Posted on Categories:Nuclear Physics, 核物理, 物理代写

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## 物理代写|核物理代考Nuclear Physics代写|Energy loss of electrons

Unlike heavy charged particles, electrons that enter a medium have a mass identical to the target particles, and the energy that is transferred ranges between 0 and half the kinetic energy of the incoming electron: $\left(E-m c^2\right) / 2$. The maximum kinetic energy that can be transferred is different from $2 m_e \gamma^2 c^2 \beta^2$ and the Bethe formula must be corrected accordingly. Besides, the formula must account for the Pauli exclusion principle since the incoming particle and the scattering center are two identical fermions. The corresponding Bethe formula can be written analytically with empirical corrections similar to the shell and density effects (Leo, 1994).

The electrons, however, show an additional mechanism of energy loss in matter. Radiation loss or bremsstrahlung, which means braking radiation in German, is the radiation produced by the acceleration or deceleration of a charged particle. Radiation losses follow from the Maxwell equations and take place in any charged particle. The irradiated power (Griffiths, 2017), however, is $\sim \gamma^6$ if the acceleration is parallel to the velocity and $\sim \gamma^4$ if it is perpendicular like, e.g., in circular accelerators. Since $\gamma=E / m$, this source of losses is negligible for heavy particles up to $\mathrm{TeV}$ energies but is the leading energy-loss mechanism for electrons. In quantum mechanics (QM), bremsstrahlung corresponds to the spontaneous emission of photons by an electron in a medium. Four-momentum conservation forbids the $e^{-} \rightarrow e^{-} \gamma$ transition in vacuum but the process can occur in the proximity of another particle and the transition probability linearly increases with the density of the medium. Even if the quantum mechanic treatment of radiation losses is complicated, its empirical description is rather simple. Radiation losses become dominant above the critical energy, which is the energy when the energy loss due to radiation overtakes the ionization loss, the loss due to the interactions with the electrons of the medium described by the Bethe formula. Unlike heavy charged particles, the medium plays a crucial role because it changes the trajectory of the incoming electron, causing the breaking radiation. The critical energy is often measured and tabulated but some empirical formulas are available, too. For solid materials,
$$E_c \simeq \frac{610 \mathrm{MeV}}{Z+1.24} .$$

## 物理代写|核物理代考Nuclear Physics代写|The discovery of antimatter

The energy loss of charged particles with matter was established at the beginning of the 20th century for all particles known at that time: electrons, protons, and light nuclei. The energy released to the atomic electrons can either bring the atoms to an excited state or move the electron to the continuum ionizing the atom (see Sec. 3.5). If the air temperature and humidity are properly tuned, highly ionized air acts as a condensation center for the formation of water droplets and, eventually, the clouds. Even if the dynamic of cloud formation is extremely complex and still at the focus of modern research in chemistry and environmental science, the basic formation principle can be exploited to visualize the trajectory of charged particles. An expansion cloud chamber consists of a vessel containing a supersaturated vapor of water. If the gas mixture is at the point of condensation, a trail of small droplets forms in the volume where the density of ions is high. The droplets are visible along the trajectory of the particle for several seconds while they fall through the vapor. The detector is called an expansion chamber because we use a diaphragm to perform the adiabatic expansion that cools the air and starts the condensation of the vapor. The detector is sensitive to particles only after the expansion of the diaphragm, which is set in coincidence with a camera that takes pictures of the tracks. Cloud chambers have been used since 1911 to observe tracks produced by cosmic rays and radioactive decays. The most celebrated application is the discovery of the first anti-particle in 1932 by C.D. Anderson (Anderson, 1933) confirmed nearly at the same time by P. Blackett and G. Occhialini (Blackett, 1933).

# 核物理代写

## 物理代写|核物理代考Nuclear Physics代写|Energy loss of electrons

$$E_c \simeq \frac{610 \mathrm{MeV}}{Z+1.24} .$$

## 物理代写|核物理代考Nuclear Physics代写|The discovery of antimatter

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。