Related papers: Unitarizing non-relativistic Coulomb scattering
In theories with unstable particles, unitarity is satisfied by the inclusion of only stable states in unitarity sums. Hence unitarity cuts are not to be taken through unstable particles. This raises a challenge to the generalized unitarity…
A new algorithm to calculate Coulomb wave functions with all of its arguments complex is proposed. For that purpose, standard methods such as continued fractions and power/asymptotic series are combined with direct integrations of the…
This paper concerns the bubbling phenomena for the $L^2$-critical half-wave equation in dimension one. Given arbitrarily finitely many distinct singularities, we construct blow-up solutions concentrating exactly at these singularities. This…
We obtain a nonperturbative, analytical solution to integral equation of scattering theory by assuming the field within the scattering object is a spherical wave with a scattering amplitude equal to that of the far field. This approximation…
In the paper the one-dimensional one-center scattering problem with the initial potential $\alpha |x|^{-1}$ on the whole axis is treated and reduced to the search for allowable self-adjoint extensions. Using the laws of conservation as…
A numerical method of solving the one-dimensional Schrodinger equation for the regular and irregular continuum states using the phase-amplitude representation is presented. Our solution acquires the correct Dirac-delta normalization by…
We derive a new integral equation that allows the calculation of the scattering or annihilation amplitude of two particles subjected to two potentials when the corresponding amplitude for one potential only is known. We assume that…
Three new iteration methods, namely the squared-operator method, the modified squared-operator method, and the power-conserving squared-operator method, for solitary waves in general scalar and vector nonlinear wave equations are proposed.…
We present a new regularization procedure called autoregularization. The new procedure regularizes the divergences, encountered previously in a scattering process, using the intrinsic scale of the process. We use autoregularization to…
Deviations from the uniform oscillator spacing, related to the shape of the confining potential, have a strong influence on few-electron states in quantum dots when Coulomb effects are included. Distinct signatures are found for level…
We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these…
We suggest a new approach for the automatic and fully numerical evaluation of one-loop scattering amplitudes in perturbative quantum field theory. We use suitably formulated dispersion relations to perform the calculation as a convolution…
Recent advances in the treatment of scattering of charged composite particles are reviewed. In a first part I report on developments of the theory. Specifically I describe the recent completion of the derivation of the co-ordinate space…
We develop a hybrid scheme based on a finite difference scheme and a rescaling technique to approximate the solution of nonlinear wave equation. In order to numerically reproduce the blow-up phenomena, we propose a rule of scaling…
We compute the one-loop corrections to \tth up to order $\mathcal{O}(\epsilon^2)$ in the dimensional regularization parameter. We apply the projector method to compute polarized amplitudes, which generalize massless helicity amplitudes to…
The infrared exponentiation properties of dimensionally-regularized multi-loop scattering amplitudes are typically hidden at the level of the integrand, materializing only after integral evaluation. We address this long-standing problem by…
We discuss three ways of obtaining the Born approximations for Coulomb scattering: The standard way, making use of a convergence factor ("screening"), Oppenheimer's way using cylindrical (instead of spherical) coordinates, and finally…
The Coulomb problem for continuous charge distributions is a central problem in physics. Powerful methods, that scale linearly with system size and that allow us to use different resolutions in different regions of space are therefore…
We construct two-electron scattering states and verify their tensor product structure in the infrared-regular massless Nelson model. The proof follows the lines of Haag-Ruelle scattering theory: Scattering state approximants are defined…
An approach based on splitting the reaction potential into a finite range part and a long range tail part to describe few-body scattering in the case of a Coulombic interaction is proposed. The solution to the Schr\"odinger equation for the…