## 物理代写|原子物理代写Atomic and Molecular Physics代考|PHYS40500

statistics-lab™ 为您的留学生涯保驾护航 在代写原子物理Atomic and Molecular 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。我们的专家在代写原子物理Atomic and Molecular Physics代写方面经验极为丰富，各种代写原子物理Atomic and Molecular 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|原子物理代写Atomic and Molecular Physics代考|Electron transfer Mediated Decay

Fig. 1 implies that ICD is mediated by energy transfer between the ionized and the neutral cluster units. One can also imagine, however, an interatomic decay process mediated by electron transfer. Indeed, such a mechanism is presented schematically in Fig. 2. It is analogous to the well-known Transfer Ionization (TI) in collisions [35] and has been first predicted for clusters in Ref. [36]. The energetic condition that needs to be fulfilled for the ETMD to become operational is that the inner or outer shell ionization energy of one atom or molecule in a cluster (Ne in Fig. 1) should exceed the double ionization energy of a neighboring atom or molecule (Ar in Fig. 1). In the case of the inner shell ionization, ETMD is usually suppressed by the much faster ICD [36]. In the case of the outer shell ionization, however, ETMD can turn out to be the main decay channel. The latter scenario is realized, for example, in miclrosolvation clusters of $\mathrm{Li}^{+}[37]$ :
$\mathrm{Li}^{2+} \mathrm{H}{2} \mathrm{O} \rightarrow \mathrm{Li}^{+} \mathrm{H}{2} \mathrm{O}^{2+}$
Interestingly, energy transfer and electron transfer mechanisms can be combined in a three-center decay process, whereby the energy released in the hole filling by a water electron is used to ionize a neighboring water molecule [37]:
$\mathrm{Li}^{2+}\left(\mathrm{H}{2} \mathrm{O}\right){2} \rightarrow \mathrm{Li}^{+}\left(\mathrm{H}{2} \mathrm{O}^{+}\right){2}$
Very recently, the basic two-center ETMD process has been measured experimentally in mixed clusters of Ar and heavier noble gases [38].

Further exploration of the fascinating subject of the interatomic decay phenomena and development of spectroscopic tools on their basis requires intensive theoretical effort to guide the experimental work. Such an effort is hardly possible without efficient, advanced theoretical tools involving both $a b$ initio description of the electron correlation driving the decay and a treatment of the ensuing dynamics of the ionized cluster fragments. The next section gives the theoretical picture of interatomic decay within the Born-Oppenheimer (BO) approximation. Ab initio theory of interatomic decay widths is presented in some detail for the case of the ICD process in Section III. Section IV is devoted to the theory of interatomic decay of doubly ionized states applied to Auger-ICD cascades and to the collective decay of two inner-shell vacancies. The state of the art of the theory of RICD is given in Section V. Some considerations on the future of the field are summarized in Section VI.

## 物理代写|原子物理代写Atomic and Molecular Physics代考|COUPLED ELECTRONIC AND NUCLEAR DYNAMICS OF INTERATOMIC DECAY

The main objective of the theory of ICD is efficient and reliable calculation of the measurable spectra, i.e. ICD electron kinetic energy spectrum and (where applicable) KER spectrum. The theoretical description is usually given within Born-Oppenheimer approximation, in which the electronic states are decoupled from nuclear motion and depend only parametrically on the nuclear coordinates. In this picture, the inner shell ionization and the subsequent ICD process can be visualized as a series of transitions between Potential Energy Surfaces (PESs) belonging to electronic states of different number of electrons (i.e. accompanied by electron emission). These transitions are represented schematically in Fig. 3. Initially, the system is assumed to be in the ground electronic state of the neutral (N-electron) system. The corresponding PESs of loosely bound clusters are characterized by shallow minima (e.g., in meV range for Van der Waals systems) and large equilibrium interatomic distances. Photoionization brings the cluster almost instantaneously into inner-shell-ionized (typically, inner-valence-ionized) $[(\mathrm{N}-1)$-electron] state, being the intermediate state of the decay The PES of the singly ionized system is affected by the charge – induced dipole interaction that increases the binding energy and decreases the equilibrium interatomic distances relative to the Van der Waals ground state. This means that after landing on the inner-shell-ionized PES, the nuclear wave packet is driven towards shorter internuclear distances. Due to the ICD, the intermediate state has finite lifetime. This means that the nuclear wave packet moving on the intermediate state PES can lose some of its density.

## 物理代写|原子物理代写Atomic and Molecular Physics代考|Electron transfer Mediated Decay

$\mathrm{Li}^{2+} \mathrm{H} 2 \mathrm{O} \rightarrow \mathrm{Li}^{+} \mathrm{H}{2} \mathrm{O}^{2+}$ 有趣的是，能量转移和电子转移机制可以结合在一个三中心衰变过程中，其中水电子在空穴填充中释放的能量用 于电离相邻的水分子 [37]: $\mathrm{Li}^{2+}(\mathrm{H} 2 \mathrm{O}) 2 \rightarrow \mathrm{Li}^{+}\left(\mathrm{H}{2} \mathrm{O}^{+}\right) 2$

## 物理代写|原子物理代写Atomic and Molecular Physics代考|COUPLED ELECTRONIC AND NUCLEAR DYNAMICS OF INTERATOMIC DECAY

ICD 理论的主要目标是有效和可靠地计算可测量光谱，即 ICD 电子动能谱和（如适用）KER 谱。理论描述通常在 Born-Oppenheimer 近似中给出，其中电子态与核运动解耦并且仅参数依赖于核坐标。在这张图片中，内壳电离和随后的 ICD 过程可以可视化为属于不同电子数的电子态的势能面 (PES) 之间的一系列跃迁（即伴随电子发射）。这些转变在图 3 中示意性地表示。最初，假设系统处于中性（N 电子）系统的接地电子状态。松散结合的簇的相应 PES 的特点是最小值浅（例如，范德华系统在 meV 范围内）和大的平衡原子间距离。光电离几乎瞬间将簇带入内壳电离（通常是内价电离）[(ñ−1)-electron] 态，是衰变的中间态 单电离系统的 PES 受电荷诱导偶极相互作用的影响，该相互作用会增加结合能并降低相对于范德华基态的平衡原子间距离。这意味着在着陆内壳电离 PES 后，核波包被驱向更短的核间距。由于 ICD，中间状态的寿命是有限的。这意味着在中间态 PES 上移动的核波包可能会失去一些密度。

## 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|原子物理代写Atomic and Molecular Physics代考|SL221463

statistics-lab™ 为您的留学生涯保驾护航 在代写原子物理Atomic and Molecular 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。我们的专家在代写原子物理Atomic and Molecular Physics代写方面经验极为丰富，各种代写原子物理Atomic and Molecular 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|原子物理代写Atomic and Molecular Physics代考|Numerical Solutions at Large Times

In mathematically rigorous procedures the point at $t \rightarrow \infty$ is approached by defining a new variable $\tau=1 / \mathrm{t}$ and going to the point $\tau=0$. Use of the $\tau$ variable gives a version of the Schrödinger equation that simply moves the singularity at infinite time to another location. Fundamental obstacles still remain; in particular the divergent “explosion” factor is still present. This factor can be removed from the wave function and the solution, thus reduced, no longer oscillates rapidly at large $r$. The function, however, still expands to fill a large volume therefore to preserve normalization its magnitude must decrease accordingly. This means, for example, that at distances of the order of 1000 au the magnitude of the wave function is of the order of $10^{-9}$ compared with starting values of the order of unity, thus making it difficult to integrate to distances where Eq. (5.5) applies.

To circumvent the dimension problem one may scale the coordinates so that space expands with time. This does not lead to new singularities if the explosion factor has been removed. The corresponding theory closely follows the earlier hidden crossing theory of Solov’ev mentioned in Sec. IV. To make the transformations somewhat more general, scaling by a factor $R_{s}=\sqrt{b_{x}^{2}+v_{x}^{2} x^{2}}$ rather than the physical internuclear distance $R=\sqrt{b^{2}+v^{2} t^{2}}$ is employed. This has the advantage that scale of the coordinates in the region near $t=0$ is selected by the parameter $b_{s}$, which can be chosen to obtain optimal precision in that crucial region while still maintaining the linear scaling with $t$ for large times. The parameter $v_{s}$ is included only for dimensional consistency since changing $v_{\mathrm{s}}$ is equivalent to changing the mesh of the time step $\Delta t$.

## 物理代写|原子物理代写Atomic and Molecular Physics代考|Hydrodynamic Representation of the Schrödinger Equation

Fluid flow is governed by the Navier-Stokes equations. For our purposes the most general form of these equations is not needed, rather a special form where both the viscosity and the bulk viscosity of the fluid vanish, are used. This special case is one of Euler’s equations [29] for fluid flow for an ideal fluid with density $\rho$
$$\frac{\partial v}{\partial t}+\boldsymbol{v} \cdot \nabla \boldsymbol{v}+\frac{\nabla \boldsymbol{p}}{\rho}-\frac{\boldsymbol{f}}{\rho}=0$$
where $f$ is the force per unit volume.
Eq. (6.6) is essentially Newton’s equation for the acceleration of a fluid element under the influence of a force due to the pressure $p$ and force $f$ per unit volume due to an external field.

Note that $f / p$ has the dimensions of force per unit mass. In addition there is the equation of continuity expressing the conservation of mass:
$$\frac{\partial}{\partial t}+\nabla \cdot(\rho v)=0$$

## 物理代写|原子物理代写Atomic and Molecular Physics代考|Hydrodynamic Representation of the Schrödinger Equation

$$\frac{\partial v}{\partial t}+\boldsymbol{v} \cdot \nabla \boldsymbol{v}+\frac{\nabla \boldsymbol{p}}{\rho}-\frac{\boldsymbol{f}}{\rho}=0$$

$$\frac{\partial}{\partial t}+\nabla \cdot(\rho v)=0$$

## 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|原子物理代写Atomic and Molecular Physics代考|PHYS144

statistics-lab™ 为您的留学生涯保驾护航 在代写原子物理Atomic and Molecular 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。我们的专家在代写原子物理Atomic and Molecular Physics代写方面经验极为丰富，各种代写原子物理Atomic and Molecular 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|原子物理代写Atomic and Molecular Physics代考|TIME IN QUANTUM MECHANICS

Time is introduced into the quantum mechanics simply by incorporating a “clock” as a part of the physical system in addition to the parts that constitute our main interest. This can be done in a general way, demonstrating that the details of the clock make no difference in final result [17]. Alternatively, one can use the simplest possible “clock” to introduce time since the exact nature of the timepiece is of peripheral importance. To that end we will suppose that time is measured by a time of flight technique [16]. That is, we suppose that if the mass and energy, or velocity of a particle is known, then its position $R=v t$ defines the time $t$. For simplicity, the coordinates of the clock are just the particle’s position $\varsigma=v t$ on the z-axis. If $H$ is the Hamiltonian for the system without the clock then the Schrödinger equation with the clock is,
$$\left(-\frac{\hbar^{2}}{2 M} \frac{\partial^{2}}{\partial \varsigma^{2}}+H\right) \Psi=E \Psi$$
where $M$ is the mass of the “clock” particle. Setting $\Psi=\exp [i K \zeta] \psi$ with $E=\frac{\hbar^{2} K^{2}}{2 M}$ in Eq. (2.1) gives the equivalent equation.
$$\left(-\frac{\hbar^{2}}{2 M} \frac{\partial^{2}}{\partial \zeta^{2}}-i \hbar^{2} \frac{K}{M} \frac{\partial}{\partial \zeta}+H\right) \psi=0$$
Eq. (2.2) is fully equivalent to Eq. (2.1) but has a rather different appearance owing to the absence of the energy $E$ on the right hand side. This is compensated for by the presence of the first derivative term on the left hand side. Using that $\hbar K / M=\mathrm{v}$, setting $\varsigma=v t$, and taking the limit that $M \rightarrow \infty$ gives the timedependent Schrödinger equation;
$$H \psi=i \hbar \frac{\partial \psi}{\partial t}$$
where the Hamiltonian $H$ may or may not depend explicitly upon the time variable $t$. In either case, the time-dependent Schrödinger equation emerges from the time-independent equation when a macroscopic clock is explicitly introduced. Note that the limit $M \rightarrow \infty$ with $v$ held constant is considered as a macroscopic limit in this construction.

## 物理代写|原子物理代写Atomic and Molecular Physics代考|BASIS SET METHODS

In those cases where the Hamiltonian $H$ is time-independent the Schrödinger equation Eq. (2.3) has solutions with a simple phase factor.

$$\psi({\Gamma}, \mathrm{t})=\phi({\mathrm{r}}) \exp [-\mathrm{i} E \mathrm{t} / h]$$
so that we recover the time-independent Schrödinger equation without the “clock” degrees of freedom.
$$\mathrm{H}{\phi}({\mathrm{r}})=\mathrm{E} \phi({\mathrm{r}}) .$$ Here $E$ is energy different from the essentially infinite value of $E=\lim {M \rightarrow \infty} \hbar^{2} M v^{2} \rightarrow \infty$, appearing in Eq. (2.1). Solutions of Eq. (2.3) include bound states $\phi_{m}$ and continuum states $\phi_{c}$. It will be assumed that the center of mass motion is factored out and the remaining particle coordinates ${\boldsymbol{r}}$ number $3 N$ as for $N$ independent particles. The set symbol ${\boldsymbol{r}}$ indicates that the coordinate includes the spin variable. Associated with each $N$ particle is a reduced mass. For simplicity we will consider that these particles are all electrons or possibly nuclei with a given, possibly time-dependent, coordinates and that the spin degrees of freedom in $H$ all refer to electron coordinates. Since $E$ is fixed the solutions are eigenstates of the energy operator $H$. To articulate the general theory as simply as possible it is assumed that $H$ describes a oneelectron species, which could be an atom or an $\mathrm{H}^{+}$-like molecular ion. In this case the set of coordinates ${\boldsymbol{r}}$ becomes just one spatial coordinate $r$. Where needed, generalizations to more than one electron will be indicated with a minimum of mathematical detail.

## 物理代写|原子物理代写Atomic and Molecular Physics代考|TIME IN QUANTUM MECHANICS

$$\left(-\frac{\hbar^{2}}{2 M} \frac{\partial^{2}}{\partial \varsigma^{2}}+H\right) \Psi=E \Psi$$

$$\left(-\frac{\hbar^{2}}{2 M} \frac{\partial^{2}}{\partial \zeta^{2}}-i \hbar^{2} \frac{K}{M} \frac{\partial}{\partial \zeta}+H\right) \psi=0$$

$$H \psi=i \hbar \frac{\partial \psi}{\partial t}$$

## 物理代写|原子物理代写Atomic and Molecular Physics代考|BASIS SET METHODS

$$\psi(\Gamma, \mathrm{t})=\phi(\mathrm{r}) \exp [-\mathrm{i} E \mathrm{t} / h]$$

$$\mathrm{H} \phi(\mathrm{r})=\mathrm{E} \phi(\mathrm{r}) .$$

## 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。