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|Scattering

In classical physics, scattering among particles may occur either due to long-range forces (e.g. the Rutherford scattering) or by impulsive forces in the collision of rigid bodies. Rigid bodies do not exist in SR (see Appendix A) and, hence, impulsive forces are never employed in particle physics. They can be replaced by finite range interactions, whose effects are negligible if the minimum distance between the particle and the scattering center is larger than the range of the force. A renowned example is the scattering of a proton on a neutron due to strong interactions. Unlike QM, a scattering in classical physics and SR is a deterministic process. If the initial conditions are perfectly known, the trajectory can be predicted at any time with infinite precision. In most practical cases, we are interested in the trajectory of the final state particles once the interactions among them can be neglected and the particles fly apart from the scattering center. In classical physics, this approximation is driven by practical reasons, that is the challenge of tracking a microscopic object at any time during the scattering process. In QM, this is an intrinsic limitation introduced by the Heisenberg uncertainty principle. As a consequence, scattering theory (Weinberg, 2012) aims to solve the equations of motion for $t \rightarrow+\infty$ and determine the scattering angles of the particles in space. The most prominent observable of scattering theory is the cross-section.

The differential cross-section is the ratio between the number of particles that are scattered in a solid angle between $\Omega$ and $\Omega+d \Omega$ per unit time divided by the flux:
$$\frac{d \sigma}{d \Omega}(E, \Omega)=\frac{1}{F} \frac{d N_s}{d \Omega}$$
The flux is the rate of incoming particles per unit surface.

## 物理代写|核物理代考Nuclear Physics代写|Fixed-target collisions

Nearly all scatterings of interest in particle physics can be classified into two groups: fixed-target and head-on (or colliding beam) collisions. The definition of cross-section given in eqn 2.113 holds for a single scattering center. In most applications, however, we steer the particles toward macroscopic bodies called targets. The targets are made up of a large number of atoms that act as scattering centers (Fig. 2.12). If the target is at rest in LAB, the scattering is called a fixed-target collision. The number of particles per unit time that are scattered by a thin target is
$$\frac{d N_s}{d \Omega}=F A \tilde{N} d x \frac{d \sigma}{d \Omega}$$
where $F$ is the incoming particle flux (particles per unit time per unit surface), $\tilde{N}$ is the density of the scattering centers, and $d x$ is the thickness of the target. $A$ is the cross-sectional area of the beam if this is smaller than the surface of the target. Otherwise, $A$ is the target surface projected in the plane perpendicular to the particle direction. In practice, $F A$ represents the number of incoming particles per unit time that undergo a collision with the atoms of the target. $\tilde{N}$ depends on the type of interaction. For instance, the interactions and energy losses of heavy charged particles in matter are dominated by the electromagnetic interactions with the atomic electrons (see Sec. 3.1). In this case, $\tilde{N}$ is the electron density $\tilde{N}=\rho Z N_A / A$ where $\rho$ is the density of the target, $N_A$ the Avogadro number, $Z$ and $A$ are the atomic and mass numbers of the target atoms.

# 核物理代写

## 物理代写|核物理代考Nuclear Physics代写|Scattering

$$\frac{d \sigma}{d \Omega}(E, \Omega)=\frac{1}{F} \frac{d N_s}{d \Omega}$$

## 物理代写|核物理代考Nuclear Physics代写|Fixed-target collisions

$$\frac{d N_s}{d \Omega}=F A \tilde{N} d x \frac{d \sigma}{d \Omega}$$

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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。