Transition probability of lithium atom and lithiumlike ions with weakest bound electron wave functions and coupled equations

One of us has presented a new theory called the Weakest Bound Electron Potential Model theory (WBEPM theory) to determine the exact potential field in atoms. A concise analytic form of the potential of the weakest‐bound electron is proposed. In the new potential and the wave function derived afterward, the integral atomic number Z and quantum numbers n and l are replaced by nonintegral Z*, n*, and l*, respectively. In this article, we employed the WBEPM theory to calculate the transition probability for the lithium atom and lithiumlike ions and obtained very good results compared with the accepted values and other results. © 1999 John Wiley & Sons, Inc. Int J Quant Chem 76: 51–61, 2000     

Propagation properties of soliton solutions under the influence of higher order effects in erbium doped fibers

Under investigation in this paper is the Hirota–Maxwell–Bloch system which governs the propagation of optical solitons in nonlinear erbium doped fibers with higher order effects. By virtue of the Darboux transformation, the Akhmediev breathers, Ma-breathers, localized solitons, bound solitons, two-breathers and localized solutions are generated for the Hirota–Maxwell–Bloch system. Considering the influences of higher order effects, propagation properties of the breathers, modulation instability conditions for the Akhmediev breathers and interaction scenarios between bound solitons and two-breather solutions are discussed.     

The arbitrary l continuum states of the hyperbolic molecular potential

Within the framework of partial-wave method, we study in this Letter the arbitrary l continuum states of the Schrödinger equation with the hyperbolic molecular potential in terms of an improved approximation to the centrifugal term. We present the normalized radial wave functions and obtain analytical formula of phase shifts. In addition, the corresponding bound states are also discussed by studying the analytical properties of the scattering amplitude. We calculate the energy spectra and scattering phase shifts by the improved, previous approximations and the accurate methods, respectively and find that the improved approximation is better than the previous one since the present results are in better agreement with the accurate ones.     

冲击模型可靠度的界

对于冲击模型H(t)=sum from k=0 to ∞ P{N(t)=k}·P_k其中{N(t),t≥0}是更新过程,间隔时间分布函数F(t)存在有限均值,在以下情况下,我们讨论了其界值问题: ①F(t)是IFR类分布;②F(t)是DFR类分布; ③F(t)是NBUE类分布;④F(t)是NWUE类分布.而且对一些特殊情况,其结论更简洁.     

A new trust region algorithm for bound constrained minimization

We introduce a new algorithm of trust-region type for minimizing a differentiable function of many variables with box constraints. At each step of the algorithm we use an approximation to the minimizer of a quadratic in a box. We introduce a new method for solving this subproblem, that has finite termination without dual nondegeneracy assumptions. We prove the global convergence of the main algorithm and a result concerning the identification of the active constraints in finite time. We describe an implementation of the method and we present numerical experiments showing the effect of solving the subproblem with different degrees of accuracy.This work was supported by FAPESP (Grants 90-3724-6 and 91-2441-3), CNPq, FINEP, and FAEP-UNICAMP.     

关于p叶α型β级近于凸函数类的一个子类

本文引入了p叶近于凸函数类的一个子类T（A，B，p，a，C，D，β），讨论了它的包含关系、系数估计和偏差定理，得到一些精确的结果．     

Validity of the one-body current for the calculation of form factors in the point form of relativistic quantum mechanics

Form factors are calculated in the point form of relativistic quantum mechanics for the lowest energy states of a system made of two scalar particles interacting via the exchange of a massless boson. They are compared to the exact results obtained by using solutions of the Bethe-Salpeter equation which are well known in this case (Wick-Cutkosky model). The relevance of the comparison is examined by considering other relativistic quantum-mechanics approaches where results are known or have been obtained recently. Deficiencies of the point-form approach together with the single-particle current are emphasized. They point to quite sizeable contributions of two-body currents. These ones are required to fulfil current conservation in any case and to reproduce the high momentum transfer behaviour expected from the Born amplitude. Received: 11 July 2001 / Accepted: 12 February 2002     

Energy levels of one-dimensional systems satisfying the minimal length uncertainty relation

The standard approach to calculating the energy levels for quantum systems satisfying the minimal length uncertainty relation is to solve an eigenvalue problem involving a fourth- or higher-order differential equation in quasiposition space. It is shown that the problem can be reformulated so that the energy levels of these systems can be obtained by solving only a second-order quasiposition eigenvalue equation. Through this formulation the energy levels are calculated for the following potentials: particle in a box, harmonic oscillator, Pöschl–Teller well, Gaussian well, and double-Gaussian well. For the particle in a box, the second-order quasiposition eigenvalue equation is a second-order differential equation with constant coefficients. For the harmonic oscillator, Pöschl–Teller well, Gaussian well, and double-Gaussian well, a method that involves using Wronskians has been used to solve the second-order quasiposition eigenvalue equation. It is observed for all of these quantum systems that the introduction of a nonzero minimal length uncertainty induces a positive shift in the energy levels. It is shown that the calculation of energy levels in systems satisfying the minimal length uncertainty relation is not limited to a small number of problems like particle in a box and the harmonic oscillator but can be extended to a wider class of problems involving potentials such as the Pöschl–Teller and Gaussian wells.     

A generalized Uhlenbeck and Beth formula for the third cluster coefficient

Relatively recently (Amaya-Tapia et al., 2011), we presented a formula for the evaluation of the third Bose fugacity coefficient–leading to the third virial coefficient–in terms of three-body eigenphase shifts, for particles subject to repulsive forces. An analytical calculation for a 1-dim. model, for which the result is known, confirmed the validity of this approach. We now extend the formalism to particles with attractive forces, and therefore must allow for the possibility that the particles have bound states. We thus obtain a true generalization of the famous formula of Uhlenbeck and Beth (Uhlenbeck and Beth, 1936; Beth and Uhlenbeck, 1937) and of Gropper (Gropper, 1936, 1937) for the second virial. We illustrate our formalism by a calculation, in an adiabatic approximation, of the third cluster in one dimension, using McGuire’s model as in our previous paper, but with attractive forces. The inclusion of three-body bound states is trivial; taking into account states having asymptotically two particles bound, and one free, is not.     

On the effects on a Landau-type system for an atom with no permanent electric dipole moment due to a Coulomb-type potential

We analyse the bound states for a Landau-type system for an atom with no permanent electric dipole moment subject to a Coulomb-type potential. By comparing the energy levels for bound states of the system with the Landau quantization for an atom with no permanent electric dipole moment (Furtado et al., 2006), we show that the energy levels of the Landau-type system are modified, where the degeneracy of the energy levels is broken. Another quantum effect investigated is a dependence of the angular frequency of the system on the quantum numbers associated with the radial modes and the angular momentum. As examples, we obtain the angular frequency and the energy levels associated with the ground state and the first excited state of the system.