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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|Binding Energy

Initially, one might have thought that the mass of a nuclide was simply the total mass of the nucleons $\mathrm{Zm}{p}+N m{n}$. In reality, the mass of a given nuclide is slightly less than this, by a quantity known as the “mass defect”, $\Delta m_{\mathcal{N}}$. When nucleons bind to form a nucleus, there is a binding energy, $B(A, Z)$, which is the energy that would be required to pull the nucleons apart. The binding energy depends on both the atomic mass number and the atomic number.

From Einstein’s Special Theory of Relativity (and the one physics equation that is familiar to almost everybody), the mass of the nuclide is therefore less than the sum of the masses of the nucleons by an amount equal to this binding energy divided by the square of the speed of light.
$$\Delta m_{\mathcal{N}}=\frac{B(A, Z)}{c^{2}},$$
so that the expression for the mass, $m_{\mathcal{N}}$, of a given nuclide is
$$m_{\mathcal{N}}=Z m_{p}+N m_{n}-\frac{B(A, Z)}{c^{2}} .$$
The binding energy is due to the strong short-range nuclear force that binds the nucleons together, as well as the long-range electromagnetic (Coulomb) repulsion between the positively charged protons. However, the strong nuclear force is far less understood than the electromagnetic force, so that the binding energy due to the strong force cannot, even in principle, be calculated analytically. All we know about it is that it is very short range, so that it acts only between neighbouring nucleons, whereas the long-range electromagnetic interactions extend over the entire nucleus (and beyond).

Binding energies per nucleon increase sharply with increasing atomic mass number, $A$, peaking at ${ }{28}^{62} \mathrm{Ni}$ (nickel) ${ }^{2}$ and then decreasing slowly for the more massive nuclei (see Fig. 3.2). This means that the nuclei of ${ }{28}^{62} \mathrm{Ni}$ and nuclei with similar mass are particularly stable, whereas the more massive nuclei are less stable and can decay into lighter nuclei by fission that will be discussed in detail in Chap. $9 .$

## 物理代写|核物理代写nuclear physics代考|Semi-Empirical Mass Formula

For all but the very lightest of nuclei, the binding energy is well reproduced by a semi-empirical formula based on the idea, originally postulated by George Gamow in 1930 [27], in which the nucleus can be thought of as a liquid drop composed of nucleons (the “Liquid Drop Model”). The volume of the liquid drop is proportional to the number of nucleons, A. The semi-empirical mass formula for the binding energy of a given nuclide, as a function of atomic number, $Z$, and atomic mass number, $A$, was derived independently by Carl von Weizsäcker [28] in 1935 and Hans Bethe [29] a year later. The formula is also known as the Bethe-Weizsäcker mass formula.

It is “semi-empirical” in that it contains a number of terms whose dependence on $Z$ and $A$ is derived from physics, but which have coefficients that are unknown and have been fit to experimental data on nuclear binding energies. There are five terms, some of which come from a purely classical description of a liquid drop comprising a number of nucleons, and others that are purely quantum effects:

1. Volume term: Each nucleon has a binding energy that binds it to the nucleus. The interactions are short range, so to a gond approximation the nuclenns only interact with their nearest neighbours. Therefore we get a term proportional to the volume of the liquid drop. This in turn is proportional to the number of nucleons, $A$, with a coefficient, $a_{V}$ :
$$a_{V} A .$$

# 核物理代写

## 物理代写|核物理代写nuclear physics代考|Binding Energy

$$\Delta m_{\mathcal{N}}=\frac{B(A, Z)}{c^{2}},$$

$$m_{\mathcal{N}}=Z m_{p}+N m_{n}-\frac{B(A, Z)}{c^{2}} .$$

## 物理代写|核物理代写nuclear physics代考|Semi-Empirical Mass Formula

1. 体积项: 每个核子都有一个结合能，可以将其结合到原子核上。相互作用是短程的，因此对于 gond 近似，核只与它们最近的邻居相互作用。因此，我们得 到一个与液滴体积成正比的项。这又与核子的数量成正比， $A$, 有一个系数 $a_{V}$ :
$a_{V} A$

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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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师