The Quantum Scattering Study for Ion-pair Formation Reaction Na+I_2→Na^+I_2^- with the LCAC-SW method

The selected-state probabilities of collinear ion-pair formation process Na+I2→Na++I2-on Aten-Laming-Los two-State potential energy surface have been calculated by using LCAC-SW method. The results show that reaction probabilities are oscillatory with collision energy; the threshold energy of this ioniZation reaction is 2.8 ev, which is in modest agreement with experimental result.

Disassociation of a one-dimensional cold molecule via quantum scattering

Motivated by the recent experimental developments in ultracold molecules and atoms,we propose a simple theoretical model to address the disassociation,reflection,and transmission probability of a one-dimensional cold molecule via quantum scattering.First,we show the Born approximation results in the weak interaction regime.Then,by employing the Lippmann-Schwinger equation,we give the numerical solution and investigate the disassociation’s dependence on the injection momentum and the interaction strengths.We find that the maximum disassociation rate has a limit when increasing the interaction strengths and injection momentum.We expect that our model can be realized in experiments in the near future.

LCAC-SW quantum scattering dynamic study on the ion-pair formation process

LCAC-SW method has been extended to study the reaction dynamics for ion-pair formation processes. M+ X2→Mt + X2 reaction system involves two potential energy surfaces, i.e., the covalence state (M + X2) and the ionic state (M + X2) and their crossing effect. The working equations for calculating state-to-state probability have been derived based on the above two-state model, Satisfied results d collinear state-to-state probabilities for K+ I2 → K+ + I2 ion-pair formation system have been obtained.

A quantum scattering study of collinear state-to-state reaction probabilities for the F+H_2(ν)→-HF(v')+H system

A new quantum scattering approach (linear combination of arrangement channels-scattering wavefunction,LCAC-SW) proposed by Deng and his co-workers is used to calculate collinear state-to-state reaction probabilities for the F + H-2(v)→HF(v')+H system.Several interesting problems such as threshold energy,compound states and enhance by translational energy of the reactants and the vibration excitation of products are discussed and they are compared with other theoretical investigations reported in the literature.It is shown that the LCAC-SW approach is the successful one of quantum scattering methods.

Search algorithm on strongly regular graphs based on scattering quantum walks

Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs（SRGs） with parameters（N, k, λ, μ） achieves full quantum speedup. The problem is reconsidered in terms of scattering quantum walk, a type of discrete-time quantum walks. Here, the search space is confined to a low-dimensional subspace corresponding to the collapsed graph of SRGs. To quantify the algorithm＇s performance, we leverage the fundamental pairing theorem, a general theory developed by Cottrell for quantum search of structural anomalies in star graphs.The search algorithm on the SRGs with k scales as N satisfies the theorem, and results can be immediately obtained, while search on the SRGs with k scales as√N does not satisfy the theorem, and matrix perturbation theory is used to provide an analysis. Both these cases can be solved in O（√N） time steps with a success probability close to 1. The analytical conclusions are verified by simulation results on two SRGs. These examples show that the formalism on star graphs can be applied more generally.

Nested Bethe Ansatz for Spin Ladder Model with Open Boundary Conditions

The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the generalboundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.

Improvement in the calculation of anti-Stokes energy transfer and experimental justification based on Er_(0.01)Yb_xY_(1 0.01 x)VO_4 crystal

The improvement on the calculation of anti-Stokes energy transfer rate is studied in the present work. The additional proportion coefficient between Stokes and anti-Stokes light intensities of quantum Raman scattering theory as compared with the classical Raman theory is introduced to successfully describe the anti-Stokes energy transfer. The theoretical formula for the improvement on the calculation of anti-Stokes energy transfer rate is derived for the first time in this study. The correctness of introducing coefficient exp{△E/kT} from well-known Raman scatter theory is demonstrated also. Moreover, the experimental lifetime measurement in Er0.01YbxY1-0.01-xVO4 crystal is performed to justify the validity of our important improvement in the original phonon-assisted energy transfer theory for the first time.

Electron Raman scattering in a cylindrical quantum dot

Electron Raman scattering（ERS） is investigated in a CdS cylindrical quantum dot（QD）.The differential cross section is calculated as a function of the scattering frequency and the size of the QD.Single parabolic conduction and valence bands are assumed,and singularities in the spectrum are found and interpreted.The selection rules for the processes are also studied.The ERS studied here can be used to provide direct information about the electron band structure of these systems.

Exact quantum and TST-CEQ study of the collinear reaction O+HCl

Exact quantum calculations of reaction probabilities have been carried out using hyperspherical coordinates for the collinear reaction O+HCl(upsilon less than or equal to 1)-->OH(upsilon' less than or equal to 1)+Cl. A generalized LEPS potential energy surface with a barrier height of 8.12 kcal/mol has been used in the calculations. According to the calculated results we found that (1) the reaction probability oscillates with energy, (2) the reaction probability shows vibrational adiabaticity, although it is poorer than that for symmetric reaction Cl+HCl. The analysis of resonance has also been done. The reaction rate constants and average cross sections have been calculated by TST-CEQ method. The rate constants are in agreement with that by QCT and smaller than the experimental one. Finally, the threshold has been estimated and is in good agreement with that of the literature.

Non-Relativistic Phase Shifts for Scattering on Generalized Radial Yukawa Potentials

Non-relativistic phase shifts for a generalized Yukawa potential V(r) =-V_0( e^(-αr)/r)-V_1( e^(-2αr)/r^2) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type approximation of power-law potential terms.Small variations of V_1 seem to have marginal effects on the effective potential and on exact phase shifts.However,as pointed out in this study,a Pekeris-type approximation in scattering applications often implies serious distortions of both effective potentials and phase shifts.The Pekeris-type based analytic approximation in this study seems to give low-quality scattering results for this model potential at low energies.

Nonadiabatic collision model calculations of ion-pair formation cross sections of Cs+O2→Cs++O2-

This paper has improved Hickman's nonadiabatic collision model by substituting Hickman's constant velocity classical straight line trajectory approximation with the solution of motion equation mR=-dV(R)/dR, and has calculated the cross sections of ion-pair formation Cs+O2 -Cs++O2- with the improved nonadiabatic collision model (INCM). A comparison of our results with other theoretical and experimental results has been made.