Related papers: Five-body systems with Bethe-Salpeter equations
The Bethe-Salpeter equation is a non-perturbative, relativistic and covariant description of two-body bound states. We derive the classical Bethe-Salpeter equation for two massive point particles (with or without spin) in a bound…
Four-body equations in momentum space are solved for neutron-$\He$, proton-$\Hh$, and deuteron-deuteron scattering; all three reactions are coupled. The Coulomb interaction between the protons is included using the screening and…
We develop a formally covariant quark-diquark model of the nucleon. The nucleon is treated as a bound state of a constituent quark and a diquark interacting via a quark exchange. We include both scalar and axial-vector diquarks. The…
Treating the quark and diquark as elementary particles, the Bethe-Salpeter equation for the nucleon is solved numerically. The dependence of the mass on the diquark mass and on the coupling constants is investigated. The resulting…
We present an effective field theory (EFT) at leading order to describe light single-$\Lambda$ hypernuclei. Owing to the weak $\Lambda$ binding and to the $\Lambda N$ short interaction range, meson exchange forces are approximated by…
We use the coordinate Bethe ansatz to exactly calculate matrix elements between eigenstates of the Lieb-Liniger model of one-dimensional bosons interacting via a two-body delta-potential. We investigate the static correlation functions of…
The three-body scattering problem in Coulombic systems is widespread, however yet unresolved problem by the mathematically rigorous methods. In this work this long term challenge has been undertaken by combining distorted waves and…
The Bethe-Salpeter equation in non-commutative QED (NCQED) is considered for three-body bound state. We study the non-relativistic limit of this equation in the instantaneous approximation and derive the corresponding Schr\"{o}dinger…
We describe a new method to treat low-energy scattering problems in few-nucleon systems, and we apply it to the five-body case of neutron-alpha scattering. The method allows precise calculations of low-lying resonances and their widths. We…
The structure of the Borromean nucleus $^9$Be ($\alpha+\alpha+n$) is addressed within a three-body approach using the analytical transformed harmonic oscillator method. The three-body formalism provides an accurate description of the…
We discuss effective field theory treatments of the problem of three particles interacting via short-range forces (range R >> a_2, with a_2 the two-body scattering length). We show that forming a once-subtracted scattering equation yields a…
In a recent experiment by Schaetz group \cite{weckesser2021}, the quantum $s$-wave regime has been attained for alkali and alkaline-earth atom-ion combination (Li-Ba$^+$). We investigate possible outcomes from interaction of this ion-atom…
We treat baryons as bound states of scalar or axialvector diquarks and a constituent quark which interact through quark exchange. This description results as an approximation to the relativistic Faddeev equation for three quarks which…
The Bethe-Salpeter amplitudes of the bound states formed by two scalar particles with unequal masses are analyzed in the massive scalar particle exchange ladder model. The norms of the amplitudes are calculated numerically, and it is…
We develop a quantum embedding method that enables accurate and efficient treatment of interactions between molecules and an environment, while explicitly including many-body correlations. The molecule is composed of classical nuclei and…
In the Wick-Cutkosky model, where two scalar massive constituents interact by means of the exchange of a scalar massless particle, the Bethe-Salpeter equation has solutions of two types, called "normal" and "abnormal". In the…
In a covariant model where constituent quarks and diquarks interact through quark exchange, the Bethe-Salpeter equation in ladder approximation for octet and decuplet baryons is solved. Quark and diquark confinement is thereby effectively…
We report four $\Sigma$'s and three $\Lambda$'s, in the 1500 - 1800 MeV region, as two meson - one baryon S-wave $(1/2)^+$ resonances. We solve Faddeev equations in the coupled channel approach. The invariant mass of one of the meson-baryon…
The complex energies of the three-body resonances for one infinitely heavy particle and two non-interacting light particles are the sum of the two contributing two-body complex resonance energies. The bound state of a Borromean system…
We present a one-dimensional multi-component model, known to be partially integrable when restricted to the subspaces made of only two components. By constructing fully anti-symmetrized bases, we find integrable excited eigenstates…