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## 物理代写|核物理代考Nuclear Physics代写|One-particle states

The nucleon has isospin $1 / 2$. In other words, each of the operators $T_1, T_2$ and $T_3$ which are associated with this particle have eigenvalues $\pm 1 / 2$. The operator $T^2=T_1^2+T_2^2+T_3^2$ is proportional to the identity with eigenvalue $3 / 4$.

The states $|\mathrm{p}\rangle$ and $|\mathrm{n}\rangle$, are, by definition, the eigenstates of the particular operator $T_3$
$$T_3|\mathrm{p}\rangle=(1 / 2)|\mathrm{p}\rangle, \quad T_3|\mathrm{n}\rangle=(-1 / 2)|\mathrm{n}\rangle$$
In actual physics, the operator $T_3$ plays a special role since electric charge is related to $T_3$ by
$$Q=T_3+1 / 2$$
The action of $T_1$ and $T_2$ on these states, with $T_{ \pm}=T_1 \pm T_2$, can be written as
\begin{aligned} T_{+}|\mathrm{p}\rangle=0 & T_{-}|\mathrm{n}\rangle=0 \ T_1|\mathrm{p}\rangle=(1 / 2)|\mathrm{n}\rangle & T_1|\mathrm{n}\rangle=(1 / 2)|\mathrm{p}\rangle \ T_2|\mathrm{p}\rangle=(\mathrm{i} / 2)|\mathrm{n}\rangle & T_2|\mathrm{n}\rangle=(-\mathrm{i} / 2)|\mathrm{p}\rangle . \end{aligned}
An arbitrary nucleon state $|N\rangle$ is written
$$|N\rangle=\alpha|\mathrm{p}\rangle+\beta|\mathrm{n}\rangle \quad|\alpha|^2+|\beta|^2=1$$
We remark that all of this is an abstraction applicable only to a world without electromagnetism. A state such as
$$\frac{1}{\sqrt{2}}\left(\left|T_3=1 / 2\right\rangle+\left|T_3=-1 / 2\right\rangle\right),$$
which is oriented along the direction $T_2$ cannot be observed physically. Since it is a superposition of a proton and a neutron, it is both of charge 0 and 1 ; at the same time it creates and doesn’t create an electrostatic field. As such, it is a superposition of two macroscopically different states, an example of a “Schrödinger cat.”

## 物理代写|核物理代考Nuclear Physics代写|The generalized Pauli principle

The Pauli principle states that two identical fermions must be in an antisymmetric state. If the proton and the neutron were truly identical particles up to the projection of their isospin along the axis $T_3$, a state of several nucleons should be completely antisymmetric under the exchange of all variables, including isospin variables. If we forget about electromagnetic interactions, and assume exact invariance under rotations in isospin space, the Pauli principle is generalized by stating that an $A$-nucleon system is completely antisymmetric under the exchange of space, spin and isospin variables. This assumption does not rest on as firm a foundation as the normal Pauli principle and is only an approximation. However, we can expect that it is a good approximation, up to electromagnetic effects.

The generalized Pauli principle restricts the number of allowed quantum states for a system of nucleons. We shall see below how this determines the allowed states of the deuteron.

# 核物理代写

## 物理代写|核物理代考Nuclear Physics代写|One-particle states

$$T_3|\mathrm{p}\rangle=(1 / 2)|\mathrm{p}\rangle, \quad T_3|\mathrm{n}\rangle=(-1 / 2)|\mathrm{n}\rangle$$

$$Q=T_3+1 / 2$$
$T_1$和$T_2$对这些状态的作用，加上$T_{ \pm}=T_1 \pm T_2$，可以写成
\begin{aligned} T_{+}|\mathrm{p}\rangle=0 & T_{-}|\mathrm{n}\rangle=0 \ T_1|\mathrm{p}\rangle=(1 / 2)|\mathrm{n}\rangle & T_1|\mathrm{n}\rangle=(1 / 2)|\mathrm{p}\rangle \ T_2|\mathrm{p}\rangle=(\mathrm{i} / 2)|\mathrm{n}\rangle & T_2|\mathrm{n}\rangle=(-\mathrm{i} / 2)|\mathrm{p}\rangle . \end{aligned}

$$|N\rangle=\alpha|\mathrm{p}\rangle+\beta|\mathrm{n}\rangle \quad|\alpha|^2+|\beta|^2=1$$

$$\frac{1}{\sqrt{2}}\left(\left|T_3=1 / 2\right\rangle+\left|T_3=-1 / 2\right\rangle\right),$$

## 物理代写|核物理代考Nuclear Physics代写|The generalized Pauli principle

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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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## 物理代写|核物理代考Nuclear Physics代写|Nuclear reactions and decays

Nuclear species can be transformed in a multitude of nuclear reactions. In nuclear reactions involving only strong and electromagnetic interactions, the number of protons and the number of neutrons are conserved separately. An important example is neutron absorption followed by photon emission, the so-called ” $(n, \gamma) “$ reaction:
$$\mathrm{n}(\mathrm{A}, \mathrm{Z}) \rightarrow \gamma(\mathrm{A}+1, \mathrm{Z}) \quad \text { i.e. } \quad(\mathrm{A}, \mathrm{Z})(\mathrm{n}, \gamma)(\mathrm{A}+1, \mathrm{Z})$$
The second form is a standard way of denoting the reaction. Other reactions are ” $(\mathrm{p}, \gamma) “$ reactions
$$\mathrm{p}(\mathrm{A}, \mathrm{Z}) \rightarrow \gamma(\mathrm{A}+1, \mathrm{Z}+1) \text { i.e. }(\mathrm{A}, \mathrm{Z})(\mathrm{p}, \gamma)(\mathrm{A}+1, \mathrm{Z}+1)$$
“( $(\mathrm{n}, \mathrm{p}) “$ reactions
$$\mathrm{n}(\mathrm{A}, \mathrm{Z}) \rightarrow \mathrm{p}(\mathrm{A}, \mathrm{Z}-1) \text { i.e. }(\mathrm{A}, \mathrm{Z})(\mathrm{n}, \mathrm{p})(\mathrm{A}, \mathrm{Z}-1)$$
and ” $(\mathrm{p}, \mathrm{n})$ ” reactions
$$\mathrm{p}(\mathrm{A}, \mathrm{Z}) \rightarrow \mathrm{n}(\mathrm{A}, \mathrm{Z}+1) \quad \text { i.e. } \quad(\mathrm{A}, \mathrm{Z})(\mathrm{p}, \mathrm{n})(\mathrm{A}, \mathrm{Z}+1) \text {. }$$
In all these reactions, the final state nucleus may be produced in an excited state so additional photons are produced in de-excitation.

## 物理代写|核物理代考Nuclear Physics代写|Conservation laws

The investigation of the fundamental constituents of matter and their interactions comes from the experimental and theoretical analysis of reactions. These reactions can be scattering experiments with or without production of particles, and decays of the unstable particles produced in these reactions.

Various fundamental conservation laws govern nuclear reactions. The laws allow the identification of particles, i.e. the determination of their masses, spins, energies, momenta etc.

The most important laws are energy-momentum conservation, angular momentum conservation and electric charge conservation. In nuclear physics, other laws play an important role such as lepton number, baryon number and isospin conservation.

In this book, we shall mainly make use of simple “selection rules” implied by these conservation laws. In this section, we will first discuss the experimental and phenomenological consequences of the most important laws. We will then show how the conservation laws are related to invariance properties of transition operators between initial and final states, or, equivalently, invariance laws of Hamiltonians of the systems under consideration.

# 核物理代写

## 物理代写|核物理代考Nuclear Physics代写|Nuclear reactions and decays

$$\mathrm{n}(\mathrm{A}, \mathrm{Z}) \rightarrow \gamma(\mathrm{A}+1, \mathrm{Z}) \quad \text { i.e. } \quad(\mathrm{A}, \mathrm{Z})(\mathrm{n}, \gamma)(\mathrm{A}+1, \mathrm{Z})$$

$$\mathrm{p}(\mathrm{A}, \mathrm{Z}) \rightarrow \gamma(\mathrm{A}+1, \mathrm{Z}+1) \text { i.e. }(\mathrm{A}, \mathrm{Z})(\mathrm{p}, \gamma)(\mathrm{A}+1, \mathrm{Z}+1)$$
($(\mathrm{n}, \mathrm{p}) “$反应)
$$\mathrm{n}(\mathrm{A}, \mathrm{Z}) \rightarrow \mathrm{p}(\mathrm{A}, \mathrm{Z}-1) \text { i.e. }(\mathrm{A}, \mathrm{Z})(\mathrm{n}, \mathrm{p})(\mathrm{A}, \mathrm{Z}-1)$$

$$\mathrm{p}(\mathrm{A}, \mathrm{Z}) \rightarrow \mathrm{n}(\mathrm{A}, \mathrm{Z}+1) \quad \text { i.e. } \quad(\mathrm{A}, \mathrm{Z})(\mathrm{p}, \mathrm{n})(\mathrm{A}, \mathrm{Z}+1) \text {. }$$

## 物理代写|核物理代考Nuclear Physics代写|Conservation laws

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。

Posted on Categories:Nuclear Physics, 核物理, 物理代写

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Quantum effects inside nuclei are fundamental. It is therefore surprising that the volume $\mathcal{V}$ of a nucleus is, to good approximation, proportional to the number of nucleons $A$ with each nucleon occupying a volume of the order of $\mathcal{V}_0=7.2 \mathrm{fm}^3$. In first approximation, stable nuclei are spherical, so a volume $\mathcal{V} \simeq A \mathcal{V}_0$ implies a radius
$$R=r_0 A^{1 / 3} \quad \text { with } \quad r_0=1.2 \mathrm{fm} \quad .$$
We shall see that $r_0$ in (1.9) is the order of magnitude of the range of nuclear forces.

In Chap. 3 we will show how one can determine the spatial distribution of nucleons inside a nucleus by scattering electrons off the nucleus. Electrons can penetrate inside the nucleus so their trajectories are sensitive to the charge distribution. This allows one to reconstruct the proton density, or equivalently the proton probability distribution $\rho_p(r)$. Figure 1.1 shows the charge densities inside various nuclei as functions of the distance to the nuclear center.

We see on this figure that for $A>40$ the charge density, therefore the proton density, is roughly constant inside these nuclei. It is independent of the nucleus under consideration and it is roughly 0.075 protons per $\mathrm{fm}^3$. Assuming the neutron and proton densities are the same, we find a nucleon density inside nuclei of
$$\rho_0 \simeq 0.15 \text { nucleons } \mathrm{fm}^{-3} .$$
If the nucleon density were exactly constant up to a radius $R$ and zero beyond, the radius $R$ would be given by (1.9). Figure 1.1 indicates that the density drops from the above value to zero over a region of thickness $\sim 2 \mathrm{fm}$ about the nominal radius $R$.

## 物理代写|核物理代考Nuclear Physics代写|Binding energies

The saturation phenomenon observed in nuclear radii also appears in nuclear binding energies. The binding energy $B$ of a nucleus is defined as the negative of the difference between the nuclear mass and the sum of the masses of the constituents:
$$B(A, Z)=N m_{\mathrm{n}} c^2+Z m_{\mathrm{p}} c^2-m(A, Z) c^2$$
Note that $B$ is defined as a positive number: $B(A, Z)=-E_B(A, Z)$ where $E_B$ is the usual (negative) binding energy.

The binding energy per nucleon $B / A$ as a function of $A$ is shown in Fig. 1.2. We observe that $B / A$ increases with $A$ in light nuclei, and reaches a broad maximum around $A \simeq 55-60$ in the iron-nickel region. Beyond, it decreases slowly as a function of $A$. This immediately tells us that energy can be released by the “fusion” of light nuclei into heavier ones, or by the “fission” of heavy nuclei into lighter ones.

As for nuclear volumes, it is observed that for stable nuclei which are not too small, say for $A>12$, the binding energy $B$ is in first approximation additive, i.e. proportional to the number of nucleons :
$$B(A, Z) \simeq A \times 8 \mathrm{MeV}$$
or more precisely
$$7.7 \mathrm{MeV}<B(A, Z) / A<8.8 \mathrm{MeV} \quad 12<A<225$$
The numerical value of $\sim 8 \mathrm{MeV}$ per nucleon is worth remembering!
The additivity of binding energies is quite different from what happens in atomic physics where the binding energy of an atom with $Z$ electrons increases as $Z^{7 / 3}$, i.e. $Z^{4 / 3}$ per electron. The nuclear additivity is again a manifestation of the saturation of nuclear forces mentioned above. It is surprising from the quantum mechanical point of view. In fact, since the binding energy arises from the pairwise nucleon-nucleon interactions, one might expect that $B(A, Z) / A$ should increase with the number of nucleon pairs $A(A-1) / 2 .{ }^1$ The additivity confirms that nucleons only interact strongly with their nearest neighbors.

# 核物理代写

$$R=r_0 A^{1 / 3} \quad \text { with } \quad r_0=1.2 \mathrm{fm} \quad .$$

$$\rho_0 \simeq 0.15 \text { nucleons } \mathrm{fm}^{-3} .$$

## 物理代写|核物理代考Nuclear Physics代写|Binding energies

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

$$B(A, Z) \simeq A \times 8 \mathrm{MeV}$$

$$7.7 \mathrm{MeV}<B(A, Z) / A<8.8 \mathrm{MeV} \quad 12<A<225$$

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。

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|Energy loss of electrons

Unlike heavy charged particles, electrons that enter a medium have a mass identical to the target particles, and the energy that is transferred ranges between 0 and half the kinetic energy of the incoming electron: $\left(E-m c^2\right) / 2$. The maximum kinetic energy that can be transferred is different from $2 m_e \gamma^2 c^2 \beta^2$ and the Bethe formula must be corrected accordingly. Besides, the formula must account for the Pauli exclusion principle since the incoming particle and the scattering center are two identical fermions. The corresponding Bethe formula can be written analytically with empirical corrections similar to the shell and density effects (Leo, 1994).

The electrons, however, show an additional mechanism of energy loss in matter. Radiation loss or bremsstrahlung, which means braking radiation in German, is the radiation produced by the acceleration or deceleration of a charged particle. Radiation losses follow from the Maxwell equations and take place in any charged particle. The irradiated power (Griffiths, 2017), however, is $\sim \gamma^6$ if the acceleration is parallel to the velocity and $\sim \gamma^4$ if it is perpendicular like, e.g., in circular accelerators. Since $\gamma=E / m$, this source of losses is negligible for heavy particles up to $\mathrm{TeV}$ energies but is the leading energy-loss mechanism for electrons. In quantum mechanics (QM), bremsstrahlung corresponds to the spontaneous emission of photons by an electron in a medium. Four-momentum conservation forbids the $e^{-} \rightarrow e^{-} \gamma$ transition in vacuum but the process can occur in the proximity of another particle and the transition probability linearly increases with the density of the medium. Even if the quantum mechanic treatment of radiation losses is complicated, its empirical description is rather simple. Radiation losses become dominant above the critical energy, which is the energy when the energy loss due to radiation overtakes the ionization loss, the loss due to the interactions with the electrons of the medium described by the Bethe formula. Unlike heavy charged particles, the medium plays a crucial role because it changes the trajectory of the incoming electron, causing the breaking radiation. The critical energy is often measured and tabulated but some empirical formulas are available, too. For solid materials,
$$E_c \simeq \frac{610 \mathrm{MeV}}{Z+1.24} .$$

## 物理代写|核物理代考Nuclear Physics代写|The discovery of antimatter

The energy loss of charged particles with matter was established at the beginning of the 20th century for all particles known at that time: electrons, protons, and light nuclei. The energy released to the atomic electrons can either bring the atoms to an excited state or move the electron to the continuum ionizing the atom (see Sec. 3.5). If the air temperature and humidity are properly tuned, highly ionized air acts as a condensation center for the formation of water droplets and, eventually, the clouds. Even if the dynamic of cloud formation is extremely complex and still at the focus of modern research in chemistry and environmental science, the basic formation principle can be exploited to visualize the trajectory of charged particles. An expansion cloud chamber consists of a vessel containing a supersaturated vapor of water. If the gas mixture is at the point of condensation, a trail of small droplets forms in the volume where the density of ions is high. The droplets are visible along the trajectory of the particle for several seconds while they fall through the vapor. The detector is called an expansion chamber because we use a diaphragm to perform the adiabatic expansion that cools the air and starts the condensation of the vapor. The detector is sensitive to particles only after the expansion of the diaphragm, which is set in coincidence with a camera that takes pictures of the tracks. Cloud chambers have been used since 1911 to observe tracks produced by cosmic rays and radioactive decays. The most celebrated application is the discovery of the first anti-particle in 1932 by C.D. Anderson (Anderson, 1933) confirmed nearly at the same time by P. Blackett and G. Occhialini (Blackett, 1933).

# 核物理代写

## 物理代写|核物理代考Nuclear Physics代写|Energy loss of electrons

$$E_c \simeq \frac{610 \mathrm{MeV}}{Z+1.24} .$$

## 物理代写|核物理代考Nuclear Physics代写|The discovery of antimatter

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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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## 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

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

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。

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|The Minkowski space-time

The covariant formalism makes very clear the rich mathematical structure of SR. It also provides simple means to construct relativistic dynamics in analogy to classical physics, as shown in Sec. A.3.

The first observable we can build using covariance is the trajectory of a point-like particle. In classical physics, the trajectory is a function that maps the position in space as a function of time. Since time is universal, the distance between two points is the same for any observer even if the coordinates of the points change among observers. The (squared) distance traveled between $t$ and $t+d t$ is thus the same in any inertial frame and is equal to:
$$d s^{2}=d x^{2}+d y^{2}+d z^{2}$$
where
$$d \mathbf{x}=d x \mathbf{i}+d y \mathbf{j}+d z \mathbf{k}$$

## 物理代写|核物理代考Nuclear Physics代写|Notations for special relativity

It is easy to get confused when classical and relativistic quantities are mixed up and we do it pretty often for the reasons mentioned in Sec. 2.2. These habits are annoying for novices but very much appreciated by experienced users, provided that a consistent notation is employed. By happy chance, particle and nuclear physicists use a nearly universal notation, which is summarized here and employed in the rest of the book. • Classical three-vectors are always written in boldface. The position in space of a particle is written as x. The scalar product of classical three-vectors is a · b and should be interpreted as axbx + ayby + azbz. The norm of a is written as |a| and is the standard Euclidean norm: |a| = (a 2 x + a 2 y + a 2 z ) 1/2 . • Four-vectors are written with Greek indexes as a µ or simply a. The squared “norm” of a µ in the Minkovsky space is a 2 ≡ aµa µ = gµνa µa ν = (a 0 ) 2 −(a 1 ) 2 −(a 2 ) 2 −(a 3 ) 2 . For convenience, you may want to write it in a neater form using three-vectors: a 2 = aµa µ = (a 0 ) 2 − |a| 2 .

# 核物理代写

## 物理代写核物理代考Nuclear Physics代写|The Minkowski space-time

$$d s^{2}=d x^{2}+d y^{2}+d z^{2}$$

$$d \mathbf{x}=d x \mathbf{i}+d y \mathbf{j}+d z \mathbf{k}$$

## 物理代写|核物理代考Nuclear Physics代写|Notations for special relativity

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。

Posted on Categories:Nuclear Physics, 核物理, 物理代写

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

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## 物理代写|核物理代考Nuclear Physics代写|The Minkowski space-time

The covariant formalism makes very clear the rich mathematical structure of SR. It also provides simple means to construct relativistic dynamics in analogy to classical physics, as shown in Sec. A.3.

The first observable we can build using covariance is the trajectory of a point-like particle. In classical physics, the trajectory is a function that maps the position in space as a function of time. Since time is universal, the distance between two points is the same for any observer even if the coordinates of the points change among observers. The (squared) distance traveled between $t$ and $t+d t$ is thus the same in any inertial frame and is equal to:
$$d s^{2}=d x^{2}+d y^{2}+d z^{2}$$
where
$$d \mathbf{x}=d x \mathbf{i}+d y \mathbf{j}+d z \mathbf{k}$$

## 物理代写|核物理代考Nuclear Physics代写|Notations for special relativity

It is easy to get confused when classical and relativistic quantities are mixed up and we do it pretty often for the reasons mentioned in Sec. 2.2. These habits are annoying for novices but very much appreciated by experienced users, provided that a consistent notation is employed. By happy chance, particle and nuclear physicists use a nearly universal notation, which is summarized here and employed in the rest of the book. • Classical three-vectors are always written in boldface. The position in space of a particle is written as x. The scalar product of classical three-vectors is a · b and should be interpreted as axbx + ayby + azbz. The norm of a is written as |a| and is the standard Euclidean norm: |a| = (a 2 x + a 2 y + a 2 z ) 1/2 . • Four-vectors are written with Greek indexes as a µ or simply a. The squared “norm” of a µ in the Minkovsky space is a 2 ≡ aµa µ = gµνa µa ν = (a 0 ) 2 −(a 1 ) 2 −(a 2 ) 2 −(a 3 ) 2 . For convenience, you may want to write it in a neater form using three-vectors: a 2 = aµa µ = (a 0 ) 2 − |a| 2 .

# 核物理代写

## 物理代写核物理代考Nuclear Physics代写|The Minkowski space-time

$$d s^{2}=d x^{2}+d y^{2}+d z^{2}$$

$$d \mathbf{x}=d x \mathbf{i}+d y \mathbf{j}+d z \mathbf{k}$$

## 物理代写|核物理代考Nuclear Physics代写|Notations for special relativity

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。

Posted on Categories:Nuclear Physics, 核物理, 物理代写

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

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

Particle physics is rooted in special relativity (SR) and the principles of the theory are embedded in the units (c = 1) and language of particle physicists. This choice comes as no surprise: SR requires a generalization (general relativity, GR) only when gravitational interactions play a role in the dynamics of a system. This situation is extremely rare in particle physics, where other interactions are overwhelming and the distances traveled by particles are so small that space-time can always be considered locally flat. In this framework, SR can be easily employed to handle non-inertial systems and accelerating particles too (see Sec. A.7). Exceptions arise, for instance, when considering the motion of a particle at cosmological distances or in the proximity of a black hole, where a description based on GR is mandatory. The concept of covariance can be introduced on a general ground to cope with SR, GR and quantum gravity and can be restricted to SR in all cases of interest for this book.

## 物理代写|核物理代考Nuclear Physics代写|Covariant and contravariant quantities Modern geometry describes and classifies objects based

For concreteness, consider a vector $\mathbf{v}$ in the origin of a coordinate system of a three-dimensional (3-D) Euclidean space. The coordinates depend on the choice of the versors or unit-vectors ${ }^{2}$ describing the points in space (see Fig. 2.1):
$$\mathbf{v}=v_{1} \mathbf{i}+v_{2} \mathbf{j}+v_{3} \mathbf{k}$$
A different choice of the versors corresponds to changing the basis of the Euclidean space and, then, of $\mathbb{R}^{3}$. The new vector $\mathbf{v}^{\prime}$ expressed in the new basis is:
$$\mathbf{v}^{\prime}=v_{1}^{\prime} \mathbf{i}^{\prime}+v_{2}^{\prime} \mathbf{j}^{\prime}+v_{3}^{\prime} \mathbf{k}^{\prime}$$

# 核物理代写

## 物理代写|核物理代考Nuclear Physics代写|Covariant and contravariant quantities Modern geometry describes and classifies objects based

$$\mathbf{v}=v_{1} \mathbf{i}+v_{2} \mathbf{j}+v_{3} \mathbf{k}$$

$$\mathbf{v}^{\prime}=v_{1}^{\prime} \mathbf{i}^{\prime}+v_{2}^{\prime} \mathbf{j}^{\prime}+v_{3}^{\prime} \mathbf{k}^{\prime}$$

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。

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|The Higgs boson

The Standard Model also predicts a spin-0 neutral elementary particle: the Higgs boson. Its existence has been disputed for decades because it does not descend straightforwardly from the basic principles of the theory. The Higgs mechanism is a technique inherited from other fields (material science and hadron physics) and adapted to particle physics to provide mass to the spin-1 bosons of the weak interactions. The interaction of the Higgs field with the elementary fermions provides masses to these fermions as well. The Higgs is, therefore, a mass generation mechanism. Without it, all elementary particles would be very similar to the photon. The mechanism gives firm predictions of the mass of the $Z^{0}$ and the $W$ s but lacks predictive power about the mass of the fermions and the Higgs boson itself. The mass generation mechanism for elementary fermions due to the Higgs is called the Yukawa sector of the SM and adds a rich set of phenomena that are at the frontier of modern research and will be recapped in the last chapter of this book. The Higgs boson was discovered in 2012 at the LHC collider at CERN and its mass is $125 \mathrm{GeV} / c^{2}$. Its lifetime is predicted by the $\mathrm{SM}$ to be $1.56 \times 10^{-22} \mathrm{~s}$, although the direct measurements are still limited by experimental uncertainties.
All known fundamental interactions of the Standard Model, its gauge bosons, and the particles that undergo these interactions are summarized in Table 1.2.

## 物理代写|核物理代考Nuclear Physics代写|Metric systems

Physical laws are constraints between physical quantities as length, time, velocity, electric charge, and the like. Only a fraction of these quantities are independent and are used as basic units in metric systems. For instance, the velocity (v) is a ratio between space x and time t and therefore x, t, and v cannot be used simultaneously to define three basic units. A metric system is fixed by the choice of the basic units and the definition of the prototypes that are associated with these units. The first metric system, formalized during the French Revolution, used the meter as the basic unit for space and the prototype was one tenmillionth of the distance from the equator to the North Pole along the earth’s circumference. ground state 0 ground state 1 Energy excited state Fig. 1.5 Energy levels of 133Cs employed for the SI definition of time. The hyperfine transition between the lowest states (the double arrow at the bottom of the figure) produces e.m. waves with a frequency of 9192631770 Hz. The “second” is defined by this frequency because of its narrow intrinsic width, which produces a nearly monochromatic line. On the other hand, NU uses a metric prototype only for energy and does not employ a dedicated prototype for time, which results in a loss of precision.

# 核物理代写

## 物理代写|核物理代考Nuclear Physics代写|Metric systems

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。