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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Klein–Nishina formula ： ウィキペディア英語版 Klein–Nishina formula The Klein–Nishina formula gives the differential cross section of photons scattered from a single free electron in lowest order of quantum electrodynamics. At low frequencies (e.g., visible light) this yields Thomson scattering; at higher frequencies (e.g., x-rays and gamma-rays) this yields Compton scattering. For an incident photon of energy $E\_\backslash gamma$, the differential cross section is:〔 〕 : $\backslash frac\; =\; \backslash alpha^2\; r\_c^2\; P(E\_\backslash gamma,\backslash theta)^2\; (+\; P(E\_\backslash gamma,\backslash theta)^\; -1\; +\; \backslash cos^2(\backslash theta))/2$ where $\backslash frac$ is a differential cross section, $d\backslash Omega$ is an infinitesimal solid angle element, $\backslash alpha$ is the fine structure constant (~1/137.04), $\backslash theta$ is the scattering angle; $r\_c=\backslash hbar/m\_e\; c$ is the "reduced" Compton wave length of the electron (~0.38616 pm); $m\_e$ is the mass of an electron (~511 keV$/c^2$); and $P(E\_\backslash gamma,\backslash theta)$ is the ratio of photon energy after and before the collision: : $$ P(E_\gamma,\theta) = \frac Note that this result may also be expressed in terms of the classical electron radius $r\_e=\backslash alpha\; r\_c$. While this classical quantity is not particularly relevant in quantum electrodynamics, it is easy to appreciate: in the forward direction (for $\backslash theta$ ~ 0), photons scatter off electrons as if these were about $r\_e=\backslash alpha\; r\_c$ (~2.8179 fm) in linear dimension, and $r\_e^2$ (~ 7.9406x10−30 m2 or 79.406 mb) in size. The Klein–Nishina formula was derived in 1928 by Oskar Klein and Yoshio Nishina, and was one of the first results obtained from the study of quantum electrodynamics. Consideration of relativistic and quantum mechanical effects allowed development of an accurate equation for the scattering of radiation from a target electron. Before this derivation, the electron cross section had been classically derived by the British physicist and discoverer of the electron, J.J. Thomson. However, scattering experiments showed significant deviations from the results predicted by the Thomson cross section. Further scattering experiments agreed perfectly with the predictions of the Klein–Nishina formula. Note that if $E\_\backslash gamma\; \backslash ll\; m\_ec^2$, $P(E\_\backslash gamma,\backslash theta)\backslash rightarrow\; 1$ and the Klein–Nishina formula reduces to the classical Thomson expression. The final energy of the scattered photon, $E\_\backslash gamma\text{'}$, depends only on the scattering angle and the original photon energy, and so it can be computed without the use of the Klein–Nishina formula: : $$ E_\gamma'(E_\gamma,\theta) = E_\gamma \cdot P(E_\gamma, \theta) \, ==Notes== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Klein–Nishina formula」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.