非共线AOTF±1级衍射光波长的研究

对非共线AOTF±1级衍射光波长进行了理论计算和实验,理论和实验结果基本一致,相对误差<±2%。这对AOTF衍射光性能的应用具有参考价值。     

The subduction of vibrational states of molecules from the momentum space of simple harmonic motion

A single-particle model of molecular vibrational states is proposed in which the normal modes are projected out of the body vibrations of an infinite simple harmonic sphere. This model assigns the spurious change of mass or centre of mass and leads to removal of mass monopoles and dipoles from the system. These conservation conditions impose strict boundary conditions on the potential and basis functions. On incorporation into the model they result in a set of loop equations in which the potential is proportional to the fundamental vibration. The simplest solutions to these equations strongly resemble the Poschl-Teller generalization of the Morse potential. The solutions have been extended to incorporate the repulsive states and generate the set of net attractive states appropriate to the anharmonic potential.The basis functions of this potential display both angular and radial node structures. The degeneracies between radial and angular mode patterns can be studied by transformation into an angular coordinate space. In this way coupling to other phenomena described in similar angular momentum space can be performed directly before subduction to real displacement space.On leave from the Department of Chemistry, Catholic University of Leuven, Celestijnenlaan 200F, B-3030 Leuven-Belgium     

Dynamics of atoms in strong laser fields I: A quasi analytical model in momentum space based on a Sturmian expansion of the interacting nonlocal Coulomb potential

In this study we present a model that we have formulated in the momentum space to describe atoms interacting with intense laser fields. As a further step, it follows our recent theoretical approach in which the kernel of the reciprocal-space time-dependent Schrödinger equation (TDSE) is replaced by a finite sum of separable potentials, each of them supporting one bound state of atomic hydrogen (Tetchou Nganso et al. 2013). The key point of the model is that the nonlocal interacting Coulomb potential is expanded in a Coulomb Sturmian basis set derived itself from a Sturmian representation of Bessel functions of the first kind in the position space. As a result, this decomposition allows a simple spectral treatment of the TDSE in the momentum space. In order to illustrate the credibility of the model, we have considered the test case of atomic hydrogen driven by a linearly polarized laser pulse, and have evaluated analytically matrix elements of the atomic Hamiltonian and dipole coupling interaction. For various regimes of the laser parameters used in computations our results are in very good agreement with data obtained from other time-dependent calculations.     

Diatomic interactions in momentum space. The 2pπ u and 3dπ g states of H 2 + system

The recently proposed method of momentum electron density for interatomic interactions is applied to the two states of the H ₂ ⁺ system. The processes of the attractive 2P _u and repulsive 3d _g interactions are analysed based on the behaviour of the momentum density and Compton profile. The results are compared with the previous ones for the 1 _{S g} and 2p _u states. The guiding principle of contraction and expansion for the energy-density relation in momentum space is shown to be common to both the and states.     

Electronic structure of Li− and F− calculated directly in momentum space

Summary A self-consistent field method is applied to compute directly in momentum space the electronic structures of the bound anions Li^– and F^– at the Hartree-Fock level. The convergence towards the Hartree-Fock limit, starting from STO-3G, 3–21G, 3–21+G and 6–311+G AO's, is stable and monotonous. Substantial improvement in the quality of the anion orbitals is noted already after one iteration. Particularly interesting is the efficiency with which the method modifies and improves the shape of the trial functions.     

Density matrices from position and momentum densities

Summary One-electron density matrices, which are representable in single-centers-orbital basis sets, have been investigated with respect to their reconstruction from densities. The maximum allowed dimension for reconstruction from a combination of position & momentum density dependent properties is only slightly bigger than the dimension in the case of position (or momentum) densities only. Since for a given one-particle basis of dimensionM, the number of one-matrix elements which can be determined is also of orderM only, while the total number of one-matrix elements is of orderM ², it is in general necessary to introduce severe constraints and restrictions. The accuracy demands on the data and algorithms increase exponentially for linearly increasing size of basis set.     

On numerical solution of the integral Hartree-Fock equations for molecules by the method of MO LCAO in the momentum space

To develop a numerical solution of mentioned equations the method of factorized projection of integral operator kernel is applied. All matrix elements of the method are calculated analytically, being expressed in terms of two types of standard integrals: the overlap integrals and one-electron Coulomb integrals. To calculate the integrals we used the O(4)-symmetry of hydrogen-like atomic orbitals as well as operational technique of differentiation with respect to scalar and vector parameters.     

Electron correlation effects in position and momentum space: the atoms Li through Ar

Electron correlation effects on the electronic structure of atoms were investigated by means of a variety of position and momentum space related properties such as radial one-electron densities and radial electron momentum densities, Compton profiles and radial electron pair distributions. The results were obtained from MR-SDCI wavefunctions utilizing very large basis sets and are discussed in a comparative manner, analysing characteristic features and trends.     

Radial electron-pair densities in momentum space and shell structure of atoms

 The radial electron-pair intracule (relative motion) H(u) and extracule (center-of-mass motion) D(R) densities in position space were known to reveal four types of maxima which are related to the four inner electron shells, K, L, M, and N, of atoms. The corresponding radial electron-pair intracule Hˉ(v) and extracule Dˉ(P) densities in momentum space are studied for the 102 atoms from He (atomic number Z=2) to Lr (Z=103). The densities Hˉ(v) and Dˉ(P) are found to have either one maximum or two maxima, and the numbers of maxima in Hˉ(v) and Dˉ(P) are the same for 98 atoms. For these atoms, the locations υ _max and P _max and the heights Hˉ _max and Dˉ _max of the corresponding maxima satisfy the approximate relations υ _max ≅ 2P _max and Hˉ _max ≅Dˉ _max /2. On the basis of their Z-dependence, the maxima in Hˉ(v) and Dˉ(P) of the 102 atoms are classified into five types. Shell-pair decompositions of the radial densities show that these maxima reflect five outer electron shells of atoms. Received: 24 January 2001 / Accepted: 12 March 2001 / Published online: 13 June 2001     

Dynamic Measurements of Impulses Generated by the Separation of Adhered Bodies under Near-Zero Gravity Conditions

The present paper is aimed at investigating the dynamics of release of objects in free-falling conditions, which constitutes a typical phase of some space applications. In the presence of surface interaction forces, a quick separation of the released body from the constraining one will result in a momentum transfer, provided that the inertial forces exceed the maximum attractive force. The release conditions as well as the related parameters affecting the momentum acquired by the released body through the adhesion rupture play a fundamental role. An experimental technique aimed at measuring the momentum transfer has been developed. The basic concept of the measuring apparatus is to suspend both bodies from two pendulums. A position sensor detects the weakly damped oscillation of one object due to the momentum transferred upon pulling the other one away. Particular attention has been placed on the capability to accurately reproduce the stress status on the adhesive contact patch between the two bodies, on the noise sources affecting the measurement, and on the performances of a noise optimal-filtering technique. This paper presents measurements of momentum transfer between adhered surfaces upon quick separation.