Related papers: Improvement to Generalized Separable Expansion Met…
A realistic nucleon-nucleon potential is transformed into a low-momentum effective one (LMNN) using the Okubo theory. The separable potentials are converted from the LMNN with a universal separable expansion method and a simple Legendre…
A general new technique to solve the two-center problem with arbitrarily-orientated deformed realistic potentials is demonstrated, which is based on the powerful potential separable expansion method. As an example, molecular single-particle…
We present an alternative organizational scheme for developing effective theories of 2- and 3-body systems that is systematic, accurate, and efficient with controlled errors. To illustrate our approach we consider the bound state and…
A solution to the relativistic generalization of the four-particle integral Faddeev-Yakubovsky equation is carried out. Only states with zero orbital angular momentum, $S$ states, are considered in the calculations. A rank-one separable…
The Gross-Pitaevskii equation (GPE) in a double well potential produces solutions that break the symmetry of the underlying non-interacting Hamiltonian, i.e., asymmetric solutions. The GPE is derived from the more general second-quantized…
A proposal is made for reducing the solution of the N-particle Lippmann-Schwinger equation to that of smaller sets of particles. This consists of first writing the N-particle equation in terms of all possible $N/2$-particle…
We propose a novel approach to solve the three-nucleon (3N) Faddeev equation which avoids the complicated singularity pattern going with the moving logarithmic singularities of the standard approach. In this new approach the treatment of…
Considering two-body integral equations we show how they can be dimensionally reduced by integrating exactly over the azimuthal angle of the intermediate momentum. Numerical solution of the resulting equation is feasible without employing a…
The homogeneous Lippmann-Schwinger integral equation is solved in momentum space by using confining potentials. Since the confining potentials are unbounded at large distances, they lead to a singularity at small momentum. In order to…
The exact solvability of several nuclear models with non-degenerate single-particle energies is outlined and leads to a generalization of integrable Richardson-Gaudin models, like the $su(2)$-based fermion pairing, to any simple Lie…
Background: One important ingredient for many applications of nuclear physics to astrophysics, nuclear energy, and stockpile stewardship are cross sections for reactions of neutrons with rare isotopes. Since direct measurements are often…
By means of transformations to nonlinear Klein-Gordon equations, we show that a generalized short pulse equation is integrable in two (and, most probably, only two) distinct cases of its coefficients. The first case is the original short…
The Poisson-Boltzmann equation (PBE) is an implicit solvent continuum model for calculating the electrostatic potential and energies of ionic solvated biomolecules. However, its numerical solution remains a significant challenge due strong…
Dimensional regularization is applied to the Lippmann-Schwinger equation for a separable potential which gives rise to logarithmic singularities in the Born series. For this potential a subtraction at a fixed energy can be used to…
We extend a new treatment proposed for two-nucleon (2N) and three-nucleon (3N) bound states to 2N scattering. This technique takes momentum vectors as variables, thus, avoiding partial wave decomposition, and handles spin operators…
We study a family of separable potentials with and without added contact interactions by solving the associated Lippmann-Schwinger equation with two coupled partial waves. The matching of the resulting amplitude matrix with the…
A recently developed three-dimensional formalism for the nucleon-deuteron breakup channel initially considered only the leading-order term of the Faddeev equations, using the nucleon-nucleon T-matrix to compute the breakup amplitude. In the…
We solve the Lippman-Schwinger equation (LSE) with a kernel that includes a regular finite-range potential and additional contact terms with derivatives. We employ distorted wave theory and dimensional regularization, as proposed in Physics…
Three-body Faddeev-type equations for bound, resonant, and scattering states in the systems with a nuclear core and two nucleons are solved using the momentum-space framework. Two approaches for eliminating the Pauli-forbidden deeply-bound…
Using separable potentials for $\bar{K}N-\pi\Sigma$ interaction, we investigated four-body kaonic nuclear systems such as $K^{-}ppn$ and $K^{-}K^{-}pp$, with the Faddeev AGS method in the momentum representation. The Faddeev calculations…