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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 Alpha particle scattering ： ウィキペディア英語版 Rutherford scattering Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction. It is a physical phenomenon explained by Ernest Rutherford in 1911〔E. Rutherford , "The Scattering of α and β rays by Matter and the Structure of the Atom",Philos. Mag., vol 6, ppioi.21, 1911〕 that led to the development of the planetary Rutherford model of the atom and eventually the Bohr model. It is now exploited by the materials analytical technique Rutherford backscattering. Rutherford scattering was first referred to as Coulomb scattering because it relies only upon static electric (Coulomb) forces, and the minimal distance between particles is set only by this potential. The classical Rutherford scattering of alpha particles against gold nuclei is an example of "elastic scattering" because the energy and velocity of the outgoing scattered particle is the same as that with which it began. Rutherford also later analyzed inelastic scattering when he projected alpha particles against hydrogen nuclei (protons); however this latter process is not referred to as "Rutherford scattering", although Rutherford was first to observe it. At the end of such processes, non-Coulombic forces come into play. These forces, and also energy gained from the scattering particle by the lighter target, change the scattering results in fundamental ways which suggest structural information about the target. A similar process probed the insides of nuclei in the 1960s, and is called deep inelastic scattering. The initial discovery was made by Hans Geiger and Ernest Marsden in 1909 when they performed the gold foil experiment under the direction of Rutherford, in which they fired a beam of alpha particles (helium nuclei) at layers of gold leaf only a few atoms thick. At the time of the experiment, the atom was thought to be analogous to a plum pudding (as proposed by J. J. Thomson), with the negative charges (the plums) found throughout a positive sphere (the pudding). If the plum-pudding model were correct, the positive "pudding", being more spread out than in the current model of a concentrated nucleus, would not be able to exert such large columbic forces, and the alpha particles should only be deflected by small angles as they pass through. However, the intriguing results showed that around 1 in 8000 alpha particles were deflected by very large angles (over 90°), while the rest passed straight through with little or no deflection. From this, Rutherford concluded that the majority of the mass was concentrated in a minute, positively charged region (the nucleus/ central charge) surrounded by electrons. When a (positive) alpha particle approached sufficiently close to the nucleus, it was repelled strongly enough to rebound at high angles. The small size of the nucleus explained the small number of alpha particles that were repelled in this way. Rutherford showed, using the method below, that the size of the nucleus was less than about 10−14 m (how ''much'' less than this size, Rutherford could not tell from this experiment alone; see more below on this problem of lowest possible size). == Derivation == The differential cross section can be derived from the equations of motion for a particle interacting with a central potential. In general, the equations of motion describing two particles interacting under a central force can be decoupled into the center of mass and the motion of the particles relative to one another. For the case of light alpha particles scattering off heavy nuclei, as in the experiment performed by Rutherford, the reduced mass is essentially the mass of the alpha particle and the nucleus off of which it scatters is essentially stationary in the lab frame. Substituting into the Binet equation yields the equation of trajectory : $\backslash fracZ\_e^\}^b^\}=-\backslash kappa,$ where $u=$, $v\_0$ is the speed at infinity, and $b$ is the impact parameter. The general solution of the above differential equation is : $u=u\_\backslash cos(\backslash theta-\backslash theta\_)-\backslash kappa,$ and the boundary condition is : $u\backslash to\; 0\; \backslash quad\; r\backslash sin\backslash theta\backslash to\; b\; \backslash quad(\backslash theta\backslash to\backslash pi).$ If we choose : $\backslash theta\_=\backslash frac+\backslash arctan\; b\backslash kappa.$ then the deflection angle Θ can be seen from solving $u\backslash to\; 0$ as : $\backslash Theta=2\backslash theta\_-\backslash pi=2\backslash arctan\; b\backslash kappa=2\backslash arctan\backslash frace^\}^b\}.$ ''b'' can be solved to give : $b=\backslash frace^\}^\}\backslash cot\backslash frac.$ To find the scattering cross section from this result consider its definition :: $(\backslash Omega)\; d\; \backslash Omega\}=\; \backslash over\; \backslash hbox\}$ Since the scattering angle is uniquely determined for a given $E$ and $b$, the number of particles scattered into an angle between $\backslash Theta$ and $\backslash Theta+d\backslash Theta$ must be the same as the number of particles with associated impact parameters between $b$ and $b+db$. For an incident intensity $I$, this implies the following equality :: $2\backslash pi\; I\; b\; \backslash left|db\backslash right|\; =\; I\; \backslash frac\; d\backslash Omega$ For a radially symmetric scattering potential, as in the case of the Coulombic potential, $d\backslash Omega\; =\; 2\backslash pi\backslash sind\backslash Theta$, yielding the expression for the scattering cross section :: $\backslash frac\; =\; \backslash frac\backslash right|$ Finally, plugging in the previously derived expression for the impact parameter $b(\backslash Theta)$ we find the Rutherford scattering cross section :: $\backslash frac\; =\backslash left(\backslash frac\backslash right)^2\; \backslash csc^4\backslash right)\}.$ 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「Rutherford scattering」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.