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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|核物理代写nuclear physics代考|Most Stable Isobars

Different isobars may convert into each other by $\beta$-decay, which will be discussed in detail in Chap. 7. This is the process in which either a neutron is converted into a proton, emitting an electron and an antineutrino, or a proton is converted into a neutron, emitting a positron (the antiparticle of an electron) and a neutrino. In both cases, sufficient energy must be liberated by the change in the mass of the isobar to create an electron, which requires an energy of $m_{e} c^{2}$.
The process
$${ }{Z}^{A}{\mathrm{Ch}} \rightarrow{ }{(Z+1)}^{A}\left{\mathrm{Ch}^{\prime}\right}+e^{-}+\bar{v}$$
is kinematically possible provided
$$B(A, Z+1)-B(A, Z) \geq\left(m_{p}+m_{e}-m_{n}\right) c^{2} .$$
Note that it was necessary to take into account the mass difference between a proton and a neutron. ${ }^{5}$ Likewise, the process
$${ }{\mathrm{Z}}^{A}{\mathrm{Ch}} \rightarrow{ }{(\mathrm{Z}-1)}^{A}\left{\mathrm{Ch}^{\prime}\right}+e^{+}+v$$ is kinematically possible provided
$$B(A, Z-1)-B(A, Z) \geq\left(m_{n}+m_{e}-m_{p}\right) c^{2} .$$

## 物理代写|核物理代写nuclear physics代考|Stability of Isotopes

Since different isotopes have different atomic mass numbers, they will have different binding energies and some isotopes will be more stable than others. It turns out (and can be seen by looking for the most stable isotopes using the semi-empirical mass formula) that for the lighter nuclei, the stable isotopes have approximately the same number of neutrons as protons. This arises as a result of the asymmetry term.

However, above $A \sim 20$ the number of neutrons required for stability increases up to about one and a half times the number of protons for the heaviest nuclei (Fig. 3.4). Qualitatively, the reason for this arises from the Coulomb term. Protons bind less tightly than neutrons because they have to overcome the Coulomb repulsion between them. It is therefore energetically favourable to have more neutrons than protons. For nuclides with a large atomic mass number, this Coulomb effect beats the asymmetry effect that favours equal numbers of protons and neutrons. Quantitatively, this phenomenon can be seen from (3.10), where for small $A$ the maximum binding energy occurs for $Z \approx \frac{1}{2} A$, i.e. the same number of protons and neutrons, but as $A$ increases the maximum binding energy occurs for $Z<\frac{1}{2} A$, i.e. nuclides with more neutrons than protons.

# 核物理代写

## 物理代写|核物理代写nuclear physics代考|Most Stable Isobars

Veft 的分隔符缺失或无法识别

$$B(A, Z+1)-B(A, Z) \geq\left(m_{p}+m_{e}-m_{n}\right) c^{2} .$$

\left 的分隔符缺失或无法识别

$$B(A, Z-1)-B(A, Z) \geq\left(m_{n}+m_{e}-m_{p}\right) c^{2} .$$

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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。

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