Related papers: Potential splitting approach to e-H and e-He${}^+$…
For a class of long-range potentials, including ultra-strong perturbations of the attractive Coulomb potential in dimension $d\geq3$, we introduce a stationary scattering theory for Schr\"odinger operators which is regular at zero energy.…
Distance-dependent phase shifts, amplitude functions, and radial wave functions for neutron-alpha elastic scattering are studied using the Variable Phase Approach. The microscopic KKNN potential is employed to calculate scattering…
We consider the nonlinear Schr{\"o}dinger equation with a short-range external potential, in a semi-classical scaling. We show that for fixed Planck constant, a com-plete scattering theory is available, showing that both the potential and…
Simultaneous analyses are performed for cross section data of elastic scattering, fusion, Coulomb breakup, and other direct yields for the $^{6}$He+$^{209}$Bi system at near-Coulomb-barrier energies. The bare and dynamical polarization…
We solve the problem of electron scattering at a soft temporal potential step. Given the relativistic nature of the problem, we use the Dirac equation, with its spinor wavefunction. We find solutions in terms of hypergeometric functions,…
We present a mathematically rigorous method for solving three-atomic bound state and scattering problems. The method is well suited for applications in systems where the inter-atomic interaction is of a hard-core nature. It has been…
The elastic collision between two ortho-positronium (e.g. S=1) atoms is studied using an ab-initio static-exchange model (SEM) in the center of mass (CM) frame considering the system as a four-body Coulomb problem where all the Coulomb…
We present a method for treatment of three charged particles. The proposed method has universal character and is applicable both for bound and continuum states. A finite rank approximation is used for Coulomb potential in three-body system…
We develop a theoretical method for solving the quantum mechanical reactive scattering problem in the presence of external fields based on a hyperspherical coordinate description of the reaction complex combined with the total angular…
We report on our analysis of the Coulomb singularity problem in the frame of the coupled channel scattering theory including spin-orbit interaction. We assume that the coupling between the partial wave components involves orbital angular…
The formalism developed in Refs.~\cite{Guo:2023ecc,Guo:2024zal,Guo:2024pvt} that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral is further…
The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the…
Wave/Schr\"{o}dinger equations with potentials naturally originates from both the quantum physics and the study of nonlinear equations. The distractive Coulomb potential is a quantum mechanical description of distractive Coulomb force…
We consider the following nonlinear Schr\"{o}dinger equation with an inverse potential: \[ i\frac{\partial u}{\partial t}+\Delta u+|u|^{\frac{4}{N}}u\pm\frac{1}{|x|^{2\sigma}}\log|x|u=0 \] in $\mathbb{R}^N$. From the classical argument, the…
Scattering and reaction cross sections of $e^{\pm}-Ps$ system are calculated for total angular momentum L=0, 1 and 2 and energies between the Ps(n=2)-Ps(n=3) threshold. We solved a set of Faddeev-Merkuriev and Lippmann-Schwinger integral…
The closed form of the first order non-linear differential equation that is satisfied by the effective range within the variable phase formulation of scattering theory is discussed. It is shown that the conventional method of determining…
We study the problem of a particle hopping on the Bethe lattice in the presence of a Coulomb potential. We obtain an exact solution to the particle's Green's function along with the full energy spectrum. In addition, we present a mapping of…
The scattering of spin-polarized electrons in an Aharonov--Bohm vector potential is considered. We solve the Pauli equation in 3+1 dimensions taking into account explicitly the interaction between the three-dimensional spin magnetic moment…
We perform a short review of the history of quantum mechanics, with a focus on the historical problems with describing ionization theoretically in the context of quantum mechanics. The essentials of the theory of resonances are presented.…
Coupled-channel dynamics for scattering and production processes in partial-wave amplitudes is discussed from a perspective that emphasizes unitarity and analyticity. We elaborate on several methods that have driven to important results in…