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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 classical electron radius ： ウィキペディア英語版 classical electron radius The classical electron radius, also known as the Lorentz radius or the Thomson scattering length, is based on a classical (i.e. non-quantum) relativistic model of the electron. According to modern research, the electron is a point particle with a point charge and no spatial extent.〔 〕 However, the classical electron radius is calculated as :$r\_\backslash text\; =\; \backslash frac\backslash frac\; =\; 2.817\; 940\; 3267(27)\; \backslash times\; 10^\; \backslash text\; ,$ where $e$ and $m\_\; =\; \backslash frac\; =\; 2.817\; 940\; 3267(27)\backslash times\; 10^\; \backslash text$ with (to three significant digits) :$e\; =\; 4.80\; \backslash times\; 10^\; \backslash text,\backslash quad\; m\_\backslash text\; =\; 9.11\; \backslash times\; 10^\; \backslash text,\backslash quad\; c\; =3.00\; \backslash times\; 10^\; \backslash text\; .$ Using classical electrostatics, the energy required to assemble a sphere of constant charge density, of radius $r\_\backslash text$ and charge $e$ is :$E=\backslash frac\backslash ,\backslash ,\backslash frac\backslash frac\backslash ,\backslash ,\backslash frac\backslash frac,$ for ''r''≤''R'' The energy is: $E=\backslash frac\backslash frac$, the above result is obtained. In simple terms, the classical electron radius is roughly the size the electron would need to have for its mass to be completely due to its electrostatic potential energy – not taking quantum mechanics into account. We now know that quantum mechanics, indeed quantum field theory, is needed to understand the behavior of electrons at such short distance scales, thus the classical electron radius is no longer regarded as the actual size of an electron. Still, the classical electron radius is used in modern classical-limit theories involving the electron, such as non-relativistic Thomson scattering and the relativistic Klein–Nishina formula. Also, the classical electron radius is roughly the length scale at which renormalization becomes important in quantum electrodynamics. The classical electron radius is one of a trio of related units of length, the other two being the Bohr radius $a\_0$ and the Compton wavelength of the electron $\backslash lambda\_\backslash text$. The classical electron radius is built from the electron mass $m\_\backslash text$, the speed of light $c$ and the electron charge $e$. The Bohr radius is built from $m\_\backslash text$, $e$ and Planck's constant $h$. The Compton wavelength is built from $m\_\backslash text$, $h$ and $c$. Any one of these three lengths can be written in terms of any other using the fine structure constant $\backslash alpha$: :$r\_\backslash text\; =\; =\; \backslash alpha^2\; a\_0\; .$ Extrapolating from the initial equation, any charged mass can be imagined to have an 'electromagnetic radius' similar to the electron's classical radius. :$r=\backslash frac\; ,$ where $k\_\backslash text$ is Coulomb's constant, $q$ is the charge of the object, $m$ is its mass, $\backslash alpha$ is the fine structure constant and $\backslash hbar$ is the reduced Planck's constant. == See also == Electromagnetic mass 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「classical electron radius」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.