An Efficient Approach for the Calculation of Nuclear Overlap Integrals by Means of Binomial Coefficients and Its Application

This paper examines the computational efficiency of the method of evaluating nuclear overlap integrals commonly encountered in nuclear reactions. As will be seen, the present formulation yields compact closed-form expressions which will make the calculation of nuclear overlap integrals easy. For practical applications, the computational technique used must be amenable to rapid evaluation and yield an acceptable degree of accuracy. Finally, the ratios for the non-Borromean two-nucleon halo systems are calculated by using new formulas which are important for the reaction analyses. The results of this calculation have been compared with those obtained according to one of the theoretical articles (Timofeyuk et al., Phys. Rev. C 68:021601(R), 2003). The same numerical results are presented for significant examples and they are briefly discussed.     

A comparative study of the energy migration and energy transfer in highly doped Nd:YAG single crystal

The donor-donor (D-D) energy migration interaction parameter C_DD in high-concentration Nd³⁺-doped YAG laser crystal is estimated, for the first time, by using the Yokota-Tanimoto (Y-T) model and the spectral overlap model (SOM) of Kushida. Firstly, the experimental luminescence decay curves of ⁴F_3/2 state of Nd³⁺ ions in YAG laser crystal at room temperature for 2.0 and 3.0 at% Nd³⁺ concentrations reported by Mao are fitted successfully by using the Y-T model and the parameter C_DD is obtained to be 1.50×10⁻³⁹ cm⁶/s. Secondly, the parameter C_DD is also directly calculated by using the SOM of Kushida: C_DD is calculated to be 2.73×10⁻³⁹ cm⁶/s. By comparing the energy migration interaction parameter C_DD and the donor-acceptor (D-A) energy transfer interaction parameter C_DA (1.794×10⁻⁴⁰ cm⁶/s), it is concluded that energy migration rate between Nd³⁺ ions in YAG laser crystal was about 11 times larger than energy transfer rate, and that energy migration would play a very important role in high-concentration Nd³⁺ -doped YAG laser crystal.     

通过HSQC和1H,13C-COSY叠合增强二维谱分辨率的方法

通常二维谱F₁维分辨率较差,F₂维分辨率较好. 即HSQC实验¹³C维度分辨率较差,¹H维度分辨率较好. 而¹H, ¹³C-COSY实验¹³C维度分辨率较好,¹H维度分辨率较差. 提出一种通过HSQC和¹H, ¹³C-COSY叠合,取较弱的值储存并显示的方法增强分辨率,采用Bruker Topspin软件AU程序实现. 该方法在不明显增加采样时间的情况下,可显著增强分辨率,信噪比也没有降低. 同时抑制了F₁噪声. 处理后,谱图美观清晰.     

The Spectrochemical Properties of Noncubic Transition Metal Complexes in Solutions. VII. Angular Overlap Treatment of the trans-bis(Salicylidene-o-aminopyridine)copper(II) Complex in Various Solvents.

The electronic absorption spectra of trans-[Cu(sap)₂], where (Hsap = salicylidene-o-aminopyridine (Schiff base)), were measured in various solvents at room temperature. The d-d transition energies is used to derive the angular overlap model (AOM) parameters in C_2h symmetry. The experimental curves were resolved by Gaussian analysis. A comparison of the spectra, ligand field parameters and stereochemistries in various solutions was made. The effect of the solvents upon the σ, π-bonding, and bite angle of the bidentate ligand is discussed.     

Computationally efficient recurrence relations for one-dimensional Franck–Condon overlap integrals

Calculations based on analytical expressions for the harmonic oscillator Franck–Condon factors often yield numerically unstable and erroneous results for large values of the oscillator quantum numbers. This instability arises from inherent machine precision limits and large number round-off associated with the products and ratios of factorial and gamma functions in these expressions; the analytical expressions themselves are exact. This paper presents, first, efficient, exact recurrence relations to evaluate Franck–Condon factors for the harmonic oscillator model. The recurrence relations, which are similar to those originally found by Manneback, Wagner and Ansbacher avoid the direct use of the factorial and gamma functions. Second, a variational strategy for the evaluation of Franck–Condon factors for the Morse oscillator is proposed. The Schrödinger equation for the Morse model is solved variationally with a large enough basis set of one-dimensional harmonic oscillator functions to get good agreement with the analytic eigenvalues of the Morse potential itself. The eigenvectors of this analysis are then used together with the associated harmonic oscillator Franck–Condon overlap matrix elements to evaluate the overlap for the Morse potential. This approach allows one, in principle, to estimate Franck–Condon overlap up to states near to the dissociation limit of the Morse oscillator.     

Calculation of molecular electric and magnetic multipole moment integrals of integer and noninteger n Slater orbitals using overlap integrals

Closed formulas are established for the magnetic multipole moment integrals of integer and noninteger n Slater‐type orbitals (ISTOs and NISTOs) in terms of electric multipole moment integrals for which the analytic expressions through the overlap integrals with ISTOs and NISTOs are derived. The overlap integrals are evaluated by the use of auxiliary functions. Using the derived expressions the multipole moment integrals, and therefore the electric and magnetic properties of molecules, can be evaluated most efficiently and accurately. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

船载炮兵作战的被弹数计算研究

本文根据船载炮作战中三种射击方式的特点，提出了船载炮兵在航行射击遭敌打击情况下的一种简单有效的被弹数计算方法。     

Approximate formulae for the overlap integral of two harmonic oscillator wave functions

The use of second-order perturbation theory to derive approximate formulae for the overlap integral of two harmonic oscillator wave functions is discussed, and the results applied to the theory of intensity distributions in vibrational progressions in electronic spectra. For the vibrational progression m←0 an approximate formula is given which, when the vibrational frequencies of the initial and final states differ by less than 10%, reproduces to an accuracy of 1% or less the intensity profile calculated using the exact formulae for the overlap integrals.