Related papers: Three-potential formalism for the three-body Coulo…
Starting from a relativistic s-wave scattering length model for the two particle input we construct an unambiguous, unitary solution of the relativistic three body problem given only the masses $m_a,m_b,m_c$ and the masses of the two body…
One has to study multivariable scattering amplitudes to extract properties of the three-body states from the generalizations of the L\"uscher finite-volume formalism. In particular, a three-body amplitude obtained from a Lattice QCD…
In this work a calculation of the cluster decomposable formalism for relativistic scattering as developed by Lindesay, Markevich, Noyes, and Pastrana (LMNP) is made for an ultra-light quantum model. After highlighting areas of the theory…
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 Faddeev-Yakubovski equations are solved in configuration space for low energy four-nucleon continuum states. Coulomb interaction was included into the formalism permitting an exact description of the scattering states in p+$^{3}$He and…
Bound and scattering states of a non-central extension of the three-dimensional Kepler-Coulomb Hamiltonian are worked out analytically within the framework of the potential groups of the problem, SO(7) for bound states and SO(6,1) for…
We derive the three-body quantization condition in a finite volume using an effective field theory in the particle-dimer picture. Moreover, we consider the extraction of physical observables from the lattice spectrum using the quantization…
In this paper, we give a simple proof of scattering result for the Schr\"odinger equation with combined term $i\pa_tu+\Delta u=|u|^2u-|u|^4u$ in dimension three, that avoids the concentrate compactness method. The main new ingredient is to…
As part of our program to develop the description of three-body effects in quantum vacuum phenomena, we study the three-body interaction of two anisotropically polarizable atoms with a perfect electrically conducting plate, a generalization…
Years ago S. Weinberg suggested the "Quasi-Particle" method (Q-P) for iteratively solving an integral equation, based on an expansion in terms of sturmian functions that are eigenfunctions of the integral kernel. An improvement of this…
We introduce a circular restricted charged three-body problem on the plane. In this model, the gravitational and Coulomb forces, due to the primary bodies, act on a test particle; the net force exerted by some primary body on the test…
We suggest a new adiabatic approach for description of three charged particles in the continuum. This approach is based on the Coulomb-Fourier transformation (CFT) of three body Hamiltonian, which allows to develop a scheme, alternative to…
The inverse scattering problem of the three-dimensional Schroedinger equation is considered at fixed scattering energy with spherically symmetric potentials. The phase shifts determine the potential therefore a constructive scheme for…
We present a systematically improvable method for numerically solving relativistic three-body integral equations for the partial-wave projected amplitudes. The method consists of a discretization procedure in momentum space, which…
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.…
The Alt-Grassberger-Sandhas equations for the five-body eta-4N problem are solved for the case of the driving eta N and NN potentials limited to s-waves. The quasi-particle (Schmidt) method is employed to convert the equations into the…
The three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential is analytically derived together with its asymptotic form without reference to partial wave expansion. The numerical solutions of the three-dimensional…
We develop a class of emulators for solving quantum three-body scattering problems. They are based on combining the variational method for scattering observables and the recently proposed eigenvector continuation concept. The emulators are…
We discuss the general three-particle quantum scattering problem, for motion restricted to the full line. Specifically, we formulate the three-body problem in one dimension in terms of the (Faddeev-type) integral equation approach. As a…
Using non-relativistic effective Lagrangians in the particle-dimer picture, we rederive the expression for the energy shift of a loosely bound three-particle bound state of identical bosons in the unitary limit. The effective field theory…