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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 neutrino decoupling ： ウィキペディア英語版 neutrino decoupling In Big Bang cosmology, neutrino decoupling refers to the epoch at which neutrinos ceased interacting with baryonic matter, and thereby ceased influencing the dynamics of the universe at early times.〔Longair (2006), p. 290〕 Prior to decoupling, neutrinos were in thermal equilibrium with protons, neutrons, and electrons, which was maintained through the weak interaction. Decoupling occurred approximately at the time when the rate of those weak interactions was slower than the rate of expansion of the universe. Alternatively, it was the time when the time scale for weak interactions became greater than the age of the universe at that time. Neutrino decoupling took place approximately one second after the Big Bang, when the temperature of the universe was approximately 10 billion kelvins, or 1 MeV.〔Longair (2006), p. 291〕 ==Derivation of decoupling time== Neutrinos are scattered (interfering with free streaming) by their interactions with electrons and positrons, such as the reaction $e^-\; +\; e^+\; \backslash longleftrightarrow\; \backslash nu\_e\; +\; \backslash bar\_e$. The approximate rate of these interactions is set by the number density of electrons and positrons, the averaged product of the cross section for interaction and the velocity of the particles. The number density $n$ of the relativistic electrons and positrons depends on the cube of the temperature $T$, so that $n\; \backslash propto\; T^3$. The product of the cross section and velocity for weak interactions for temperatures (energies) below W/Z boson masses (~100 GeV) is given approximately by $\backslash langle\; \backslash sigma\; v\; \backslash rangle\; \backslash sim\; G\_F^2\; T^2$, where $G\_F$ is Fermi's constant (as is standard in particle physics calculations, factors of the speed of light $c$ are set equal to 1). Putting it all together, the rate of weak interactions $\backslash Gamma$ is $\backslash Gamma\; =\; n\; \backslash langle\; \backslash sigma\; v\; \backslash rangle\; \backslash sim\; G\_F^2\; T^5$. This can be compared to the expansion rate which is given by the Hubble parameter $H$, with $H\; =\; \backslash sqrtG\; \backslash rho\}$, where $G$ is the gravitational constant and $\backslash rho$ is the energy density of the universe. At this point in cosmic history, the energy density is dominated by radiation, so that $\backslash rho\; \backslash propto\; T^4$. As the rate of weak interaction depends more strongly on temperature, it will fall more quickly as the universe cools. Thus when the two rates are approximately equal (dropping terms of order unity, including an effective degeneracy term which counts the number of states of particles which are interacting) gives the approximate temperature at which neutrinos decouple: $G\_F^2\; T^5\; \backslash sim\; \backslash sqrt$. Solving for temperature gives $T\; \backslash sim\; \backslash left(\; \backslash frac\; \backslash right)\; ^\; \backslash sim\; 1~\backslash textrm$.〔Bernstein (1989), p. 27.〕 While this is a very rough derivation, it illustrates the important physical phenomena which determined when neutrinos decoupled. 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「neutrino decoupling」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.