耦合Schrödinger系统的周期振荡折叠孤子

引入对称延拓和非线性变换, 将(G'/G)展开法扩展到研究(1+1)维非线性耦合Schrödinger系统, 构造出该系统的一些分离变量形式的精确解. 通过对解中的任意函数进行适当的设置, 获得了两类周期振荡折叠孤子. 关键词： 耦合Schrö dinger系统 G'/G)展开法')" href="#">(G'/G)展开法 精确解 周期振荡折叠孤子     

Analytical solutions and rogue waves in (3+1)-dimensional nonlinear Schrödinger equation

Analytical solutions in terms of rational-like functions are presented for a (3+1)-dimensional nonlinear Schrödinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct ansatz. Several free functions of time t are involved to generate abundant wave structures. Three types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.     

Resonances and Gamow States in Non-Local Potentials

For a large class of non-local, non separable potentials with non-compact support, the solution of the radial integrodifferential equation may be reduced to the solution of a homogeneous linear integral equation of Fredholm type with a quadratically integrable kernel. In this way we derive expansions of the wave functions and the Green's function of the Schrödinger equation with a non-local potential in terms of bound states, resonant states and a continuum of scattering functions with complex wave number. The rules of normalization, orthogonality and completeness satisfied by the eigenstates of the Schrödinger equation belonging to complex eigenvalues with Im E_n < 0, (Gamow or resonant states) are also derived. Finally, by means of a realistic example, it is shown how to use these expansions to exhibit the resonant behaviour of the differential cross section. Explicit expressions for the transition amplitudes and the partial widths in terms of expectation values of operators computed with Gamow functions are given.     

Hulthén势散射态的解析解

在任意l波的离心项1/r²用λ²e^-λr/(1-e^-λr)²近似表达的条件下,对Hulthén势的径向Schrdinger方程作自变量指数变换,使此转化为超几何微分方程,获得了Hulthén势s波散射态的精确解和非s波散射态的近似解析解.给出了相移的解析表达式和按“k/2π标度”归一化的用超几何函数表示的径向波函数.讨论了解析解的意义.     

The relativistic bound and scattering states of the Manning-Rosen potential with an improved new approximate scheme to the centrifugal term

The approximately analytical bound and scattering state solutions of the arbitrary l-wave Klein-Gordon equation for the mixed Manning-Rosen potentials are carried out by an improved new approximation to the centrifugal term. The normalized analytical radial wave functions of the l-wave Klein-Gordon equation with the mixed Manning-Rosen potentials are presented and the corresponding energy equations for bound states and phase shifts for scattering states are derived. It is shown that the energy levels of the continuum states, reduce to the bound states of those at the poles of the scattering amplitude. Some useful figures are plotted to show the improved accuracy of our results and the special case for wave is studied briefly.      

Selected Topics in Correlated Hyperspherical Harmonics

Correlated hyperspherical-harmonic basis functions are used to expand the three- and four-nucleon wave functions. Bound and scattering states are considered. Results for the binding energies of ³H, ³He, and ⁴He calculated using modern two- and three-nucleon forces are given and discussed. For scattering states, results for N-d differential cross section and vector analyzing powers are shown. The importance of the Coulomb and magnetic moment effects are discussed.     

Perturbative role in the inelastic electron scattering from <Superscript>29</Superscript>Si

Inelastic electron scattering form factors away from the closed sd -shell are investigated. This investigation covers the low-lying states in ²⁹Si , which is considered according to the many-particle configuration mixing shell model as the ¹⁶O core, plus thirteen nucleons distributed over the entire sd -shell orbits. The investigation concentrates on the perturbative role of the core, which is called core polarization effects, on the inelastic electron scattering form factors. Core polarization effects are taken into consideration through the excitation of nucleons from 1s and 1p core orbits, and also from the 2s -1d valence orbits into higher shells, with 2ℏω excitations. Core polarization matrix elements are calculated with the M3Y effective interaction. For the sd -shell model space, a new Hamiltonian, based on a renormalized G -matrix, USDB, is used. All calculations are performed without adjusting any parameters.     

The Relativistic Scattering States of the Hulthén Potential with an Improved New Approximate Scheme to the Centrifugal Term

The approximately analytical scattering state solutions of the l-wave Klein-Gordon equation with the unequal scalar and vector Hulthén potentials are carried out by an improved new approximate scheme to the centrifugal term. The normalized analytical radial wave functions of the l-wave Klein-Gordon equation with the mixed Hulthén potentials are presented and the corresponding calculation formula of phase shifts is derived. It is well shown that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. Some useful figures are plotted to show the improved accuracy of our results and two special cases for s-wave (l=0) and for l=0 and equal scalar and vector Hulthén potentials are also studied briefly.     

Low energy atomic collisions

The Schrödinger equation for the system H⁺-H developed in a previous paper is considered using new expansion functions for electronic states obtained from H₂ ⁺ molecular ion electronic eigenfunctions by a unitary transformation. These new functions have the advantage of remaining orthonormal at all internuclear separations and asymptotically becoming symmetrized atomic hydrogen states. Although they are eigenfunctions of the H₂ ⁺ hamiltonian only in the limit of large internuclear distance, the effect of the H₂ ⁺ hamiltonian on these functions is readily found.

Due to coupling which remains non-zero in the limit of large interproton distance, each independent formal solution of the H⁺-H equations involves more than one expansion state in this limit. These solutions may be expressed asymptotically as column vectors multiplied by incoming or outgoing spherical waves.

The formal theory of scattering as developed by Gell-Mann and Goldberger has been utilized along with the projection formalism of Feshbach to obtain the correct asymptotic form of the scattering wave function. The procedure employed involves formulating the problem in terms of two-potential scattering and requires application of renormalization techniques for treating level shifts produced by the infinite-ranged coupling. This asymptotic form may be used in imposing scattering boundary conditions on numerical solutions of coupled equations for H⁺-H scattering.

Finally, it is shown that one cannot interpret coefficients of all outgoing spherical waves as scattering amplitudes. In addition, new interference phenomena are found to result from the presence of the infinite-ranged coupling. The present formalism is shown to reduce to the usual perturbed stationary-states method in the approximation that the infinite-ranged coupling is neglected.     

Resonances inη-light nucleus systems

We locate resonances inη-light nucleus elastic scattering using the time delay method. We solve few-body equations within the finite rank approximation in order to calculate the t-matrices and hence the time delay for theη-³He andη-⁴He systems. We find a resonance very close to the threshold inη-³He elastic scattering, at about 0.5 MeV above threshold with a width of ∼2 MeV. The calculations also hint at the presence of sub-threshold states in both the cases     

Approximate analytical solutions of scattering states for Klein-Gordon equation with Hulthén potentials for nonzero angular momentum

In this paper, using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthén potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of t-waves scattering states are presented. The normalized wave functions expressed in terms of hypergeometric functions of scattering states on the “k/2π scale” and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solution is discussed.      

Collisional excitation of neon-like Ni XIX using the Breit-PauliR-matrix method

Collision strength for the transition within the first five fine-structure levels in Ni XIX are calculated using the Breit-PauliR-matrix method. Configuration interaction wave functions are used to represent the target states included in theR-matrix expansion. The relativistic effects are incorporated in the Breit-Pauli approximation by including the one-body mass correction, Darwin and spin-orbit interaction terms in scattering equations.     

Elastic scattering, muon transfer, bound states and resonances in the three-body mesic molecular systems in the reduced adiabatic hyperspherical approach

The uniform method of numerical investigation of bound states and scattering processes 2→ 2 (including resonance states) in the Coulomb three-body (CTB) systems is developed. It is based on the adiabatic hyperspherical approach (AHSA) and includes the numerical realization and applications to the three-body mesic atomic systems. The results of calculations of bound states of these systems (including the local characteristics of the wave functions) and the scattering processes 2→ 2 (including the characteristics of the resonance states) are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Inverse Scattering Transform and Solitons for Square Matrix Nonlinear Schrödinger Equations with Mixed Sign Reductions and Nonzero Boundary Conditions

The inverse scattering transform (IST) with nonzero boundary conditions at infinity is developed for a class of 2 × 2 matrix nonlinear Schrödinger-type systems whose reductions include two equations that model certain hyperfine spin F = 1 spinor Bose-Einstein condensates, and two novel equations that were recently shown to be integrable, and that have applications in nonlinear optics and four-component fermionic condensates. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows us to develop the IST on the standard complex plane instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity, symmetries and asymptotics of the scattering eigenfunctions and scattering data are derived, and properties of the discrete spectrum are analyzed in detail. In addition, the general behavior of the soliton solutions for all four reductions is discussed, and some novel soliton solutions are presented.     

Approximate analytical solution of continuous states for the l-wave Schrödinger equation with a diatomic molecule potential

The continuous states of the l-wave Schrödinger equation for the diatomic molecule represented by the hyperbolical function potential are carried out by a proper approximation scheme to the centrifugal term. The normalized analytical radial wave functions of the l-wave Schrödinger equation for the hyperbolical function potential are presented and the corresponding calculation formula of phase shifts is derived. Also, we interestingly obtain the corresponding bound state energy levels by analyzing analytical properties of scattering amplitude.     

Decay of 1.643 h <Superscript>95</Superscript>Ru and its daughter's level structure

The decay of ⁹⁵Ru has been investigated by means of γ-ray spectroscopy. The ⁹⁵Ru nuclei were produced by the reaction ⁹²Mo( α, n) ⁹⁵Ru at a beam energy of 17MeV. High-purity Ge detectors have been used singly and in coincidence to study γ-rays in the decay of ⁹⁵Ru to ⁹⁵Tc. 132 γ-rays are reported, among them, energies and intensities for 127 transitions have been determined. A decay scheme of ⁹⁵Ru with 31 levels is proposed which accommodates 127 of these transitions. Spins and parities for three new levels are proposed from calculated log ft values, measured γ-ray branching ratios, and in-beam experiment results of the daughter nucleus ⁹⁵Tc. Combining with the high-spin states observed by in-beam γ-ray spectroscopy of previous decay works, the structure of the excited states of ⁹⁵Tc is discussed in the framework of the projected shell model.     

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.     

Two-Photon Channel in <Emphasis Type="Italic">B</Emphasis>−<Emphasis Type="Italic">L</Emphasis> Models

In this paper we examine the possibility of having an exception to the recent observation by L. Randall amd M. Wise, which states that “a significant branching ratios to both e ⁺ e ⁻ and γ γ is possible only if new physics beyond that in the SM couples directly to electrons”. We consider resonances decaying into diphotons and dielectrons final states predicted in U(1) _B−L extensions of the SM. We find that these new resonances can’t decay into e ⁺ e ⁻ and γ γ final states with comparably measurable branching ratios although such resonances are directly coupled to electrons.     

Anomalies in Elastic Scattering at Isobaric Analogue States

Excitation functions for proton elastic scattering on Mn⁵⁵ at proton energies from 1320 KeV to 1480 KeV have been measured at the angles 135° and 150°. Anomalies in the differential elastic scattering were observed at E_p = 1350 ± 4 KeV, 1385 ± 4 KeV and 1445 ± 4 KeV respectively. These resonance states are the isobaric analogues of the ground, first excited and second excited states in Mn⁵⁶ respectively. Analysis of the results showed that these resonance states are best fitted to a J^π = 3⁺, 2⁺ and 1⁺ which is in excellent agreement with the J^π values of the corresponding states in Mn⁵⁶. The total widths and proton widths of these states were determined.     

Optical Potentials for Elastic and Inelastic Scattering of Non-Electronic Projectiles from Electronic Targets

The usual text book one-particle Green's function possesses a self-energy that is known to be an optical potential for elastic scattering. The introduction of an optical potential reduces the complex many-body scattering problem into a tractable one-body problem. In this work the definition of the Green's functions is extended. The defined inelastic functions are shown to possess self-energies that can be expressed in closed form in terms of the target states. It is proven that these self-energies are optical potentials for inelastic scattering. The properties of these potentials and working equations for the scattering wave functions are discussed. Received January 2, 1996; revised June 7, 1996; accepted for publication June 19, 1996