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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 Doppler broadening ： ウィキペディア英語版 Doppler broadening In atomic physics, Doppler broadening is the broadening of spectral lines due to the Doppler effect caused by a distribution of velocities of atoms or molecules. Different velocities of the emitting particles result in different Doppler shifts, the cumulative effect of which is the line broadening. This resulting line profile is known as a Doppler profile. A particular case is the thermal Doppler broadening due to the thermal motion of the particles. Then, the broadening depends only on the frequency of the spectral line, the mass of the emitting particles, and their temperature, and therefore can be used for inferring the temperature of an emitting body. Saturated absorption spectroscopy, also known as Doppler-free spectroscopy, can be used to find the true frequency of an atomic transition without cooling a sample down to temperatures at which the Doppler broadening is minimal. == Derivation == When thermal motion causes a particle to move towards the observer, the emitted radiation will be shifted to a higher frequency. Likewise, when the emitter moves away, the frequency will be lowered. For non-relativistic thermal velocities, the Doppler shift in frequency will be: :$f\; =\; f\_0\backslash left(1+\backslash frac\backslash right)$ where $\backslash \; f$ is the observed frequency, $\backslash \; f\_0$ is the rest frequency, $\backslash \; v$ is the velocity of the emitter towards the observer, and $c$ is the speed of light. Since there is a distribution of speeds both toward and away from the observer in any volume element of the radiating body, the net effect will be to broaden the observed line. If $\backslash ,P\_v(v)dv$ is the fraction of particles with velocity component $\backslash ,v$ to $\backslash ,v+dv$ along a line of sight, then the corresponding distribution of the frequencies is :$P\_f(f)df\; =\; P\_v(v\_f)\backslash fracdf$, where $\backslash ,v\_f\; =\; c\backslash left(\backslash frac\; -\; 1\backslash right)$ is the velocity towards the observer corresponding to the shift of the rest frequency $\backslash ,f\_0$ to $\backslash ,f$. Therefore, ::P_v\left(c\left(\frac - 1\right)\right)df. |} We can also express the broadening in terms of the wavelength $\backslash ,\backslash lambda$. Recalling that in the non-relativistic limit $\backslash frac\}\; \backslash approx\; -\backslash frac$, we obtain ::P_v\left(c\left(1 - \frac\right)\right)d\lambda. |} In the case of the thermal Doppler broadening, the velocity distribution is given by the Maxwell distribution :$P\_v(v)dv\; =\; \backslash sqrt\}\backslash ,\backslash exp\backslash left(-\backslash frac\backslash right)dv$, where $\backslash ,m$ is the mass of the emitting particle, $\backslash ,T$ is the temperature and $\backslash ,k$ is the Boltzmann constant. Then, :$P\_f(f)df=\backslash left(\backslash frac\backslash right)\backslash sqrt\}\backslash ,\backslash exp\backslash left(-\backslash frac-1\backslash right)\backslash right"\; TITLE="c\backslash left(\backslash frac-1\backslash right)\backslash right">)^2\}\backslash right)df$. We can simplify this expression as :$P\_f(f)df=\backslash sqrt^2\}\}\backslash ,$ \exp\left(-\frac\right)df, which we immediately recognize as a Gaussian profile with the standard deviation :$\backslash sigma\_\; =\; \backslash sqrt\}f\_0$ and full width at half maximum (FWHM) ::}f_. |} 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「Doppler broadening」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.