Analytical solution of the inverse spectroscopic problem: Determination of electron moments of vibrational transitions of diatomic molecules by their probabilities

The inverse problem of spectroscopy of vibrational transitions of diatomic molecules was analytically solved on the basis of wave functions of the Morse oscillator. An example of the determination of the transition dipole-moment function by intensities of several lines of molecule vibrational-rotational spectra measured experimentally was considered. A similar approach based on simple expressions for matrix elements can be applied to consider optimal lasing conditions of the CO electronic transition laser.     

On a method for solving the inverse problem in potential scattering

A method for solving the inverse problem in the non-relativistic elastic scattering theory, using the analytic and asymptotic properties of the scattering amplitude is proposed and the influence of the discontinuity parameters of the scattering amplitude on the properties of the resulting potentials is discussed. The case with spherically symmetric forces and without bound states is considered. The possibility for solving the inverse problem by this method, leading to the singular repulsive potentials is mentioned.     

BH分子基态和激发态解析势能函数和光谱性质

运用多参考组态相互作用的方法和Dunning’s相关调和基函数并含扩散基的大基组aug-cc-pV5Z,获得了BH分子基态（X¹Σ⁺）和6个电子激发态（a³П, A¹П, B¹Σ⁺, b³Σ⁺, b³ 关键词： 势能曲线 解析势能函数 多参考组态相互作用方法 光谱常数     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

Exact propagator for an electron in a quadratic saddle-point potential and a magnetic field

We study the propagator for an electron moving in a two-dimensional (2D) quadratic saddle-point potential,in the presence of a perpendicular uniform magnetic field. A closed-form expression for the propagator is derived using the Feynmann path integrals.     

AlH分子结构与分析势能函数

本文运用群论及原子分子反应静力学方法,推导了 AlH分子的基态(X1Σ+)、第一激发态(A1Π)及第三激发态(C1S+)的电子态及相应的离解极限.并使用SAC/SAC-CI方法,采用D95 (d)、6-311g(d)和cc-PVTZ等基组对AlH分子的基态(X1Σ+)、第一激发态(A1Π)和第三激发态(C1S+)的平衡结构和谐振频率进行了几何优化计算.通过对三个基组的计算结果与实验结果的比较,得到cc-PVTZ基组是三个基组中最优基组的结论.使用cc-PVTZ基组,对AlH 分子的基态(X1Σ+)、第一激发态(A1Π)和第三激发态(C1S+)进行了单点能扫描计算,并给出了AlH的基态(X1Σ+)、第一激发态(A1Π) 和第三激发态(C1S+)的Murrell-Sorbie函数形式的电子态的完整势能函数,进而得到了AlH分子第一激发态(A1Π)的激发能较小的结论.     

Exact solution of the inverse acoustic scattering problem for the one-dimensional density profile in cylindrical geometry

The inhomogeneous acoustic wave equation in cylindrically symmetric geometry, is reduced to a one-dimensional Schrödinger equation for time harmonic waves. The scattering potential so formed is uniquely reconstructed by the Gelfand-Levitan theory. In physical terms, the scattering potential is a function of the impedance profile, which is then recovered. If the velocity profile is known (or constant) the density profile, as a function of the radial coordinate, can be deduced. A practical experiment is envisaged whereby the back-scattered time sequence is measured in a pulse-echo mode, and the data are used to reconstruct the density profile.     

Few-electron molecular states and their transitions in a single InAs quantum dot molecule

We study electronic configurations in a single pair of vertically coupled self-assembled InAs quantum dots, holding just a few electrons. By comparing the experimental data of nonlinear single-electron transport spectra in a magnetic field with many-body calculations, we identify the spin and orbital configurations to confirm the formation of molecular states by filling both the quantum mechanically coupled symmetric and antisymmetric states. Filling of the antisymmetric states is less favored with increasing magnetic field, and this leads to various magnetic field induced transitions in the molecular states.     

Analysis of the πN invariant amplitudes in terms of algebraic functions and a new determination of the πN low-energy parameters

We have analysed the energy dependence of the πN invariant amplitudes in terms of algebraic functions which automatically fulfill fixed-t dispersion relations. The amplitudes were taken from several phase shift solutions. The analysis was repeated for nine t-values between 0 ? t ? ?0.3 GeV². By evaluating the resulting analytic amplitudes at threshold and at ν = 0 we recalculate the S, P, D scattering lengths and the current algebra σ term. We also discuss the trajectories of the zeros and poles in the complex energy plane.     

Collective electron excitations in a spherical potential well and the polarizability of the fullerene molecule

The collective motion of the electron system of the C60 molecule was investigated within the framework of the linear response theory. The model originally proposed by Mukhopadhyay and Lundqvist [1, 2, 3] and applied for C60 by Östling et al [4] was used with an electron density calculated from a spherical well potential. From the calculated dynamic polarizability a main plasmon peak at 14.4 eV in the photoabsorption cross section of the C60 molecule and a broad double peaked structure around 25 eV in the transmission electron energy loss spectrum of the solid C60 can be derived.     

A Zakharov-Shabat inverse scattering problem with a polynomial spectral dependence in the potential

The inverse scattering problem for the Zakharov-Shabat system , is considered. It is solved by reduction to the inverse scattering problem for two coupled Zakharov-Shabat systems in a 4n-dimensional space: . This work has been done as part of the program ‘Recherche Coopérative sur Programme No. 264: Etude interdisciplinaire des problèmes inverses’. Physique Mathématique et Théorique, Equipe de recherche associée au CNRS, No. 154.     

Correlation functions and differential mobility in the hot electron problem

A projection operator technique is developed to study the far from équilibrium steady state transport problem. It is shown that the results previously obtained by Monte Carlo methods for the various correlation functions and differential mobility are satisfactorily predicted analytically. The temporal behavior of the velocity autocorrelation function predicted previously by intuitive arguments is formally justified.     

Exact expressions for the precession of a planet and the deflection of light

Exact expressions for the precession of a planet's orbit and for the deflection of light near a massive object are presented.     

Dispersion sum rules for the amplitudes of radiative transitions in quarkonium

A dispersion approach is suggested, based on the asymptotic freedom in QCD and on analyticity, which leads to sum rules for the amplitudes of radiative transitions in quarkonium $\text{(}\text{c}\text{c}\text{,}\text{b}\text{b}\text{, …)}$ and allows one to estimate these amplitudes in a model-independent way. As an example such sum rules are derived for the ${}^3\text{P}{}_0\text{?}{}^3\text{S}{}_1$ and ${}^3\text{S}{}_1\text{?}{}^1\text{S}{}_0$ transitions. For charmonium they agree with the available data and with the predictions of nonrelativistic models.