), Feng Feng(冯锋), Ying-Jun Li(李英骏)

School of Science, China University of Mining and Technology, Beijing 100083, China

收稿日期:2015-08-23 修回日期:2015-12-18 出版日期:2016-05-05 发布日期:2016-05-05
通讯作者: Chuang Xu, Ying-Jun Li E-mail:xu.chuang.phy@gmail.com;lyj@aphy.iphy.ac.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11374360, 11405266, and 11505285) and the National Basic Research Program of China (Grant No. 2013CBA01504).

Path integral approach to electron scattering in classical electromagnetic potential

Chuang Xu(许闯), Feng Feng(冯锋), Ying-Jun Li(李英骏)

School of Science, China University of Mining and Technology, Beijing 100083, China

Received:2015-08-23 Revised:2015-12-18 Online:2016-05-05 Published:2016-05-05
Contact: Chuang Xu, Ying-Jun Li E-mail:xu.chuang.phy@gmail.com;lyj@aphy.iphy.ac.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11374360, 11405266, and 11505285) and the National Basic Research Program of China (Grant No. 2013CBA01504).

摘要/Abstract

摘要： As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon single-particle Schrodinger equation or Dirac equation in quantum mechanics rather than the method of quantum field theory. In this paper, by using the path integral approach of quantum field theory, we perturbatively evaluate the scattering amplitude up to the second order for the electron scattering by the classical electromagnetic potential. The results we derive are convenient to apply to all sorts of potential forms. Furthermore, by means of the obtained results, we give explicit calculations for the one-dimensional electric potential.

关键词: electron scattering, path integral approach, quantum field theory

Abstract: As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon single-particle Schrodinger equation or Dirac equation in quantum mechanics rather than the method of quantum field theory. In this paper, by using the path integral approach of quantum field theory, we perturbatively evaluate the scattering amplitude up to the second order for the electron scattering by the classical electromagnetic potential. The results we derive are convenient to apply to all sorts of potential forms. Furthermore, by means of the obtained results, we give explicit calculations for the one-dimensional electric potential.

Key words: electron scattering, path integral approach, quantum field theory

中图分类号: (Quantum mechanics)

03.65.-w

03.70.+k (Theory of quantized fields)

许闯, 冯锋, 李英骏. Path integral approach to electron scattering in classical electromagnetic potential[J]. 中国物理B, 2016, 25(5): 50303-050303.

Chuang Xu(许闯), Feng Feng(冯锋), Ying-Jun Li(李英骏). Path integral approach to electron scattering in classical electromagnetic potential[J]. Chin. Phys. B, 2016, 25(5): 50303-050303.

参考文献 32

[1]	Dirac P A M 1933 Physik. Zeits. Sowjetunion 3 64
[2]	Feynman R P 1948 Rev. Mod. Phys. 20 367
[3]	Feynman R P 1963 Acta Phys. Pol. 24 697
[4]	Faddeev L D and Popov V N 1967 Phys. Lett. B 25 29
[5]	Hooft G't 1971 Nucl. Phys. B 35 167
[6]	Englert F and Brout R 1964 Phys. Rev. Lett. 13 321
[7]	Higgs P W 1964 Phys. Rev. Lett. 13 508
[8]	Higgs P W 1966 Phys. Rev. 145 1156
[9]	Weinberg S 1976 Phys. Rev. Lett. 36 294
[10]	Yanovsky V, Chvykov V, Kalinchenko G, Rousseau P, Planchon T, Matsuoka T, Maksimchuk A, Nees J, Cheriaux G, Mourou G and Krushelnick K 2008 Opt. Express 16 2109
[11]	Faure J, Glinec Y, Pukhov A, Kiselev S, Gordienko S, Lefebvre E, Rousseau J P, Burgy F and Malka V 2004 Nature 431 541
[12]	Faure J, Rechatin C, Norlin A, Lifschitz A, Glinec Y and Malka V 2006 Nature 444 737
[13]	Schoenlein R W, Leemans W P, Chin A H, Volfbeyn P, Glover T E, Balling P, Zolotorev M, Kim K J, Chattopadhyay S and Shank C V 1996 Science 274 236
[14]	Tomassini P, Giulietti A, Giulietti D and Gizzi L A 2005 Appl. Phys. B 80 419
[15]	Schwoerer H, Liesfeld B, Schlenvoigt H P, Amthor K U and Sauerbrey R 2006 Phys. Rev. Lett. 96 014802
[16]	Jochmann A, Irman A, Bussmann M, Couperus J P, Cowan T E, Debus A D, Kuntzsch M, Ledingham K W D, Lehnert U, Sauerbrey R, Schlenvoigt H P, Seipt D, Stohlker Th, Thorn D B, Trotsenko S, Wagner A and Schramm U 2013 Phys. Rev. Lett. 111 114803
[17]	Hartemann F V and Kerman A K 1996 Phys. Rev. Lett. 76 624
[18]	Bula C, McDonald K T, Prebys E J, Bamber C, Boege S, Kotseroglou T, Melissinos A C, Meyerhofer D D, Ragg W, Burke D L, Field R C, Horton-Smith G, Odian A C, Spencer J E, Walz D, Berridge S C, Bugg W M, Shmakov K and Weidemann A W 1996 Phys. Rev. Lett. 76 3116
[19]	Boca M and Florescu V 2009 Phys. Rev. A 80 053403
[20]	Seipt D and Kampfer B 2011 Phys. Rev. A 83 022101
[21]	Liang G H, Lü Q Z, Teng A P and Li Y J 2014 Chin. Phys. B 23 054103
[22]	Fan H Y, Zhang P F and Wang Z 2015 Chin. Phys. B 24 050303
[23]	Peskin M E and Schroeder D V 1995 An Introduction to Quantum Field Theory (Westview Press)
[24]	Lehmann H, Symanzik K and Zimmermann W 1955 Nuovo Cimento 1 205
[25]	Leo S D and Rotelli P 2009 Eur. Phys. J. C 62 793
[26]	Klein O 1929 Z. Phys. 53 157
[27]	Nikishov A I 1970 Nucl. Phys. B 21 346
[28]	Hansen A and Ravndal F 1981 Phys. Scr. 23 1033
[29]	McKellar B H J and Stephenson G J 1987 Phys. Rev. A 36 2566
[30]	Manogue C A 1988 Ann. Phys. 181 261
[31]	Dombey N and Calogeracos A 1999 Phys. Rep. 315 41
[32]	Katsnelson M I, Novoselov K S and Geim A K 2006 Nat. Phys. 2 620

Path integral approach to electron scattering in classical electromagnetic potential

Path integral approach to electron scattering in classical electromagnetic potential

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 32

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Li Wang(王莉), Lie-Juan Li(李烈娟), Melike Mohamedsedik(麦丽开·麦提斯迪克), Rong An(安荣), Jing-Jing Li(李静静), Bo-Song Xie(谢柏松), and Feng-Shou Zhang(张丰收). Enhancement of electron-positron pairs in combined potential wells with linear chirp frequency[J]. 中国物理B, 2023, 32(1): 10301-010301.
[2]	Shu-Xing Wang(汪书兴) and Lin-Fan Zhu(朱林繁). Integral cross sections for electron impact excitations of argon and carbon dioxide[J]. 中国物理B, 2022, 31(8): 83401-083401.
[3]	Xiaoli Zhao(赵小利) and Kedong Wang(王克栋). Elastic electron scattering with CH₂Br₂ and CCl₂Br₂: The role of the polarization effects[J]. 中国物理B, 2022, 31(8): 83402-083402.
[4]	M Jiang(江淼), D D Su(苏丹丹), N S Lin(林南省), and Y J Li(李英骏). Creation and annihilation phenomena of electron and positron pairs in an oscillating field[J]. 中国物理B, 2021, 30(7): 70306-070306.
[5]	Kedong Wang(王克栋), Yan Wang(王言), Jie Liu(刘洁), Yiwen Wang(王怡文), and Haoxing Zhang(张浩兴). Elastic electron scattering with formamide-(H₂O)_n complexes (n=1, 2): Influence of microsolvation on the π^* and σ^* resonances[J]. 中国物理B, 2021, 30(12): 123401-123401.
[6]	王宁月, 焦利光, 刘爱华. Relativistic electron scattering from freely movable proton/μ⁺ in the presence of strong laser field[J]. 中国物理B, 2019, 28(9): 93402-093402.
[7]	田红春, 徐龙泉, 朱林繁. Selection rules for electric multipole transition of triatomic molecule in scattering experiments[J]. 中国物理B, 2018, 27(4): 43101-043101.
[8]	朱林繁, 田红春, 刘亚伟, 康旭, 刘国兴. Selection rules for electric multipole transition of diatomic molecule in scattering experiments[J]. 中国物理B, 2015, 24(4): 43101-043101.
[9]	张永志, 周雅君. Ionization cross sections for electron scattering from metastable rare-gas atoms (Ne^* and Ar^*)[J]. 中国物理B, 2013, 22(7): 73402-073402.
[10]	吕元杰, 冯志红, 蔡树军, 敦少博, 刘波, 尹甲运, 张雄文, 房玉龙, 林兆军, 孟令国, 栾崇彪. Influence of drain bias on the electron mobility in the AlGaN/AlN/GaN heterostructure field-effect transistors[J]. 中国物理B, 2013, 22(6): 67104-067104.
[11]	王远成, 马佳, 周雅君. Momentum-space calculation of electron-CO elastic collision[J]. 中国物理B, 2013, 22(2): 23402-023402.
[12]	谭晓明, 王艳文. Total cross sections for electron scattering from sulfur compounds[J]. 中国物理B, 2013, 22(2): 23403-023403.
[13]	Siddharth H. Pandya, B. G. Vaishnav, K. N. Joshipura. Electron inelastic mean free paths in solids: A theoretical approach[J]. 中国物理B, 2012, 21(9): 93402-093402.
[14]	谭晓明, 赵刚. Total cross sections for electron scattering from fluoromethanes: A revised additivity rule method[J]. 中国物理B, 2012, 21(6): 63402-063402.
[15]	曹猛, 王芳, 刘婧, 张海波. Charging dynamics of polymer due to electron irradiation: A simultaneous scattering-transport model and preliminary results[J]. Chin. Phys. B, 2012, 21(12): 127901-127901.