assignmentutor™您的专属作业导师

assignmentutor-lab™ 为您的留学生涯保驾护航 在代写粒子物理particle physics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写粒子物理particle physics代写方面经验极为丰富，各种代写粒子物理particle physics相关的作业也就用不着说。

• 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|粒子物理代写particle physics代考|Diffraction

We account for the charge distribution of the nucleus by writing the differential cross section as
$$\frac{d \sigma}{d \Omega}=\left.\frac{d \sigma}{d \Omega}\right|_{\mid \text {Mott }}\left|F\left(q^2\right)\right|^2 .$$
The correction factor $F\left(q^2\right)$ is called the “electric form factor” and $\mathbf{q}$ is the momentum transferred by the electron in the scattering, i.e. the difference between the final electron momentum, $\boldsymbol{p}_f$, and the initial momentum, $\boldsymbol{p}_i$, both of which have the same magnitude, $p$, but differ in direction by the scattering angle, $\theta$. This electric form factor, $F\left(q^2\right)$, is in general a complex quantity, and it is the square modulus of this complex quantity which enters into the expression for the differential cross section.

From Fig. 2.1, and a little trigonometry, the magnitude of the momentum transferred (also shown in Appendix 1) is given by
$$q=2 p \sin \left(\frac{\theta}{2}\right) .$$
To understand the structure of the electric form factor, we need to consider quantum effects. Recall that in Quantum Physics the electron behaves as a wave with de Broglie wavelength
$$\lambda=h / p .$$
More precisely, we can relate the “wave-vector”, $\mathbf{k}$, to the momentum p,
$$\boldsymbol{p}=\hbar \boldsymbol{k},$$
where the magnitude, $k$, of the wave-vector, $k$, is $2 \pi / \lambda$ and its direction is the direction of the wave-motion.

We know from considering waves in optics that when a wavefront is incident on an object whose dimensions are of the order of the wavelength, the scattered wave displays maxima and minima. Precisely the same thing happens to de Broglie waves. When the de Broglie wavelength of the incident particle is of the order of the nuclear radius we get a diffraction pattern, in which the differential cross section displays maxima and minima in directions when the waves from different parts of the nucleus are in phase or out of phase.

## 物理代写|粒子物理代写particle physics代考|The Saxon–Woods Distribution

A more realistic model for the charge distribution is the Saxon-Woods distribution [22] for which
$$\rho_p(r)=\rho_0 f_{R, \delta}(r),$$
where $R$ is the nuclear radius and the function $f_{a, b}(r)$ is called a “Saxon-Woods potential”, with parameters $(a, b)$. Such a potential is given by
$$f_{a, b}(r)=\frac{1}{1+e^{(r-a) / b}},$$
The overall normalization, $\rho_0$ is chosen such that total charge is $Z e$, i.e.
$$Z e=4 \pi \rho_0 \int r^2 d r \frac{1}{1+\exp ((r-R) / \delta)} .$$
The Saxon-Woods distribution is shown in Fig. 2.6. We take $R$ to be the nuclear charge radius and $\delta$ is the “surface depth” – it measures the range in $r$ over which the charge distribution is substantially reduced from its value at $r=R$. It is a parameter, which needs to be fit to data for every nucleus.

This leads to a differential cross section which is shown in Fig. 2.7, where we have taken the values $R=3.4 \mathrm{fm}$ and $\delta=0.58 \mathrm{fm}$. We see that this predicted differential cross section has dips but no zeros and is much more similar in shape to the experininentăl results.

In fact, the Saxon-Woods modêl fits data from most nucléi ratherr wêll for nuclêi with atomic mass number $A>40$, with the charge radius given by (2.4) for atomic number, $Z$, and atomic mass number, $A$, and the parameter $\delta$ in the range $0.4-0.5 \mathrm{fm}$.

The Saxon-Woods model has been further refined, e.g. by multiplying the charge density by a polynomial in $r$. This leads to an enhancement of the quality of the fit to data, but at the expense of introducing more parameters.

# 粒子物理代考

## 物理代写|粒子物理代写particle physics代考|Diffraction

$$\frac{d \sigma}{d \Omega}=\left.\frac{d \sigma}{d \Omega}\right|_{\mid \text {Mott }}\left|F\left(q^2\right)\right|^2 .$$

$$q=2 p \sin \left(\frac{\theta}{2}\right) .$$

$$\lambda=h / p .$$

$$\boldsymbol{p}=\hbar \boldsymbol{k},$$

## 物理代写|粒子物理代写particle physics代考|The Saxon–Woods Distribution

$$\rho_p(r)=\rho_0 f_{R, \delta}(r),$$

$$f_{a, b}(r)=\frac{1}{1+e^{(r-a) / b}},$$

$$Z e=4 \pi \rho_0 \int r^2 d r \frac{1}{1+\exp ((r-R) / \delta)} .$$
Saxon-Woods 分布如图 $2.6$ 所示。我们采取 $R$ 为核电荷半径和 $\delta$ 是 “表面深度” – 它测量范围 $r$ 在其上，电荷分布从其值大幅减少 $r=R$. 它是一个参数，需要适合每个 核的数据。

Saxon-Woods 模型得到了进一步改进，例如通过将电荷密度乘以 $r$. 这会提高对数据的拟合质量，但代价是引入更多参数。

## 有限元方法代写

assignmentutor™作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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