氦原子Rydberg态10G—10M磁精细结构的计算

通过自洽迭代求解Hartree方程，得到了氦原子1snl组态下的严格数值解波函数，以此构造LS耦合谱项(支项)波函数作为基矢.采用线性变分法，同时考虑交换作用和Breit-Bethe近似下的磁相互作用项，计算了氦Rydberg态10G—10M系列能级的磁精细结构，计算结果很好地符合已有的实验值.对计算方法的进一步改进提出了设想和讨论. 关键词： 氦原子 Rydberg态 磁精细结构 自洽迭代     

数值求解三维含时Schr?dinger方程及其应用

发展了一套高精度、高效率的伪谱方法,以非微扰的方式求解真实原子三维含时Schrdinger方程.该方法选用二阶劈裂算符作为时间演化算子,分别选择能谱表象和坐标表象作为含时波函数演化的两个表象.在坐标表象下波函数的径向部分使用库仑波函数离散变量表象来离散;角向波函数展开在两维的Gauss-Legendre-Fourier格点上.以H原子的光激发和光电离过程为例,进行了数值计算并和解析解进行了比对.结果表明二者符合很好.该方法很好地处理了库仑奇点问题.还计算了强激光辐照H原子的多光子电离过程,并和其他的数值方案进行了比较.结果表明,在计算收敛的前提下本方法计算效率更高. 关键词： 三维含时Schrdinger方程 库仑奇点 强场 含时波包传播     

参数微扰法计算氦原子基态能量

根据参数微扰法理论,选择有效核电荷数为z*=2-σ的两个类氢原子的ns态的波函数的组合,作为氦原子基态的1级至4级近似波函数.应用参数微扰法计算了氦原子基态4级近似能量.计算结果表明参数微扰法得到的氦原子基态4级近似能量与实验值的误差为ΔE=0.004922028e_s~2/a_0.     

氦原子1sns组态能量及其相对论修正

利用Mathemtica语言开发了一套计算氦原子1sns组态能量的程序.提出了构造氦原子1sns组态波函数的新方法,利用Rayleigh-Ritz变分法对氦原子1sns(n=2—5)组态的非相对论能量进行了计算,并计算了其相对论修正值(包括质量修正、单体达尔文修正、双体达尔文修正、自旋-自旋接触相互作用修正、轨道-轨道相互作用修正),计算结果与实验值相当接近. 关键词： 氦原子 能量 变分法 Mathemtica程序     

流体动力学相似模型计算弱简谐电场中的基态氦原子

采用基于Schrödinger方程的流体动力学相似模型的变分微扰法计算了弱时间简谐电场中基态氦原子的扰动波函数、极化率和第一共振频率,并将计算值与实验值进行了比较。     

积分方法处理多体微扰计算中无穷项求和问题

在多体微扰计算中,二级以上微扰展开会得到无穷级数.本文将计算得到的有限级数项进行数据拟合,利用所得到的函数形式对余项进行了积分处理.以计算氦原子1snd组态1D-3D能级分裂为例,利用最小二乘法,给出了一种有效的拟合函数形式以及合理的余项处理结果.     

Rydberg原子nS1/2→(n+1)S1/2双光子激发EIT-AT光谱

主要研究了热原子蒸气池中铯Rydberg原子nS_1/2→(n+1)S_1/2微波耦合的双光子光谱.铯原子基态(6S_1/2)、第一激发态(6P_3/2)、Rydberg态(69S_1/2)形成阶梯型三能级系统,弱探测光作用于基态到激发态6S_1/2→6P_3/2的跃迁,强耦合光则作用于6P_3/2→69S_1/2的Rydberg跃迁形成电磁感应透明(EIT)效应,实现对Rydberg原子的光学探测.频率fMW=11.735 GHz的微波场耦合69S_1/2→70S_1/2的Rydberg跃迁,形成微波双光子光谱.利用EIT-AT分裂光谱研究微波电场强度对双光子光谱的影响.研究表明:在强微波场作用时,EIT-AT分裂与微波场功率成正比,而弱微波场时的EIT-AT分裂与微波场功率成非线性依赖关系,理论计算与实验测量结果相一致.本文的研究对微波电场的精密测量具有一定的指导意义.     

Rydberg原子nS1/2→(n+1)S1/2双光子激发EIT-AT光谱

主要研究了热原子蒸气池中铯Rydberg原子nS_1/2→(n+1)S_1/2微波耦合的双光子光谱.铯原子基态(6S_1/2)、第一激发态(6P_3/2)、Rydberg态(69S_1/2)形成阶梯型三能级系统,弱探测光作用于基态到激发态6S_1/2→6P_3/2的跃迁,强耦合光则作用于6P_3/2→69S_1/2的Rydberg跃迁形成电磁感应透明(EIT)效应,实现对Rydberg原子的光学探测.频率fMW=11.735 GHz的微波场耦合69S_1/2→70S_1/2的Rydberg跃迁,形成微波双光子光谱.利用EIT-AT分裂光谱研究微波电场强度对双光子光谱的影响.研究表明:在强微波场作用时,EIT-AT分裂与微波场功率成正比,而弱微波场时的EIT-AT分裂与微波场功率成非线性依赖关系,理论计算与实验测量结果相一致.本文的研究对微波电场的精密测量具有一定的指导意义.     

一种透镜形人造原子的能级结构及电子波函数

对一种透镜形人造原子的Schrödinger方程进行了求解，给出了人造原子能级结构所满足的关系式及电子波函数，并对这种人造原子的Rydberg态进行了着重的讨论.     

氦原子1s2p态的有限元近似能量

用有限元方法近似计算了1s2p态氦原子单态和三重态的能量,所得结果的相对误差:三重态为10^-6,单态为10^-4.这一结果比Schertzer^[1]对基态氦原子的相应结果稍好.有限元法导致的大型广义矩阵特征值问题,对于基态是对称的,而对于1s2p态是非对称的,给求解带来了难度.由波函数的图形说明,在有界区域上求Schrödinger方程的近似解是合理的.     

多参考组态相互作用方法研究ZnHg低激发态(1∏，3∏)的势能曲线和解析势能函数

采用多参考组态相互作用方法计算了ZnHg二聚体两个低激发∏态(¹∏，³∏)的原子间相互作用势能曲线. 用Murrel-Sorbie函数拟合得到了相应的解析势能函数，并用其计算力常数，进而确定了光谱常数. 所得结果与仅有的理论工作进行了比较. 基于所得势能曲线，通过解分子中原子核运动的薛定谔方程预测了各电子态的振动能级. 关键词： 势能曲线 解析势能函数 光谱常数 振动能级     

德拜势中类氢原子能级近似解析式与幂级数求解

对德拜势(Debye)中类氢原子的能级问题采用Rayleigh-Schrdinger微扰展开,给出了能级的一阶修正与原子能级的近似解析式.同时,采用波函数幂级数解法,求得了德拜势下相关的递推关系.在此基础上,利用能量自洽法,求出了相当于二阶修正的德拜势下类氢原子的能级值,并就其计算结果与数值解进行了比较.同时,讨论了相应的临界束缚能态与截断条件.     

原子薛定谔猫态中角动量的压缩及其时间演化

在低Q值腔内，原子相干态在一些特定时刻可以演化为原子薛定谔猫态.讨论了在这种原子薛定谔猫态中原子角动量的涨落和高阶涨落.根据不确定性原理，进一步研究了原子角动量的压缩和高阶压缩性质及其演化.研究表明，原子薛定谔猫态可以被压缩到二阶和六阶，但不能被压缩到四阶.当原子薛定谔猫态中被叠加的原子相干态数为无限多项时，其压缩特性与原子相干态相同. 关键词： 原子相干态 薛定谔猫态 角动量压缩 Bloch态     

The Semileptonic Decay Modes {\bar{B} \rightarrow D\ell \bar{\nu}} and {\bar{B}_{s} \rightarrow D_{s} \ell \bar{\nu}}: A New Analysis in Potential Model

We consider the Schrödinger equation with a combination of Deng–Fan-type and harmonic terms. To solve the corresponding differential equation, we split the equation to two parts: the parent and the perturbation terms. We use the Nikiforov–Uvarov technique to solve the parent part. For the perturbation part, we apply the series expansion method. Next, using the calculated wave function, we investigate some bottom and charm mesons within the Isgur–Wise function formalism. We present especially semileptonic \({\bar{B} \rightarrow D\ell \bar{\nu}}\) and \({\bar{B}_{s} \rightarrow D_s \ell \bar{\nu }}\) decay widths, branching ratios and \({|V_{cb}|}\) (element of the CKM matrix). Masses of some pseudoscalar mesons are also indicated. Comparisons of our results with experimental values and other approaches are included.     

微扰的耦合非线性薛定谔方程的近似求解

将直接微扰方法应用于可积的含修正项的非线性薛定谔方程，通过近似解与精确解的比较确定了直接微扰方法的可靠性.继而，将该方法应用于微扰的耦合非线性薛定谔方程，并获得了该微扰方程的可靠的近似解. 关键词： 直接微扰方法 微扰 耦合非线性薛定谔方程 近似解     

Rovibrational Energies of Triatomic Molecules by Means of the Rayleigh-Schrödinger Perturbation Theory

A Rayleigh-Schr?dinger perturbation theory approach based on the adiabatic (Born-Oppenheimer) separation of vibrational motions was previously developed and used to evaluate for a system of coupled oscillators the adiabatic energy levels and their nonadiabatic corrections. This method is applied here to calculate rotation-vibration energies of the triatomic molecular ions HeH(+)(2) and ArNO(+) consisting of a strongly bound diatomic fragment and a relatively loosely bound rare gas atom. In these systems the high-frequency stretching motion of the diatomic fragment can be separated from the other two low-frequency motions without substantial loss of accuracy. Treating the diatomic fragment as a rigid rotor, the low-frequency stretching motion is decoupled from the bending motion in analogy to the concept of the adiabatic (Born-Oppenheimer) separation of motions and the strong nonadiabatic couplings between these two motions are accounted for perturbationally. Although the resulting perturbation series may show poor convergence, they turn out to be accurately summable by applying standard techniques for the summation of divergent series. Comparison with the results obtained from full-dimensional calculations for the two ions shows that the approach is capable of providing accurate energies for quite a few of the bound rotation-vibration states and that in the case of the HeH(+)(2) ion it is even able to predict the positions and widths of some low-lying resonance states with good accuracy. The perturbation approach yields zeroth-order energies and corrections in terms of the relevant quantum numbers. It thus allows a direct assignment of the energy levels without any reference to the corresponding eigenfunctions. The weak couplings between the high- and low-frequency motions can easily be treated by the same perturbative approach and numerically exact energies can finally be obtained. Copyright 2000 Academic Press.     

Hulthén势散射态的解析解

在任意l波的离心项1/r²用λ²e^-λr/(1-e^-λr)²近似表达的条件下,对Hulthén势的径向Schrdinger方程作自变量指数变换,使此转化为超几何微分方程,获得了Hulthén势s波散射态的精确解和非s波散射态的近似解析解.给出了相移的解析表达式和按“k/2π标度”归一化的用超几何函数表示的径向波函数.讨论了解析解的意义.     

Calculation of vibrational energy levels of triatomic molecules with the C2v and Cs symmetries by summing divergent series of the Rayleigh-Schr?dinger perturbation theory

The Rayleigh-Schr?dinger perturbation theory is applied to calculation of vibrational energy levels of triatomic molecules with the C _2v and C _s symmetries: SO₂, H₂S, F₂O, HOF, HOCl, and DOCl. Particular attention is given to the states coupled by anharmonic resonances; for such states, the perturbation theory series diverge. To sum these series, the known methods of Padé, Padé-Borel, and Padé-Hermite and the method of power moments are used. For low-lying levels, all the summation methods give satisfactory results, while the method of quadratic Padé-Hermite approximants appears to be more efficient for high-excited states. Using these approximants, the structure of singularities of the vibrational energy, as a function in the complex plane, is studied.     

类锂“洞原子”2s2s2p2P0和2s2p2p2D三激发共振系列的能量、精细结构和寿命

采用多通道鞍点和鞍点复数转动方法，计算了类锂离子(Z=3—10)2s2s2p²P⁰和2s2p2p²D三激发共振态系列的能量、精细结构和寿命.Auger宽度由耦合主要的通道得到，相对论效应计算到一级微扰，质量极化效应计算到无穷级. 关键词：     

Interatomic potentials at short range using Madelung’s equations

Interatomic potentials at short range are investigated starting from the united atom electron density. Prior work has utilised time independent Rayleigh-Schr?dinger perturbation theory, adapted to overcome difficulties with convergence of the power series in internuclear distance, and has been confined to diatomic species. This work presents a time dependent approach, based on Madelung’s equations, in which the electron density evolves continuously from that of the united atom to the density of the polyatomic system; no power series is involved, there are no convergence difficulties and the approach is applicable to polyatomic systems. Electronic separation and interaction energies are calculated and compared to previous calculations. Some triatomic and tetratomic arrays of hydrogen atoms are examined and three and four body interaction terms estimated.