Relativistic Faddeev equations for three-body scattering are solved at arbitrary energies in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is incorporated withing the framework of Poincaré invariant quantum mechanics. Based on a Malfliet-Tjon interaction, observables for elastic and breakup scattering are calculated and compared to non-relativistic ones.
Relativistic Faddeev-Yakubovsky four-nucleon scattering equations are derived including a 3-body force. We present these equations in the momentum space representation. The quadratic integral equations using the iteration method, in order to obtain boosted potentials and 3-body force, are demonstrated.
We analyze 6Li elastic scattering in a wide range of incident energies (Ein), assuming the n + p + alpha + target four-body model and solving the dynamics with the four-body version of the continuum-discretized coupled-channels method (CDCC). Four-body CDCC well reproduces the experimental data with no adjustable parameter for 6Li + 209Bi scattering at Ein = 24-50 MeV and 6Li + 208Pb scattering at Ein = 29-210 MeV. In the wide Ein range, 6Li breakup is significant and provides repulsive corrections to the folding potential. As an interesting property, d breakup is strongly suppressed in 6Li-br…
Based on the spectator expansion of the multiple scattering series we employ a nonlocal translationally invariant nuclear density derived from a chiral next-to-next-to-leading order (NNLO) and the very same interaction for consistent full-folding calculations of the effective (optical) potential for nucleon-nucleus scattering for light nuclei.
The proton's tensor charges are calculated at leading order in a symmetry-preserving truncation of all matter-sector equations relevant to the associated bound-state and scattering problems. In particular, the nucleon three-body bound-state equation is solved without using a diquark approximation of the two-body scattering kernel. The computed charges are similar to those obtained in contemporary simulations of lattice-regularised quantum chromodynamics, an outcome which increases the tension between theory and phenomenology. Curiously, the theoretical calculations produce a value of the scale…
Poincare' covariant definitions for the spin-dependent spectral function and for the momentum distributions within the light-front Hamiltonian dynamics are proposed for a three-fermion bound system, starting from the light-front wave function of the system. The adopted approach is based on the Bakamjian-Thomas construction of the Poincare' generators, that allows one to easily import the familiar and wide knowledge on the nuclear interaction into a light-front framework. The proposed formalism can find useful applications in refined nuclear calculations, like the ones needed for evaluating the…
In this present work, the scattering state solutions of the Spinless Salpeter equation with the Varshni potential model were investigated. The approximate scattering phase shift, normalization constant, bound state energy, wave number and wave function in the asymptotic region were obtained. The behaviour of the phase shift with the two-body mass index η were discussed and presented.
We study the scattering of a light particle on a bound pair of heavy particles (e.g., the deuteron) within the fixed center approximation in the case of light-heavy attraction, solving the integral equation for the three-body Green's function both in the coordinate and in the momentum space. The results for the three-body scattering amplitude appear to be ambiguous -- they depend on a single real parameter. This parameter may be fixed by a three-body input, e.g., the three-body scattering length. We also solve the integral equation for the three-body Green function in the momentum space, intro…
Fully converged calculations of deuteron-deuteron elastic scattering observables are performed at energies above three- and four-body breakup threshold. Differential cross sections and analyzing powers are obtained using realistic nucleon-nucleon force models together with the Coulomb repulsion between protons. For all observables we find a very reasonable agreement with the available experimental data limited to deuteron beam energies up to 25.3 MeV.
We outline a separable matrix ansatz for the potentials in effective field theories of nonrelativistic two-body systems with short-range interactions. We use this ansatz to construct new fixed points of the renormalisation-group equation for these potentials. New fixed points indicate a much richer structure than previously recognized in the RG flows of simple short-range potentials.
A Euclidean formulation of relativistic quantum mechanics is discussed. Representations of the Hilbert space inner product and Poincaré generators are all expressed in terms of Euclidean space-time variables. The formulation does not require analytic continuation and can be used to directly calculate scattering observables. A toy model is used to demonstrate the feasibility of performing scattering calculations using the suggested computational methods.
The low-energy scattering of three bosons or distinguishable particles with short-range interactions is characterized by a fundamental parameter, the three-body scattering hypervolume. Its imaginary part is directly related to the three-body recombination rate in a quantum gas consisting of such particles. We derive an analytical formula of it for weak interactions, and perform its first numerical calculations for bosons with a variable nonzero-range potential. For attractive interactions, we identify several three-body resonances at which the three-body scattering hypervolume becomes divergen…
We consider a model of relativistic three-body scattering with a bound state in the two-body sub-channel. We show that the naïve K-matrix type parametrization, here referred to as the B-matrix, has nonphysical singularities near the physical region. We show how to eliminate such singularities by using dispersion relations and also show how to reproduce unitarity relations by taking into account all relevant open channels.
For a general two-body bound state in quantum mechanics, both in the stable and decaying cases, we establish a way to extract its two-body wave function in momentum space from the scattering amplitude of the constituent two particles. For this purpose, we first show that the two-body wave function of the bound state corresponds to the residue of the off-shell scattering amplitude at the bound state pole. Then, we examine our scheme to extract the two-body wave function from the scattering amplitude in several schematic models. As a result, the two-body wave functions from the Lippmann--Schwing…
