Exact scattering states in one-dimensional Hermitian and non-Hermitian potentials

The scattering states in one-dimensional Hermitian and non-Hermitian potentials are investigated. An analytical solution for the scattering states is presented in terms of Heun functions. It is shown that for some specially chosen parameter conditions, an infinite number of the exact scattering states is obtained. In the Hermitian potentials, they correspond to the reflectionless states. In the non-Hermitian complex potentials with parity-time symmetry, they are the unidirectionally reflectionless states.

The scattering states of the generalized Hulthén potential with an improved new approximate scheme for the centrifugal term

This paper finds the approximate analytical scattering state solutions of the arbitrary 1-wave Schrodinger equation for the generalized Hulthen potential by taking an improved new approximate scheme for the centrifugal term. The normalized analytical radial wave functions of the 1-wave SchrSdinger equation for the generalized Hulthen potential are presented and the corresponding calculation formula of phase shifts is derived. Some useful figures are plotted to show the improved accuracy of the obtained results and two special cases for the standard Hulthen potential and Woods-Saxon potential are also studied briefly.

Scattering Resonance States and Partial Potential Energy Surface of Reaction I+HI(v=0)→IH(v′=0) +I

The partial potential energy surface of the I ＋ HI →IH ＋ I reaction involving the translational and vibrational motions has been constructed at the QCISD（ T ）//MP4SDQ level with the pseudo potential method that is helpful to interpreting the scattering resonance states. The lifetimes of the scattering resonance states in the title reaction obtained from the partial potential energy surface are about 90-120 fs, which agrees with the result of high-resolved threshold photodetachment spectroscopy of anion IHI^- measured by Neumark.

Approximate Analytical Solutions for Scattering States of D-dimensional Hulthen Potentials

Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie 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 solutions is discussed.

Elastic scattering of surface states on three-dimensional topological insulators

Topological insulators as a new type of quantum matter materials are characterized by a full insulating gap in the bulk and gapless edge/surface states protected by the time-reversal symmetry. We propose that the interference patterns caused by the elastic scattering of defects or impurities are dominated by the surface states at the extremal points on the constant energy contour. Within such a formalism, we summarize our recent theoretical investigations on the elastic scattering of topological surface states by various imperfections, including non-magnetic impurities, magnetic impurities, step edges, and various other defects, in comparison with the recent related experiments in typical topological materials such as BiSb alloys, Bi2Te3, and Bi2Se3 crystals.

Scattering states of modified PSschl-Teller potential in D-dimension

We present a new approximation scheme for the centrifugal term, and apply this new approach to the SchrSdinger equation with the modified P5schl Teller potential in the -dimension for arbitrary angular momentum states. The approximate analytical solutions of the scattering states are derived. The normalized wave functions expressed in terms of the hypergeometric functions of the scattering states on the 2 scale and the calculation formula of the phase shifts are given. The numerical results show that our results are in good agreement with those obtained by using the amplitude-phase method （APM）.

Theoretical Research on Scattering Resonance States of Reaction I＋HI（v=O）→IH（v＇=0）＋I： Partial Potential Energy Surface and One-dimensional Quantum Reactive Scattering Calculation

Based on the vibrational potential curves coupled with the minimum energy reaction path, the partial potential energy surface of the reaction I＋HI→IH＋I was constructed at the QCISD（T）//MP4SDQ level with pseudo potential method. And the formation mechanism of the scattering resonance states of this reaction was well interpreted with the partial potential energy surface. The scattering resonance states of this reaction should belong to Feshbach resonance because of the coupling of the vibrational mode and the translational mode. With the one-dimensional square potential well model, the resonance width and lifetime of the I＋HI（v=0）→IH（v＇=0）＋I state-to-state reaction were calculated, which preferably explained the high-resolved threshold photodetachment spectroscopy of the IHI- anion performed by Neumark et al..

Relativistic Scattering States of Coulomb Potential Plus a New Ring-Shaped Potential

In this paper, exact solutions of scattering states of the Klein-Gordon equation with Coulomb potential plus a new ring-shaped potential are studied under the condition that the scalar potential is equal to the vector potential. The normalized wave functions of scattering states on the “k/27π scale” and the calculation formula of phase shifts are presented. Analytical properties of the scattering amplitude are discussed.

Scattering states of modified Pschl-Teller potential in D-dimension

We present a new approximation scheme for the centrifugal term,and apply this new approach to the Schrdinger equation with the modified Pschl-Teller potential in the D-dimension for arbitrary angular momentum states.The approximate analytical solutions of the scattering states are derived.The normalized wave functions expressed in terms of the hypergeometric functions of the scattering states on the k/2π scale and the calculation formula of the phase shifts are given.The numerical results show that our results are in good agreement with those obtained by using the amplitude-phase method(APM).

Direct observation of melted Mott state evidenced from Raman scattering in 1T-TaS_2 single crystal

The evolution of electron correlation and charge density wave （CDW） in 1T-TaS2 single crystal has been investi- gated by temperature-dependent Raman scattering, which undergoes two obvious peaks of Aig modes about 70.8 cm-t and 78.7 cm I at 80 K, respectively. The former peak at 70.8 cm-t is accordant with the lower Hubbard band, resulting in the electron-correlation-driven Mott transition. Strikingly, the latter peak at 78.7 cm-1 shifts toward low energy with increasing the temperature, demonstrating the occurrence of nearly commensurate CDW phase （melted Mott phase）. In this case, phonon transmission could be strongly coupled to commensurate CDW lattice via Coulomb interaction, which likely induces appearance of hexagonal domains suspended in an interdomain phase, composing the melted Mott phase characterized by a shallow electron pocket. Combining electronic structure, atomic structure, transport properties with Ra- man scattering, these findings provide a novel dimension in understanding the relationship between electronic correlation, charge order, and phonon dynamics.

Single-photon scattering controlled by an imperfect cavity

We study the single-photon transport in the coupled-resonator waveguide(CRW)controlled by an imperfect cavity.A Lorentzian spectrum is introduced to describe the dissipation.We find that the probability current conservation can be broken,although the imperfect cavity is a Hermitian system.The coupling strength between the imperfect cavity and the CRW has significant influences near the resonant frequency.With the increase of the coupling strength,the transmission coeffi-cient becomes smaller.The spectral width plays a dominant role under the off-resonant condition,where the transmission coefficient is greatly suppressed with the increase of the spectral width.We also observe an abrupt jump of the transmission and reflection coefficients when the hopping amplitude is large enough.All the distinctive behaviors are closely related to the complex effective potential induced by the imperfect cavity.

Single-photon scattering by two separated atoms in a supercavity

We study the single-photon scattering along a one-dimensional cavity array with two distant two-level atoms in a supercavity,which aims to simulate a recent x-ray experiment [Nature 482,199（2012）].Without introducing dissipation,we find that when one atom is exactly located at a node of a mode of the supercavity and the other is at the antinode of that mode,no splitting of the reflectivity peak can appear.Nevertheless,the atom at the node significantly changes the positions of the reflectivity valleys.On the other hand,when the atom is shifted a little from the exact node,then the splitting can appear.We also explain these results with an analysis based on the general formal scattering theory.Our result implies the importance of non-resonant modes of the supercavity in our problem.

Theoretical Study of the Scattering Resonance State, Reaction Mechanism and Partial Potential Energy Surface of the F+CH4→HF+CH3 Reaction

The partial potential energy surface was constructed by ab initio method [QCISD（T）/6- 311＋＋G（2df,2pd）]for F＋CH4→HF＋CH3 reaction system. It not only explained the reaction mechanism brought forward by Diego Troya by means of quasiclassical trajectory （QCT） but also successfully validated Kopin Liu＇s experimental phenomena about the existence of the reactive resonance. The lifetime of the scattering resonance state was about 0.07 ps. All these were in agreement with the experiments.

Polarization dependence of gain and amplified spontaneous Brillouin scattering noise analysis for fiber Brillouin amplifier

The polarization dependences of gain and amplified spontaneous Brillouin scattering(ABS) noise for fiber Brillouin amplifier(FBA) are analyzed through theories, simulations, and experiments.Modified vector propagation equations for calculating the gain of the probe signal and the ABS noise are derived and analyzed in the Stokes spaces.In simulations and experiments, we prove that the gain of the probe signal and the ABS noise are strongly dependent on the relative state of polarization(SOP) of the pump and probe signals.The closer the relative SOP of the pump and probe signals is, the more obvious ABS noise suppression effect will be brought by increasing the power of the input probe signal.

Electron Raman scattering in semiconductor quantum well wire of cylindrical ring geometry

We study the electron states and the differential cross section for an electron Raman scattering process in a semi- conductor quantum well wire of cylindrical ring geometry. The electron Raman scattering developed here can be used to provide direct information about the electron band structures of these confinement systems. We assume that the system grows in a GaAs/Al0.35Ga0.65As matrix. The system is modeled by considering T = 0 K and also a single parabolic con- duction band, which is split into a sub-band system due to the confinement. The emission spectra are discussed for different scattering configurations, and the selection rules for the processes are also studied. Singularities in the spectra are found and interpreted.

In-situ Characterization of Non-aqueous Nano-dispersion Systems by Freeze-etching TEM and Comparative Study with Laser Scattering Method

In-situ characterization of non-aqueous nano-dispersion systems（NANDS） by freeze-etching transmission electron microscope（FETEM） was reported.To improve just-for-once successive rate of specimen preparation and get good characterization results,an improving specimen preparation method of freezing etching was developed.Size,distribution and morphology of NANDS were directly visualized.Some information of particle dispersion feature and particle density can also be obtained.Reproductivity of the FETEM characterization is excellent.Comparing with laser scattering method,which is liable to give positive error especially for small size particle anchoring disperser,FETEM characterization can give more accurate measurement of particle size.Moreover,FETEM can give dispersion feature of nanoparticle in non-aqueous medium.

Theoretical Studies on Formation Mechanism of Resonance States for Na+I_2→Na^++I_2^-System

An extended linear combination of arrangement channels-scattering wave-function(LCAC-SW) quantum scattering dynamic method combined with ab initio quantum chemical calculation was used to study the formation mechanism of the resonance states for the collinear Na+I 2→Na ++I - 2 ion-pair formation process on Aten-Lanting-Los potential energy surface. The resonance energy and the resonance width or the lifetime for the first resonance peak were calculated. The resonance can be identified as the Feshbach type and the physical interpretation is given. The geometric structure of the resonance state for the title system has been optimized.

Empirical Effective Interaction in 22MeV Proton Scattering

Inelastic differential cross sections of 22 MeV proton scattering for 5 excited states of 28Si have been measured from 10°to 115°.Empirical effective interactions were extracted within the frame of DWBA from the normal parity state data which transition densities were known from electron scattering.The fitting is good except for the forward angle of 4^(+)_(1) and 0^(+)_(2) states.The results are discussed.

S-Wave Scattering Properties for Na-K Cold Collisions

Scattering properties of ultracold atoms are sensitive to the interatomic potential.Based on the accurate triplet least-bound state energy,we calculate the triplet s-wave scattering length for ^(23)Na-^(40)K.The scattering length is-814.1^(+29)_(-31.3) a_(0) with a_(0) being the Bohr radius.By using the mass scaling method,those scattering lengths are also obtained for ^(23)Na-^(41)K and ^(23)Na-^(39)K.The degenerate internal state approximation is used to estimate the scattering data of atoms colliding in different spin states.

发射光谱法诊断空气电弧的稳态电子密度分布

空气电弧是一种常见的等离子体,对其稳态阶段的微观参数进行研究,对准确把握等离子体内部的反应机制有重要意义。发射光谱法是一种成熟的诊断等离子体电子密度的技术,具有非接触式测量、瞬态探测、灵敏度高、响应速度快、仪器简单等优点。文中以H_(α)656.28 nm谱线做特征谱线,以石墨为电极材料在250 A、200 V的条件下对空气电弧进行发射光谱的测量,对实验获得的发射光谱作阿贝尔反变换和佛克脱线型拟合,反卷积得到斯塔克展宽,最终获得空气电弧电子数密度的径向分布。同时利用汤姆逊散射法测量相同参数条件下空气电弧的电子数密度以验证发射光谱法测量结果的正确性,经验证两种方法的测量结果具有良好的一致性。该实验为空气电弧等离子体电子数密度的测量提供了参考思路和方法。