## 物理代写|核物理代写nuclear physics代考|FYS3500

statistics-lab™ 为您的留学生涯保驾护航 在代写核物理nuclear 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。我们的专家在代写核物理nuclear physics代写方面经验极为丰富，各种代写核物理nuclear physics相关的作业也就用不着说。

## 物理代写|核物理代写nuclear physics代考|Classical cross-sections

Classically, cross-sections are calculated from the trajectories of particles in force fields. Consider a particle in Fig. 3.9 that passes through a spherically symmetric force field centered on the origin. The particle’s original trajectory is parametrized by the “impact parameter” $b$ which would give the particle’s distance of closest approach to the force center if there were no scattering.
The scattering angle $\theta(b)$ depends on the impact parameter, as in the figure. The relation $\theta(b)$ or $b(\theta)$ can be calculated by integrating the equations of motion with the initial conditions $p_z=p, p_x=p_y=0$. The probability that a particle is scattered into an interval $\mathrm{d} \theta$ about $\theta$ is proportional to the area of the annular region between $b(\theta)$ and $b(\theta+\mathrm{d} \theta)=b+\mathrm{d} b$, i.e. $\mathrm{d} \sigma=2 \pi b \mathrm{~d} b$. The solid angle corresponding to $\mathrm{d} \theta$ is $\mathrm{d} \Omega=2 \pi \sin \theta \mathrm{d} \theta$. The differential elastic scattering cross-section is therefore
$$\frac{\mathrm{d} \sigma}{\mathrm{d} \Omega}(\theta)=\frac{2 \pi b \mathrm{~d} b}{2 \pi \sin \theta \mathrm{d} \theta}=\left|\frac{b(\theta)}{\sin \theta} \cdot \frac{d b}{d \theta}\right| .$$
A measurement of $\mathrm{d} \sigma / \mathrm{d} \Omega$ determines the relation $b(\theta)$ which in turn gives information about the potential $V$.

We can apply (3.38) to several simple cases:

Scattering of a point particle on a hard immovable sphere. The angleimpact parameter relation is
$$b=R \cos \theta / 2,$$
where $R$ is the radius of the sphere. The cross section is then
$$\frac{\mathrm{d} \sigma}{\mathrm{d} \Omega}=R^2 / 4 \quad \Rightarrow \quad \sigma=\pi R^2$$
so the total cross-section is just the geometrical cross section of the sphere. In the case of scattering of two spheres of the same radius, the total scattering cross-section is $\sigma=4 \pi R^2$.

Scattering of a charged particle in a Coulomb potential
$$V(r)=\frac{Z_1 Z_2 e^2}{4 \pi \epsilon_0 r},$$
where $Z_1$ is the charge of the scattered particle, and $Z_2$ is the charge of the immobile target particle. This historically important reaction is called “Rutherford scattering” after E. Rutherford who demonstrated the existence of a compact nucleus by studying $\alpha$-particle scattering on gold nuclei. The unbound orbits in the Coulomb potential are hyperbolas so the scattering angle is well-defined in spite of the infinite range of the force. For an incident kinetic energy $E_k=m v^2 / 2$, the angle-impact parameter relation is
$$b=\frac{Z_1 Z_2 e^2}{8 \pi \epsilon_0 E_k} \cot (\theta / 2) .$$
The cross-section is then
$$\frac{d \sigma}{d \Omega}=\left(\frac{Z_1 Z_2 e^2}{16 \pi \epsilon_0 E_k}\right)^2 \frac{1}{\sin ^4 \theta / 2}$$

## 物理代写|核物理代写nuclear physics代考|Asymptotic states and their normalization

In studying nuclear, or elementary interactions, we are most of the time not interested in a space-time description of phenomena. ${ }^2$ Instead, we study processes in which we prepare initial particles with definite momenta and far away from one another so that they are out of reach of their interactions at an initial time $t_0$ in the “distant past” $t_0 \sim-\infty$. We then study the nature and the momentum distributions of final particles when these are also out of range of the interactions at some later time $t$ in the “distant future” $t \rightarrow+\infty$. (The size of the interaction region is of the order of $1 \mathrm{fm}$, the measuring devices have sizes of the order of a few meters.) Under these assumptions, the initial and final states of the particles under consideration are free particle states. These states are called asymptotic states. The decay of an unstable particle is a particular case. We measure the energy and momenta of final particles in asymptotic states.

By definition, the asymptotic states of particles have definite momenta. Therefore, strictly speaking, they are not physical states, and their wave functions $\mathrm{e}^{\mathrm{i} p x / \hbar}$ are not square integrable. Physically, this means that we are actually interested in wave packets who have a non vanishing but very small extension $\Delta p$ in momentum, i.e. $\Delta p /|p| \ll 1$.

It is possible to work with plane waves, provided one introduces a proper normalization. A limiting procedure, after all calculations are done, allows to get rid of the intermediate regularizing parameters. This is particularly simple in first order Born approximation, which we will present first. The complete manipulation of wave packets is possible but somewhat complicated. However, it gives interesting physical explanations for various specific problems, and we shall discuss it in Sect. 3.3.5.

We will consider that the particles are confined in a (very large but finite) box of volume $L^3$. We will let $L$ tend to infinity at the end of the calculation. Besides its simplicity, this procedure allows to incorporate relativistic kinematics of ingoing and outgoing particles in a simple manner.
In such a box of size $L$, the normalized momentum eigenstates are
\begin{aligned} |\boldsymbol{p}\rangle \rightarrow \psi_{\boldsymbol{p}}(\boldsymbol{r}) & =L^{-3 / 2} \mathrm{e}^{\mathrm{i} \boldsymbol{p} \cdot \boldsymbol{r} / \hbar} \quad \text { inside the box }, \ \psi_{\boldsymbol{p}}(\boldsymbol{r}) & =0 \quad \text { outside the box } . \end{aligned}
These wave functions are normalized in the sense that
$$\int\left|\psi_{\boldsymbol{p}}(\boldsymbol{r})\right|^2 \mathrm{~d}^3 \boldsymbol{r}=1 .$$

# 核物理代写

## 物理代写|核物理代写nuclear physics代考|Classical cross-sections

$$\frac{\mathrm{d} \sigma}{\mathrm{d} \Omega}(\theta)=\frac{2 \pi b \mathrm{~d} b}{2 \pi \sin \theta \mathrm{d} \theta}=\left|\frac{b(\theta)}{\sin \theta} \cdot \frac{d b}{d \theta}\right| .$$

$$b=R \cos \theta / 2,$$

$$\frac{\mathrm{d} \sigma}{\mathrm{d} \Omega}=R^2 / 4 \quad \Rightarrow \quad \sigma=\pi R^2$$

$$V(r)=\frac{Z_1 Z_2 e^2}{4 \pi \epsilon_0 r},$$

$$b=\frac{Z_1 Z_2 e^2}{8 \pi \epsilon_0 E_k} \cot (\theta / 2) .$$

$$\frac{d \sigma}{d \Omega}=\left(\frac{Z_1 Z_2 e^2}{16 \pi \epsilon_0 E_k}\right)^2 \frac{1}{\sin ^4 \theta / 2}$$

## 物理代写|核物理代写nuclear physics代考|Asymptotic states and their normalization

\begin{aligned} |\boldsymbol{p}\rangle \rightarrow \psi_{\boldsymbol{p}}(\boldsymbol{r}) & =L^{-3 / 2} \mathrm{e}^{\mathrm{i} \boldsymbol{p} \cdot \boldsymbol{r} / \hbar} \quad \text { inside the box }, \ \psi_{\boldsymbol{p}}(\boldsymbol{r}) & =0 \quad \text { outside the box } . \end{aligned}

$$\int\left|\psi_{\boldsymbol{p}}(\boldsymbol{r})\right|^2 \mathrm{~d}^3 \boldsymbol{r}=1 .$$

## 有限元方法代写

tatistics-lab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。

## 物理代写|核物理代写nuclear physics代考|NUC-303

statistics-lab™ 为您的留学生涯保驾护航 在代写核物理nuclear 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。我们的专家在代写核物理nuclear physics代写方面经验极为丰富，各种代写核物理nuclear physics相关的作业也就用不着说。

## 物理代写|核物理代写nuclear physics代考|Inelastic and total cross-sections

In general for a reaction creating $N$ particles
$$a b \rightarrow x_1 x_2 \ldots x_N$$
the probability to create the particles $x_i$ in the momentum ranges $\mathrm{d}^3 \boldsymbol{p}i$ centered on the momenta $\boldsymbol{p}_i$ is given by $$\mathrm{d} P=\frac{\mathrm{d} \sigma}{\mathrm{d}^3 \boldsymbol{p}_1 \ldots \mathrm{d}^3 \boldsymbol{p}_N} n_b \mathrm{~d} z \mathrm{~d}^3 \boldsymbol{p}_1 \ldots \mathrm{d}^3 \boldsymbol{p}_N .$$ The differential cross-section $\mathrm{d} \sigma / \mathrm{d}^3 \boldsymbol{p}_1 \ldots \mathrm{d}^3 \boldsymbol{p}_N$ will be a singular function because only energy-momentum conserving combinations have non-vanishing probabilities. The total probability for the reaction $a b \rightarrow x_1 \ldots x_N$ is $$\mathrm{d} P{a b \rightarrow x_1 \ldots x_N}=\sigma_{a b \rightarrow x_1 \ldots x_N} n_b \mathrm{~d} z$$

where the reaction cross-section is
$$\sigma_{a b \rightarrow x_1 \ldots x_N}=\int \mathrm{d}^3 \boldsymbol{p}1 \ldots \int \mathrm{d}^3 \boldsymbol{p}_N \frac{\mathrm{d} \sigma}{\mathrm{d}^3 \boldsymbol{p}_1 \ldots \mathrm{d}^3 \boldsymbol{p}_N} \mathrm{~d}^3 \boldsymbol{p}_1 \ldots \mathrm{d}^3 \boldsymbol{p}_N .$$ The total probability that “anything” happens to the incident particle as it traverses the target of thickness $\mathrm{d} z$ is just the sum of the probabilities of the individual reactions $$\mathrm{d} P=\sigma{\text {tot }} n_b \mathrm{~d} z$$
where the total cross-section is
$$\sigma_{\mathrm{tot}}=\sum_i \sigma_i$$

## 物理代写|核物理代写nuclear physics代考|The uses of cross-sections

Cross-sections enter into an enormous number of calculations in physics. Consider a thin target (Fig. 3.1 ) containing a density $n$ of target particles that is subjected to a flux of beam particles $F$ (particles per unit area per unit time). If particles that interact in the target are considered to be removed from the beam (scattered out of the beam or changed into other types of particles), then the probability for interaction $\mathrm{d} P=\sigma n_{\mathrm{b}} \mathrm{d} z$ implies that the $F$ is reduced by
$$\mathrm{d} F=-F \sigma n \mathrm{~d} z,$$
equivalent to the differential equation
$$\frac{\mathrm{d} F}{\mathrm{~d} z}=-\frac{F}{l},$$
where the “mean free path” $l$ is
$$l=\frac{1}{n \sigma} .$$
For a thick target, (3.25) implies that the flux declines exponentially
$$F(z)=F(0) \mathrm{e}^{-z / l} .$$
If the material contains different types of objects $i$ of number density and cross-section $n_i$ and $\sigma_i$, then (3.6) implies that the mean free path is given by
$$l^{-1}=\sum_i n_i \sigma_i .$$
The mean lifetime of a particle in the beam is the mean free path divided by the beam velocity $v$
$$\tau=\frac{l}{v}=\frac{1}{n_{\mathrm{T}} \sigma_{\mathrm{tot}} v} .$$

The inverse of the mean lifetime is the “reaction rate”
$$\lambda=n \sigma_{\text {tot }} v .$$
We will see that quantum-mechanical calculations most naturally yield the reaction rate from which one can derive the cross-section by dividing by $n v$.

# 核物理代写

## 物理代写|核物理代写nuclear physics代考|Inelastic and total cross-sections

$$a b \rightarrow x_1 x_2 \ldots x_N$$

$$\sigma_{a b \rightarrow x_1 \ldots x_N}=\int \mathrm{d}^3 \boldsymbol{p}1 \ldots \int \mathrm{d}^3 \boldsymbol{p}N \frac{\mathrm{d} \sigma}{\mathrm{d}^3 \boldsymbol{p}_1 \ldots \mathrm{d}^3 \boldsymbol{p}_N} \mathrm{~d}^3 \boldsymbol{p}_1 \ldots \mathrm{d}^3 \boldsymbol{p}_N .$$当入射粒子穿过厚度目标时，“任何事情”发生的总概率$\mathrm{d} z$只是单个反应概率的总和$$\mathrm{d} P=\sigma{\text {tot }} n_b \mathrm{~d} z$$ 总横截面在哪里 $$\sigma{\mathrm{tot}}=\sum_i \sigma_i$$

## 物理代写|核物理代写nuclear physics代考|The uses of cross-sections

$$\mathrm{d} F=-F \sigma n \mathrm{~d} z,$$

$$\frac{\mathrm{d} F}{\mathrm{~d} z}=-\frac{F}{l},$$
“平均自由路径”$l$在哪里
$$l=\frac{1}{n \sigma} .$$

$$F(z)=F(0) \mathrm{e}^{-z / l} .$$

$$l^{-1}=\sum_i n_i \sigma_i .$$

$$\tau=\frac{l}{v}=\frac{1}{n_{\mathrm{T}} \sigma_{\mathrm{tot}} v} .$$

$$\lambda=n \sigma_{\text {tot }} v .$$

## 有限元方法代写

tatistics-lab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。

## 物理代写|核物理代写nuclear physics代考|SH2302

statistics-lab™ 为您的留学生涯保驾护航 在代写核物理nuclear 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。我们的专家在代写核物理nuclear physics代写方面经验极为丰富，各种代写核物理nuclear physics相关的作业也就用不着说。

## 物理代写|核物理代写nuclear physics代考|The shell model and magic numbers

In atomic physics, the ionization energy $E_I$, i.e. the energy needed to extract an electron from a neutral atom with $Z$ electrons, displays discontinuities around $Z=2,10,18,36,54$ and 86 , i.e. for noble gases. These discontinuities are associated with closed electron shells.

An analogous phenomenon occurs in nuclear physics. There exist many experimental indications showing that atomic nuclei possess a shell-structure and that they can be constructed, like atoms, by filling successive shells of an effective potential well. For example, the nuclear analogs of atomic ionization energies are the “separation energies” $S_{\mathrm{n}}$ and $S_{\mathrm{p}}$ which are necessary in order to extract a neutron or a proton from a nucleus
$$S_{\mathrm{n}}=B(Z, N)-B(Z, N-1) \quad S_{\mathrm{p}}=B(Z, N)-B(Z-1, N) .$$
These two quantities present discontinuities at special values of $N$ or $Z$, which are called magic numbers. The most commonly mentioned are:

$$\begin{array}{lllllll} 2 & 8 & 20 & 28 & 50 & 82 & 126 . \end{array}$$
As an example, Fig. 2.7 gives the neutron separation energy of lead isotopes ( $Z=82$ ) as a function of $N$. The discontinuity at the magic number $N=126$ is clearly seen.

The discontinuity in the separation energies is due to the excess binding energy for magic nuclei as compared to that predicted by the semi-empirical Bethe-Weizsäcker mass formula. One can see this in Fig. 2.8 which plots the excess binding energy as a function of $N$ and $Z$. Large positive values of $B / A$ (experimental)- $B / A$ (theory) are observed in the vicinity of the magic numbers for neutrons $N$ as well as for protons $Z$. Figure 2.9 shows the difference as a function of $N$ and $Z$ in the vicinity of the magic numbers 28,50 , 82 and 126 .

## 物理代写|核物理代写nuclear physics代考|The shell model and the spin-orbit interaction

It is possible to understand the nuclear shell structure within the framework of a modified mean field model. If we assume that the mean potential energy is harmonic, the energy levels are
$$E_n=(n+3 / 2) \hbar \omega \quad n=n_x+n_y+n_z=0,1,2,3 \ldots,$$
where $n_{x, y, z}$ are the quantum numbers for the three orthogonal directions and can take on positive semi-definite integers. If we fill up a harmonic well with nucleons, 2 can be placed in the one $n=0$ orbital, i.e. the $\left(n_x, n_y, n_z\right)=$ $(0,0,0)$. We can place 6 in the $n=1$ level because there are 3 orbitals, $(1,0,0),(0,1,0)$ and $(0,0,1)$. The number $N(n)$ are listed in the third row of Table 2.2.

We note that the harmonic potential, like the Coulomb potential, has the peculiarity that the energies depend only on the principal quantum number $n$ and not on the angular momentum quantum number $l$. The angular momentum states, $|n, l, m\rangle$ can be constructed by taking linear combinations of the $\left|n_x, n_y, n_z\right\rangle$ states (Exercise 2.4). The allowed values of $l$ for each $n$ are shown in the second line of Table 2.2.

The magic numbers corresponding to all shells filled below the maximum $n$, as shown on the fourth line of Table 2.2, would then be 2, 8, 20, 40, 70, 112 and 168 in disagreement with observation (2.37). It might be expected that one could find another simple potential that would give the correct numbers. In general one would find that energies would depend on two quantum numbers: the angular momentum quantum number $l$ and a second giving the number of nodes of the radial wavefunction. An example of such a l-splitting is shown in Fig. 2.10. Unfortunately, it turns out that there is no simple potential that gives the correct magic numbers.

The solution to this problem, found in 1949 by M. Göppert Mayer, and by D. Haxel J. Jensen and H. Suess, is to add a spin orbit interaction for each nucleon:
$$\hat{H}=V_{\mathrm{s}-\mathrm{o}}(r) \hat{\boldsymbol{\ell}} \cdot \hat{\boldsymbol{s}} / \hbar^2$$

# 核物理代写

## 物理代写|核物理代写nuclear physics代考|The shell model and magic numbers

$$S_{\mathrm{n}}=B(Z, N)-B(Z, N-1) \quad S_{\mathrm{p}}=B(Z, N)-B(Z-1, N) .$$

$$\begin{array}{lllllll} 2 & 8 & 20 & 28 & 50 & 82 & 126 . \end{array}$$

## 物理代写|核物理代写nuclear physics代考|The shell model and the spin-orbit interaction

$$E_n=(n+3 / 2) \hbar \omega \quad n=n_x+n_y+n_z=0,1,2,3 \ldots,$$

${ }^{180 \mathrm{~m}} \mathrm{Ta}$。

## 有限元方法代写

tatistics-lab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。

## 物理代写|核物理代写nuclear physics代考|ERICE2022

statistics-lab™ 为您的留学生涯保驾护航 在代写核物理nuclear 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。我们的专家在代写核物理nuclear physics代写方面经验极为丰富，各种代写核物理nuclear physics相关的作业也就用不着说。

• 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|Feynman Diagrams

We therefore have a relativistic expression for the scattering amplitude of two particles, $a$ and $b$ (masses $m_a$ and $m_b$ ) with initial energies and momenta $\left(E_1, \boldsymbol{p}_1\right),\left(E_2, \boldsymbol{p}_2\right)$ and final energies and momenta $\left(E_3, \boldsymbol{p}_3\right),\left(E_4, \boldsymbol{p}_4\right)$. The amplitude can be represented diagrammatically as shown in Fig.16.1, which represents the scattering of two (different) particles due to the exchange of a gauge boson (force carrier) with mass $M$. This is known as a “Feynman diagram” (or “Feynman graph”) [89]. The amplitude for the process is obtained by applying a set of “Feynman rules” for each vertex, where particles interact with each other, and each internal line (the propagation of the virtual off mass-shell particle). The full set of Feynman rules takes into account the spins of the external and internal particles, which requires a detailed study of Quantum Field Theory.

Some of the Feynman rules for constructing the contribution to the amplitude from a Feynman diagram are:

• Include a (dimensionless) factor of $-g_a / \sqrt{\hbar c}$ at each vertex involving particle interacting with an exchanged gauge boson, with coupling constant $g_a$.
• Conserve energy and momentum at each vertex.
• Include a propagator factor:
$$\Delta(E, \boldsymbol{p}, M)=-\frac{1}{\left(E^2-p^2 c^2-M^2 c^4\right)},$$
for each internal particle of mass $M$ carrying energy $E$ and momentum $\boldsymbol{p}$.
• Include a factor of $(\hbar c)^{3 / 2} / \sqrt{V}$ for each outgoing particle.
For the process described by the Feynman diagram of Fig. 16.1, conservation of energy and momentum at each vertex leads to
$$\begin{gathered} E_q=\left(E_3-E_1\right)=\left(E_2-E_4\right) \ \boldsymbol{q}=\boldsymbol{p}_3-\boldsymbol{p}_1=\boldsymbol{p}_2-\boldsymbol{p}_4 \end{gathered}$$

## 物理代写|核物理代写nuclear physics代考|Multiple Feynman Graphs

The internal particles must be attached to the external particles in all possible ways. Figure 16.1 represents the scattering of two different particles in which the internal gauge boson couples the initial particle with energy and momentum $\left(E_1, \boldsymbol{p}1\right)$ to the final particle with energy $\left(E_3, \boldsymbol{p}_3\right)$ at one end, and the other initial particle with energy and momentum $\left(E_2, \boldsymbol{p}_2\right)$ to the other final particle with energy $\left(E_4, p_4\right)$ at the other end. This diagram also appears in Fig. 16.2a. In the case of identical particles, it is also possible for the gauge boson to couple the initial particle with energy and momentum $\left(E_1, \boldsymbol{p}_1\right)$ to the final particle with energy $\left(E_4, \boldsymbol{p}_4\right)$ at one end, and to couple the initial particle with energy and momentum $\left(E_2, \boldsymbol{p}_2\right)$ to the final particle with energy $\left(E_3, p_3\right)$ at the other as shown in Fig. 16.2b. For diagram $(b)$, the internal particle carries energy and momentum $\left(E{q^{\prime}}, \boldsymbol{q}^{\prime}\right)$, given by
\begin{aligned} E_{q^{\prime}} & =E_1-E_4=E_3-E_2 \ \boldsymbol{q}^{\prime} & =\boldsymbol{p}1-\boldsymbol{p}_4=\boldsymbol{p}_3-\boldsymbol{p}_2 . \end{aligned} The scattering amplitude is the sum of the contributions from the two graphs. When the square modulus of the amplitude ${ }^2$ is taken, in order to calculate the cross section, there is a quantum interference term, namely the product of the contribution from the one Feynman diagram with the complex conjugate of the contribution from the other Feynman diagram. If the contributions from the two diagrams in Fig. 16.2 are $\mathcal{A}{(a)}$ and $\mathcal{A}{(b)}$, respectively, then the square modulus of the amplitude is given by $$|\mathcal{A}|^2=\left|\mathcal{A}{(a)}\right|^2+\left|\mathcal{A}{(b)}\right|^2+\mathcal{A}{(a)}^* \mathcal{A}{(b)}+\mathcal{A}{(b)}^* \mathcal{A}_{(a)} .$$

# 核物理代写

## 物理代写|核物理代写nuclear physics代考|Feynman Diagrams

• 包括一个 (无量纲) 因素 $-g_a / \sqrt{\hbar c}$ 在涉及粒子与交换规范玻色子相互作用的每个顶点，具有耦合 常数 $g_a$.
• 在每个顶点保存能量和动量。
• 包括传播因子:
$$\Delta(E, \boldsymbol{p}, M)=-\frac{1}{\left(E^2-p^2 c^2-M^2 c^4\right)}$$
对于每个内部质量粒子 $M$ 承载能量 $E$ 和势头 $\boldsymbol{p}$.
• 包括一个因素 $(\hbar c)^{3 / 2} / \sqrt{V}$ 对于每个传出粒子。 对于图 16.1 的费曼图所描述的过程，每个顶点的能量和动量守恒导致
$$E_q=\left(E_3-E_1\right)=\left(E_2-E_4\right) \boldsymbol{q}=\boldsymbol{p}_3-\boldsymbol{p}_1=\boldsymbol{p}_2-\boldsymbol{p}_4$$

## 有限元方法代写

tatistics-lab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。

## 物理代写|核物理代写nuclear physics代考|MATR316

statistics-lab™ 为您的留学生涯保驾护航 在代写核物理nuclear 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。我们的专家在代写核物理nuclear physics代写方面经验极为丰富，各种代写核物理nuclear physics相关的作业也就用不着说。

• 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|Relativistic Approach to Interactions

In Particle Physics, we are studying the interactions between sub-microscopic particles that are usually moving with velocities close to the speed of light. We therefore need a synthesis of Quantum Physics and Special Relativity in order to describe these interactions.

There are two fundamental differences between non-relativistic and relativistic Quantum Physics:

1. The Schroedinger equation describes a particle moving under a certain potential. In Special Relativity there is no such thing as a potential since this would imply an instantaneous action at the distance.
2. Since energy can be converted into mass and vice versa, particle number in a relativistic scattering event is not conserved – particles can annihilate with each other and new particles can be created. A Schroedinger wavefunction, which is normalized such that the probability of finding a particle somewhere in space is always unity, is clearly an unsuitable tool for describing such processes.

We therefore seek to modify the non-relativistic concept of potential in such a way that relativistic invariance is satisfied.

The potential due to a force, whose force carrier (gauge boson) has mass $M$, is given by the Yukawa potential [105]:
$$V(r)=\frac{g^2}{4 \pi r} e^{-M c r / \hbar}$$
where $g^2$ is a measure of the strength of the interaction that generates this potential. The quantum matrix element, $\mathcal{A}(q)$, of this potential between an initial state of a free particle with momentum $\boldsymbol{p}$ and a final state of a free particle with momentum $p+q$ (confined to a box of volume $V$ ) is $$\mathcal{A}(\boldsymbol{q})=\frac{1}{V} \int d^3 \boldsymbol{r} \frac{g^2}{4 \pi r} \exp \left{\frac{(i \boldsymbol{q} \cdot \boldsymbol{r}-M c \boldsymbol{r})}{\hbar}\right}=\frac{1}{V} \frac{g^2 \hbar^2}{\left(\boldsymbol{q}^2+M^2 c^2\right)}$$
This is not a relativistically invariant expression as the momentum transfer, $\boldsymbol{q}$, changes under a Lorentz transformation. The expression of the RHS of (16.2) can be modified to cast it into a relativistically invariant quantity, by altering it to
$$\mathcal{A}\left(E_q, \boldsymbol{q}\right)=\frac{1}{V}(g \hbar c)^2 \Delta\left(E_q, \boldsymbol{q}, M\right)$$
where
$$\Delta\left(E_q, \boldsymbol{q}, M\right)=-\frac{1}{\left(E_q^2-\boldsymbol{q}^2 c^2-M^2 c^4\right)}$$

## 物理代写|核物理代写nuclear physics代考|Relativistic Momentum Transfer

In Chap. 13 we introduced the relativistically invariant variable $s$, which in the CM frame is equal to the total energy of the incoming (or outgoing) particles. In the same way, the relativistically invariant variable $t$ is used to generalize the momentum transfer. This quantity $[101]$ is defined as
$$t=E_q^2-q^2 c^2$$
In terms of $t$, the propagator is
$$\Delta(t, M)=-\frac{1}{t-M^2 c^4}$$
In the $\mathrm{CM}$ frame, $t$ is very simply related to the scattering angle, $\theta_{\mathrm{CM}}$, between the directions of the initial and final particle momentum. $\boldsymbol{p}1$ and $\boldsymbol{p}_3$. $$t=-2 p{\mathrm{CM}}^2 c^2\left(1-\cos \theta_{\mathrm{CM}}\right)=-\left(2 p_{\mathrm{CM}} c \sin \left(\frac{\theta_{\mathrm{CM}}}{2}\right)\right)^2,$$
where $p_{\mathrm{CM}}$ is the magnitude of the momentum of the particles in the $\mathrm{CM}$ frame. In this frame, $\sqrt{-t} / c$ is the momentum transfer (see (2.7)). The (negative) value of $t$ ranges from $-4 p_{\mathrm{CM}}^2 c^2$ to zero.

The magnitude, $p_{\mathrm{CM}}$, of the momentum of the incident particles in the CM frame can be related to $s$ using the relation between energy and momentum
$$\sqrt{s}=E_1+E_2=\sqrt{p_{\mathrm{CM}}^2 c^2+m_a^2 c^4}+\sqrt{p_{\mathrm{CM}}^2 c^2+m_b^2 c^4},$$
where $m_a$ and $m_b$ are the masses of the two incoming particles. After some algebra we can write $p_{\mathrm{CM}}$ in a manifestly Lorentz invariant form, as a function of $s, m_a$ and $m_b$.

# 核物理代写

## 物理代写|核物理代写nuclear physics代考|Relativistic Approach to Interactions

1. 薛定谔方程描述了在一定电势下运动的粒子。在狭义相对论中，没有势这样的东西，因为这意味着 远处的瞬时作用。
2. 由于能量可以转化为质量，反之亦然，相对论散射事件中的粒子数不守恒一一粒子可以相互湮灭并 产生新粒子。薛定谔波函数被归一化，使得在空间某处找到粒子的概率始终为 1，显然不适合描述 此类过程的工具。
因此，我们寻求以满足相对论不变性的方式修改势的非相对论概念。
由于力的势能，其力载体（规范玻色子）具有质量 $M$ ，由汤川势 [105] 给出:
$$V(r)=\frac{g^2}{4 \pi r} e^{-M c r / \hbar}$$
在哪里 $g^2$ 是衡量产生这种潜力的相互作用的强度。量子矩阵元， $\mathcal{A}(q)$ ，具有动量的自由粒子的初始状态 之间的这种势能 $p$ 和具有动量的自由粒子的最终状态 $p+q$ (限于一盅体积 $V$ ) 是
这不是动量传递的相对论不变表达式， $\boldsymbol{q}$, 在洛伦兹变换下发生变化。可以修改 (16.2) 的 RHS 表达式以 将其转换为相对论不变的量，方法是将其更改为
$$\mathcal{A}\left(E_q, \boldsymbol{q}\right)=\frac{1}{V}(g \hbar c)^2 \Delta\left(E_q, \boldsymbol{q}, M\right)$$
在哪里
$$\Delta\left(E_q, \boldsymbol{q}, M\right)=-\frac{1}{\left(E_q^2-\boldsymbol{q}^2 c^2-M^2 c^4\right)}$$

## 物理代写|核物理代写nuclear physics代考|Relativistic Momentum Transfer

$$t=E_q^2-q^2 c^2$$

$$\Delta(t, M)=-\frac{1}{t-M^2 c^4}$$

$$\sqrt{s}=E_1+E_2=\sqrt{p_{\mathrm{CM}}^2 c^2+m_a^2 c^4}+\sqrt{p_{\mathrm{CM}}^2 c^2+m_b^2 c^4}$$

## 有限元方法代写

tatistics-lab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。

## 物理代写|核物理代写nuclear physics代考|PHYS161

statistics-lab™ 为您的留学生涯保驾护航 在代写核物理nuclear 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。我们的专家在代写核物理nuclear physics代写方面经验极为丰富，各种代写核物理nuclear physics相关的作业也就用不着说。

• 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|Force Carriers

A force has a field associated with it and, as discussed above, every field has a particle associated with it. Thus we see that each force has a particle associated with it, which is a “force carrier”. With the exception of gravity, these force carriers have intrinsic spin one (gravity is mediated by gravitons that have spin two). For reasons that we will not go into, they are more normally called “gauge bosons”.

The potential, $V_f(r)$, of a force of type $f$ decreases with distance $r$ from the source of the force as
$$V_f(r) \propto \frac{e^{-M_f c / r h}}{r},$$
where $M_f$ is the mass of the corresponding force carrier. For forces whose gauge bosons have a non-zero mass, the potential has an exponential attenuation in addition to the relatively mild $1 / r$ dependence. The range of the force is equal to the Compton wavelength of the gauge boson.

• Electromagnetic force carriers: The gauge boson of electromagnetic interactions is the photon. Since the photon is massless (it travels with the speed of light), electromagnetic interactions are long range and there is no exponential attenuation of the potential.
• Weak-interaction force carriers: Weak interactions can change the electric charge of the particle undergoing the weak interaction. For example the conversion of a neutron into a proton in a $\beta$-decay, generated by the weak interactions. In order to conserve electric charge, the gauge bosons themselves carry electric charge $\pm e$. They are called ” $W^{+}$-bosons”. The $W$-boson mass is $80.4 \mathrm{GeV} / \mathrm{c}^2$.
• These interactions are extremely short range $-$ of the order of the Compton wavelength of the $W$-boson, which is about $2.5 \times 10^{-3} \mathrm{fm}$.
• In addition to weak-interaction processes in which the interacting particle changes electric charge, there are weak interactions in which there is no change in electric charge. Such neutral weak interactions are mediated by a neutral gauge boson called the ” $Z$-boson”, whose mass, $91.2 \mathrm{GeV} / \mathrm{c}^2$, is a little greater than that of the charged $W$-boson.

## 物理代写|核物理代写nuclear physics代考|Resonances

On the other hand, particles with lifetimes much shorter than $10^{-13} \mathrm{~s}$ (“short-lived” particles) decay far too fast to leave an identifiable track in a detector. Instead, their lifetime has to be deduced from their “decay width”, $\Gamma$.

If an unstable particle of mass $M$ is produced in a scattering process in which the incident particles annihilate each other, and then decays almost immediately, the cross section has a peak at a $\mathrm{CM}$ energy $E=M c^2$, where all of the incoming energy goes into producing that particle at rest. This peak is known as a “resonance”. However, if the particle only lives for a very short time, $\tau$, the peak is not a perfectly sharp peak but is spread out over an energy range $\Gamma$, reflecting the fact that from Heisenberg’s uncertainty principle (in terms of time and energy) a process that occurs over a short period, $\tau$, leads to an energy uncertainty, $\Gamma$, where
$$\Gamma=\frac{\hbar}{\tau} \equiv \hbar \lambda,$$
$\lambda$ being the decay rate. More precisely, in the region $E \sim M c^2$, the cross section $\sigma(E)$, as a function of $\mathrm{CM}$ energy, $E$, is proportional to the “Breit-Wigner distribution”, $f(E){ }^9$ $$f(E)=\frac{1}{\left(E-M c^2\right)^3+\frac{1}{4} \Gamma^2} .$$
We see from (12.8) that this distribution has a peak at $E=M c^2$ and falls to onehalf of this value at $E=M c^2 \pm \frac{1}{2} \Gamma$. The energy interval between the two values of $E$ for which the cross section is one-half of its peak value is called the “full width at half maximum (FWHM)” and is equal to $\Gamma$.
As an example, consider the cross section for the process
$$e^{+}+e^{-} \rightarrow \mu^{+}+\mu^{-},$$
measured by the Aleph collaboration at the Large Electron-Positron Collider (LEP), shown in Fig. 12.1. The cross section has a peak at $E=91.2 \mathrm{GeV}$. This is due to the production and almost immediate decay of the $Z$-boson. The two-stage process is
$$e^{+}+e^{-} \rightarrow Z \rightarrow \mu^{+}+\mu^{-} .$$

# 核物理代写

## 物理代写|核物理代写nuclear physics代考|Force Carriers

$$V_f(r) \propto \frac{e^{-M_f c / r h}}{r}$$

• 电磁力载体：电磁相互作用的规范玻色子是光子。由于光子是无质量的 (它以光速传播)，电磁相 互作用是长程的，并且没有势能的指数衰减。
• 弱相互作用力载流子：弱相互作用可以改变经历弱相互作用的粒子的电荷。例如，将中子转化为质 子 $\beta$-衰变，由弱相互作用产生。为了保存电荷，规范玻色子本身携带电荷 $\pm e$. 他们叫 ” $W^{+}$-玻色 子”。这 $W$-玻色子质量是 $80.4 \mathrm{GeV} / \mathrm{c}^2$.
• 这些相互作用的范围极短一的康普顿波长的数量级 $W$-玻色子，这是关于 $2.5 \times 10^{-3} \mathrm{fm}$.
• 除了相互作用粒子改变电荷的弱相互作用过程之外，还有电荷没有变化的弱相互作用。这种中性弱 相互作用由称为” $Z$-玻色子”，其质量， $91.2 \mathrm{GeV} / \mathrm{c}^2$ ，比带电的稍大 $W$-玻色子。

## 物理代写|核物理代写nuclear physics代考|Resonances

$$\Gamma=\frac{\hbar}{\tau} \equiv \hbar \lambda$$
$\lambda$ 是衰减率。更确切地说，在该地区 $E \sim M c^2$ ，截面 $\sigma(E)$ ，作为函数CM活力， $E$ ，与“reit-Wigner 分 布”成正比， $f(E)^9$
$$f(E)=\frac{1}{\left(E-M c^2\right)^3+\frac{1}{4} \Gamma^2}$$

$$e^{+}+e^{-} \rightarrow \mu^{+}+\mu^{-}$$

$$e^{+}+e^{-} \rightarrow Z \rightarrow \mu^{+}+\mu^{-} \text {. }$$

## 有限元方法代写

tatistics-lab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。

## 物理代写|核物理代写nuclear physics代考|PHYSICS404

statistics-lab™ 为您的留学生涯保驾护航 在代写核物理nuclear 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。我们的专家在代写核物理nuclear physics代写方面经验极为丰富，各种代写核物理nuclear physics相关的作业也就用不着说。

• 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|What Is Particle Physics

Particle Physics explores the properties of elementary particles and their interactions with each other through the fundamental forces of Nature. The only known stable particles are the proton, neutron, electron and neutrino. Many other particles exist, but they decay very rapidly to the stable particles (possibly in stages). Such decays are energetically allowed since the particles are more massive than the stable particles. Because of their instability, these particles are not found naturally but can be produced in experiments using incident particles at sufficiently high energies, i.e. energies exceeding the rest energy of these massive particles. For this reason, Particle Physics is also called “High Energy Physics” (HEP).

The most massive particles that have been discovered so far are the top-quark with a mass of $173 \mathrm{GeV} / \mathrm{c}^2$, the Higgs boson with a mass of $125 \mathrm{GeV} / \mathrm{c}^2$, the $Z$ boson with a mass of $91.2 \mathrm{GeV} / \mathrm{c}^2$ and the $W$-boson with a mass of $80.4 \mathrm{GeV} / \mathrm{c}^2$. The masses of these particles are measured with accuracy better than $1 \%$. All these particles are around 100 times heavier than the proton. So we need really high energies in order to produce them.

Another way of seeing that we need high energies is to note that we need to probe very short distances in order to explore the properties and possible substructure of known particles – to find out if they are truly elementary, i.e. do not consist of smaller constituents.

At the very least we want to probe distances that are small compared with a typical nuclear radius, i.e.
$$x \ll 1 \mathrm{fm}=10^{-15} \mathrm{~m} .$$
In order to do this the uncertainty in the position, $\Delta x$, must be much smaller than 1 $\mathrm{fm}$, and by Heisenberg’s uncertainty principle $$\Delta x \Delta p \geq \hbar / 2$$
the uncertainty in momentum $\Delta p$ must obey the inequality
$$\Delta p \gg \frac{\hbar}{1 \mathrm{fm}}=197 \mathrm{MeV} / \mathrm{c} .$$
This in turn means that the momenta (and consequently the energy) of the particles used as a probe must be much larger than this value.

In fact, the weak interactions have a range that is about three orders of magnitude shorter than this and so particles used to investigate the mechanism of weak interactions have to have energies of at least $100 \mathrm{GeV}$.

Non-elementary particles ${ }^3$ that interact strongly are called “hadrons”. These are further divided into two sub-categories:

• “Mesons”: These are bosons with integer spin. The lightest of these are pions $(\pi)$, which come with one of three charges: $\pi^{\pm}$and $\pi^0$. The mass of the $\pi^0$ is $135 \mathrm{MeV} / \mathrm{c}^2$, which is slightly less than the mass of the $\pi^{\pm}$, whose mass is $140 \mathrm{MeV} / \mathrm{c}^2$

The $\pi^{\pm}$decays via the weak interactions into leptons. The decay mode is nearly always
$$\pi^{\pm} \rightarrow \mu^{\pm}+v_\mu\left(\bar{v}_\mu\right),$$
with a mean lifetime of $8.5 \times 10^{-8} \mathrm{~s}$. This is regarded as a “long-lived” particle. ${ }^4$ The $\pi^0$ usually decays by the electromagnetic interactions into two photons. As the electromagnetic interactions extend over much longer distance than the weak interactions, electromagnetic reaction rates are much greater so that the $\pi^0$ has a much shorter lifetime than the $\pi^{\pm}$. The lifetime of the $\pi^0$ is only $8.5 \times$ $10^{-17} \mathrm{~s}$.Since the discovery of the pion in 1947 [96], more than 200 additional mesons have been identified, with masses considerably larger than the pion. Often, these mesons decay to pions or other lighter mesons rather than directly to leptons. Lepton number has to be conserved, so that whenever there is a lepton in the final state, there is also an antilepton. A decay into leptons only is called a “leptonic decay”, whereas a decay into mesons plus leptons is called a “semi-leptonic decay”, and a decay into mesons only is called a “hadronic decay”. For example, the meson $K^{+}$can decay to one of several different final states (known as “decay channels”) amongst which are

\begin{aligned} K^{+} & \rightarrow \mu^{+}+v_\mu \text { (leptonic) } \ & \rightarrow \pi^0+e^{+}+v_e \text { (semi-leptonic) } \ & \rightarrow \pi^{+}+\pi^0 \text { (hadronic). } \end{aligned}

• “Baryons”: The name baryon comes from the Greek barys meaning heavy. Protons and neutrons are examples of baryons. Originally, the known baryons were heavier than the known mesons. The lightest baryons (the proton and neutron) have a mass more than six times greater than the lightest mesons pions. The distinctions between baryons and mesons are:
• Baryons have half odd-integer spin. Most known baryons have spin $\frac{1}{2}$ (such as protons and neutrons) or spin $\frac{3}{2}$, but some baryons have been identified with larger spins – always half odd-integer. Baryons are fermions, whereas mesons are bosons.
• Unlike mesons, the number of baryons (baryon number) is conserved. ${ }^5 \mathrm{~A}$ baryon can therefore decay into a lighter baryon plus one or more mesons and possibly leptons, but there must be a baryon in the final state.
The classification of particles is summarized in Table $12.1$.

# 核物理代写

## 物理代写|核物理代写nuclear physics代考|What Is Particle Physics

$$x \ll 1 \mathrm{fm}=10^{-15} \mathrm{~m} .$$

$$\Delta x \Delta p \geq \hbar / 2$$

$$\Delta p \gg \frac{\hbar}{1 \mathrm{fm}}=197 \mathrm{MeV} / \mathrm{c} .$$

• “介子”：这些是具有整数自旋的玻色子。其中最轻的是 $介$ 介子 $(\pi)$ ，它带有以下三种费用之一： $\pi^{\pm}$ 和 $\pi^0$. 的质量 $\pi^0$ 是 $135 \mathrm{MeV} / \mathrm{c}^2$ ，略小于 $\pi^{\pm}$，其质量为 $140 \mathrm{MeV} / \mathrm{c}^2$
这 $\pi^{\pm}$通过弱相互作用衰变为轻子。衰减模式几乎总是
$$\pi^{\pm} \rightarrow \mu^{\pm}+v_\mu\left(\bar{v}\mu\right),$$ 平均寿命为 $8.5 \times 10^{-8} \mathrm{~s}$. 这被视为“长寿命”粒子。 ${ }^4$ 这 $\pi^0$ 通常通过电磁相互作用衰减成两个光子。由于 电磁相互作用比弱相互作用延伸的距离长得多，因此电磁反应速率要大得多，因此 $\pi^0$ 寿命比 $\pi^{\pm}$. 的生命 周期 $\pi^0$ 只是 $8.5 \times 10^{-17} \mathrm{~s}$. 自从 1947 年发现介子 [96] 以来，又发现了 200 多个介子，其质量比介子大 得多。通常，这些介子会衰变成币介子或其他更轻的介子，而不是直接变成轻子。轻子数必须守恒，因此 只要有一个处于最终状态的轻子，就会有一个反轻子。仅衰变成轻子称为“轻子衰变”，而衰变成介子加轻 子称为“半轻子衰变”，仅衰变成介子称为“强子衰变”。例如，介子 $K^{+}$可以衰减到几种不同的最终状态之 -(称为“衰减通道”)，其中包括 $$K^{+} \rightarrow \mu^{+}+v\mu \text { (leptonic) } \quad \rightarrow \pi^0+e^{+}+v_e \text { (semi-leptonic) } \rightarrow \pi^{+}+\pi^0 \text { (hadronic) }$$
• “重子”：重子这个名字来自希腊语 barys，意思是重。质子和中子是重子的例子。最初，已知的重 子比已知的介子重。最轻的重子 (质子和中子) 的质量是最轻的介子π介子的六倍多。重子和介子 的区别是:
• 重子具有半奇数自旋。大多数已知的重子都有自旋 $\frac{1}{2}$ （例如质子和中子）或自旋 $\frac{3}{2}$ ，但一些重子已 被确定具有更大的自旋一一总是半奇数。重子是费米子，而介子是玻色子。
-与介子不同，重子的数量 (重子数) 是守恒的。 ${ }^5 \mathrm{~A}$ 因此，重子可以衰变为更轻的重子加上一个或 多个介子，可能还有轻子，但最终状态必须有一个重子。
颗粒的分类总结在表中 $12.1$.

## 有限元方法代写

tatistics-lab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。