Rotational dependence of Franck-Condon factors for molecules of astrophysical interest

The rotational dependence of Franck-Condon factors has been computed for selected bands of CN, CaH, C₂, NH, TiO, MgH and CH using Morse-Pekeris eigenfunctions. Some bands show a rotational dependence which may be significant for the determination of rotational temperatures and abundances of elements and isotopes, and for opacity distribution function (“giant line]rd) calculations. The predicted rotational dependence for the (0, 1) band of the CH 4300 Å system is supported by an analysis of observed solar intensities.     

r-centroids and Franck-Condon factors for the b'-X and b'-b band systems of the NO+ molecule

The r-centroids and Franck-Condon factors for bands of the b'-X and b'-b systems of the NO⁺ molecule have been evaluated by using an approximate analytical method of Jarmain and Fraser. The appearance of some of the bands is discussed in terms of F.C. factors.     

CH2+, NH2+和HBr2+的解析势能函数

对于有势能极大和势能极小的带两个单位正电荷的双原子分子,王藩侯和朱正和两位教授曾提出了一个六参数的解析势能函数用于描述该系统.本文将以基态的CH2 ,NH2 和HBr2 为例,对该函数进行详细的讨论.对CH2 ,NH2 和HBr2 分别采用MP3/6-311 G**,CISD/6-311 G**和CID/LanL1dz进行了大量的单点计算,根据这些点作出了它们的势能曲线,并采用最小二乘法进行拟合,拟合出了该势能函数的六个参数.在此基础上计算出了力常数和光谱数据.     

Rotational excitations of NH 4 + in (NH4) x K1−x I

We propose a gaussian model for the distribution of rotational tunneling lines which constitute the experimentally observed inelastic neutron scattering spectra in the range 0 to 0.6 meV from the mixed system (NH₄) _x K_1−x I. The intensity profiles generated by this model are in remarkable agreement with the experimentally observed ones.     

Isotropic hyperfine coupling constants for NH2, OH and SH radicals

The phosphorescent state of 2,3-dichloroquinoxaline doped into single crystals of durene and 1,2,4,5-tetrachlorobenzene has been studied using several methods based upon optical detection of magnetic resonance (ODMR). Flash excitation and continuous optical pumping methods are described and analysed. Phosphorescent transient effects caused by spin-lattice relaxation and variable intersystem crossing rates are observed and described using first-order solutions of the appropriate rate equations. The effects of spatial polarization of the phosphorescence (anisotropic spatial distribution of phosphorescence intensity) of single crystals on ODMR signals is observed and discussed. The spatial polarization of emission can cause difficulties in determining relative radiative rate constants of the triplet sublevels in oriented samples, but can yield information about the linear polarization of the emission analogous to that obtained by conventional means using polarizers.     

r-Centroids and Franck-Condon factors of the ScO molecule

The r-centroids and Franck-Condon factors for the bands of the A^∠π−X^∠Σ and B²Σ−X²Σ systems of the astrophysically important ScO molecule have been determined. The characteristic bands of this molecule are found in M-type stars as well as in disk and spot spectra. The Franck-Condon factors are determined by the approximate analytical method of Fraser and Jarmain and are compared with those of Bates' method. From the magnitude of Franck-Condon factors, it can be concluded that the bands of the Δν = 0 sequence are dominant in both systems.     

An analytic formula of one-dimensional Franck-Condon factors for linear harmonic oscillators

With the aid of an addition theorem for harmonic oscillator wave functions, the Franck-Condon factors between two displaced linear oscillators with unequal vibrational frequencies are transformed into an analytic form which is programmable for numerical evaluations. Franck-Condon factors for the A¹Σ_u⁺-X¹Σ_g⁺ system and the B¹Π_u-X¹Σ_g⁺ system of ⁷Li₂ are calculated via this analytic formula.     

The magnetic susceptibilities of NO and OH

A non-isothermal kinetic equation for the distribution function of a sub-system weakly coupled to a bath is derived by modification of the analysis and assumptions of a previous paper [1]. The equation has the form of a generalized non-isothermal Fokker-Planck equation when it is linearized in thermodynamic gradients and only terms through second order in the coupling parameters are retained. Higher order terms in the coupling parameter do not diverge with time. The equation is compared with certain ‘exact’ model results of Ullersma and with the coherence time method. The equation is used to calculate a jump rate for diffusion of a harmonic particle weakly coupled to a lattice and it is found that the jump rate becomes independent of the mass of the particle for a heavy enough particle. The source of the discrepancy of this result with a similar calculation of Prigogine and Bak is indicated. The model of the jump rate is inappropriate for diffusion in a thermal gradient and more appropriate models of the jump are briefly considered. A brief comparison of the derivation of the kinetic equation with the Fano coherence time approximation is made and a difference is noted.     

Electron scattering cross sections with HF,OH, NH and CH molecules

Total cross sections including elastic scattering, electronic excitation-ionisation and the dipole rotational excitation are calculated for electron impact on HF, OH, NH, and CH molecules. The additivity rules as well as single-centre expansion are employed for this purpose. A comparison was possible for the e-HF system only. Our results are expected to be good at intermediate to high energies (> 50 eV).     

Outer shell excitations of He and Ne using projectiles of C+, N+, O+, F+,20Ne+,22Ne+, Na+ and Mg+

The ground state energy, the mean square displacement of the molecules, the lattice constant, and the effective quadrupole-quadrupole coupling constant are calculated variationally and compared with the experiments. Both the orientationally ordered fcc-phases and the hcp-phases are considered. Nosanow's cluster expansion is used and its convergence is discussed.     

A new formula to calculate Franck-Condon factors for displaced and distorted harmonic oscillators

A new formula has been derived to calculate Franck-Condon factors for two harmonic oscillators with different equilibrium positions and different vibrational frequencies. The derivation is simple and straightforward, and a new expression for calculating the matrix element 〈v|xⁿ|v′〉 has also been derived.     

Franck-Condon factors and r-centroids for the B2Σ-X2Σ systems of HgCl,HgBr, and HgI

Available spectroscopic data have been analyzed and used for calculations of Franck-Condon Factors and r-centroids for B²Σ-X²Σ bands of HgCl³⁵, HgCl³⁷, HgBr⁷⁹, HgBr⁸¹, and HgI.     

NH_4NO_3掺杂Na~+、K~+、Ag~+、Pb_(2+)晶体相变拉曼峰强行为研究:掺杂效应的标度性

从掺杂晶体（Ｎａ＋、Ｋ＋、Ａｇ＋、Ｐｂ２＋）ｘ（ＮＨ４）１－ｘＮＯ３相变时，拉曼峰强与温度的变化关系着手，深入讨论了掺杂离子的效应，揭示了其中的标度性质。本文分下列章节：（１）前言、（２）实验、（３）ｌｎＩＲ与ｌｎ｜Ｔ－Ｔｃ｜之线性关系、（４）不同振动模对不同掺杂程度的反应、（５）ν１振动模对不同离子掺杂的刻画、（６）‘反转’行为、（７）ｄｃ与Ｍ１／２的线性关系、（８）掺杂效应的标度性、（９）结语     

Quantum mechanical calculation of rotational constants and Franck-Condon factors of diatomic molecules

In this paper, the question of reliability of the Morse potential as a potential curve for a diatomic molecule is investigated on the basis of calculating the rotational constant. It is shown that the Morse potential describes well potential curves of X¹Σ _q ⁺ and B¹Π_u electronic states of a Na₂ molecule. Calculations of Franck-Condon factors for X¹Σ _q ⁺ ? B¹Π_u band of a Na₂ molecule using wave functions of the Morse potential confirm the known correlation between the values of Franck-Condon factors and rotational constants of combined electronic states.