arXiv subjects
Publications and source records attributed to J. Carbonell.
We present the main features of the explicitly covariant Light-Front Dynamics formalism and a summary of our recent works on this topic. They concern the bound states of two scalar particles in the Wick-Cutkosky model and of two fermions interacting via the usual OBEP ladder kernels.
The low energy scattering of heavy positively charged particles on hydrogen atoms (H) are investigated by solving the Faddeev equations in configuration space. A resonant value of the pH scattering length, $a=750\pm 5$ a.u., in the pp antisymmetric state was found. This large value indicates the existence of a first excited state with a binding energy B=1.14$\times10^{-9}$ a.u. below the H ground state. Several resonances for non zero angular momenta states are predicted.
We develop a general method to construct two relativistic fermions bound states with a given $J^π$, in the framework of the explicitly covariant light-front dynamics.
The covariant light-front equations have been solved exactly for a two fermion system with different boson exchange ladder kernels. We present a method to study the cutoff dependence of these equations and to determine whether they need to be regularized or not. Results are presented for scalar and pseudo-scalar exchange. This latter furthermore exhibits some strange particularities which will be discussed.
We show that in the system of two fermions interacting by scalar exchange, the solutions for J$^π$=$0^+$ bound states are stable without any cutoff regularization, for values of the coupling constant $α$ below a critical value $α_c$. This latter is calculated from an eigenvalue equation.
The bound state solutions of two fermions interacting by a scalar exchange are obtained in the framework of the explicitly covariant light-front dynamics. The stability with respect to cutoff of the J$^π$=$0^+$ and J$^π$=$1^+$ states is studied. The solutions for J$^π$=$0^+$ are found to be stable for coupling constants $α={g^2\over4π}$ below the critical value $α_c\approx 3.72$ and unstable above it. The asymptotic behavior of the wave functions is found to follow a ${1\over k^{2+β}}$ law. The coefficient $β$ and the critical coupling constant $α_c$ are calculated from an eigenvalue equation. The binding energies for the J$^π$=$1^+$ solutions diverge logarithmically with the cutoff for any value of the coupling constant. For a wide range of cutoff, the states with different angular momentum projections are weakly split.
Some of the last results on low energy antiproton physics are reviewed. First Faddeev calculations for nd scattering length are presented.
The Faddeev-Yakubovsky equations in configuration space have been solved for the four nucleon system with special interest in their scattering states. We present results concerning the structure of the first $^4$He, scattering states in different (T,S) channels including the first inelatic threshold N+3N$\to$NN+NN and the n-t cross section using realistic potentials.
The recent calculation of the four nucleon continuum spectrum are reviewed. Faddeev-Yakubovsky equations in configuration space have been solved for the four nucleon system with special interest in their scattering states. We present results concerning the structure of the first $^4$He, scattering states in different (T,S) channels including the first inelatic threshold N+3N$\to$NN+NN and the n-t cross section using realistic potentials.
We show that in the system of two fermions interacting by scalar exchange, the solutions for J$^π$=$0^+$ bound states are stable without any cutoff regularization for coupling constant below some critical value.
Light-front dynamics (LFD) is a powerful approach to the theory of relativistic composite systems (hadrons in the quark models and relativistic nucleons in nuclei). Its explicitly covariant version has been recently applied with success to describe the new CEBAF/TJNAF data on the deuteron electromagnetic form factors. The solutions used in were however not obtained from solving exactly the LFD equations but by means of a perturbative calculation with respect to the non relativistic wave function. Since, a consequent effort has been made to obtain exact solutions of LFD equations. The first results concerning J=0 states in a scalar model have been published in nucl-th/9912050. The construction of $J \ne 0$ states in LFD is complicated by the two following facts. First, the generators of the spatial rotations contain interaction and are thus difficult to handle. Second, one is always forced to work in a truncated Fock space, and consequently, the Poincaré group commutation relations between the generators -- ensuring the correct properties of the state vector under rotation -- are in practice destroyed. In the standard approach, with the light-front plane defined as $t+z=0$, this violation of rotational invariance manifests by the fact that the energy depends on the angular momentum projection on $z$-axis. We present here a method to construct $J\ne0$ states in the explicitly covariant formulation of LFD and show how it leads to a restoration of rotational invariance.
We show some results concerning the weak binding limit for J=0 states -- which turn out to strongly differ from the non relativistic case -- together with the construction of non zero angular momentum states. The calculation of such states in the Light-Front Dynamics (LFD) framework has some peculiarities which are absent in other approaches. They are related to the fact that the rotation generators contain interaction. We present here the construction of non zero angular momentum states in LFD and show how it leads to a restoration of rotational invariance. For this purpose, the use of Light-Front Dynamics in its explicitly covariant formulation is of crucial importance since the dependence of the wave function on the light-front plane is explicitly parametrized.
The Faddeev-Yakubovsky equations have been solved in configuration space for the four nucleon system. The n+t elastic cross section has been calculated using several realistic interactions and a phenomenological three-nucleon force. Special attention is devoted to the description of the observed resonant structure at $T_{lab}\approx 4$ MeV. In the present state of the calculations, the realistic NN interactions are unable to describe the energy region considered, i.e. n+t S- and P- waves. Whereas the inclusion of a three-nucleon force improves the zero energy region, the disagreement in the resonant peak remains. This failure contrasts with the results of a pure phenomenological model. The origin of this disagreement as well as the possible issues are discussed.
The deuteron form factors are calculated in the framework of the relativistic nucleon-meson dynamics, by means of the explicitly covariant light-front approach. The inflluence of the nucleon electromagnetic form factors is discussed. At $Q^2\leq 3$ (GeV/c)$^2$ the prediction for the structure function $A(Q^2)$ and for the tensor polarization observable $t_{20}$ are in agreement with the recent data of CEBAF/TJNAF.
The deuteron form factors are calculated in the framework of the relativistic nucleon-meson dynamics. The relativistic effects change considerably the S- and D-waves of the deuteron, result in the dominating extra component in the deuteron wave function and generate the contact interaction between the nucleon, mesons and photon. The prediction for the polarization observable $t_{20}$ is in good agreement with the recent data of TJNAF/CEBAF.
The recent experimental data obtained by the OBELIX group on total $\bar{p}p$ annihilation cross section are analysed; the low energy spin averaged parameters of the $\bar{p}p$ scattering amplitude (the imaginary parts of the S-wave scattering length and P-wave scattering volume) are extracted from the data. Their values are found to be equal to $Im a_{sc} = - 0.69 \pm 0.01 (stat) \pm 0.03 (sys) fm, Im A_{sc} = - 0.76 \pm 0.05 (stat) \pm 0.04 (sys) fm^3$. The results are in very good agreement with existing atomic data.
The main properties of the interaction of ultra low-energy antiprotons ($% E\le10^{-6}$ a.u.) with atomic hydrogen are established. They include the elastic and inelastic cross sections and Protonium (Pn) formation spectrum. The inverse Auger process ($Pn+e \to H+\bar{p}$) is taken into account in the framework of an unitary coupled-channels model. The annihilation cross-section is found to be several times smaller than the predictions made by the black sphere absorption models. A family of $\bar{p}H$ nearthreshold metastable states is predicited. The dependence of Protonium formation probability on the position of such nearthreshold S-matrix singularities is analysed. An estimation for the $H\bar{H}$ annihilation cross section is obtained.
The Faddeev-Yakubowski equations have been solved in configuration space for the four nucleons system. Results for bound and scattering states in the isospin and S-wave approximation for different (T,S) channels are presented. The n-t elastic cross section has been also calculated with realistic interactions. A special interest was devoted to the description of the observed resonant structure at $T_{lab}\approx 3$ MeV which is well reproduced only by the simple MT I-III potential.