Humberto Garcilazo

Corrections to the closure approximation for the pion-nucleon T-matrix inside the nucleus

Abstract We give a solution to the three-body model of the optical potential of Revai, and Tandy, Redish and Bolle, which is valid in the case when the projectile is very light. The resulting potential includes corrections to the projectile-nucleon t -matrix which arise because the target nucleon is in interaction with the rest of the nucleus. We study the pion-carbon optical potential at energies below the 3,3 resonance by calculating the elastic differential cross section and reaction cross sections to the inelastic channels. As shown in the work of Tandy, Redish and Bolle the reactive content of the optical potential consists of two inelastic channels corresponding to nucleon knockout and nucleon pick-up. We use the pick-up channel as a model of pion absorption with one-nucleon emission, by treating the nucleon as a bound state of a pion and a nucleon.

The πNN bound-state problem☆

Abstract Bound-state solutions for the system composed of a pion and two nucleons are studied, and it is shown that their existence is essentially determined by the range of the πN interaction in momentum space. The relativistic Faddeev equations are solved to search for bound-state solutions of a negative pion and two neutrons, using the newly constructed πN separable potentials that reproduce the phase shift of the P 33 channel from 0 to 350 MeV, and realistic NN interactions such as the Reid soft-core, Paris, and Malfliet-Tjon potentials. It is found that bound-state solutions are possible for some of the πN interactions that have very long range in momentum space.

Basis states for relativistic three-body calculations of particles with spin

Using a linear combination of the three‐body helicity states constructed by Wick, a new set of basis states is constructed that can be used to perform three‐body calculations with relativistic treatment of the spin. These states are diagonal in the usual angular momentum quantum numbers of a pair liSiu2009ji, where li is the orbital angular momentum, Si the spin, and ji the total angular momentum of the pair jk. These states are used to write down the relativistic Faddeev equations obtaining two sets of uncoupled integral equations that are identified as corresponding to the states of positive and negative parity. It is also shown, by means of some simple examples, that the relativistic recoupling coefficients reduce to the usual nonrelativistic ones if one neglects the effects of relativity. Some possible applications involving particles off the mass shell are discussed.

Three-body helicity formalism applied to pion-deuteron scattering

Abstract We apply Wicks three-body helicity formalism, to covariantly reduce the relativistic Faddeev equations that describe pion-deuteron elastic scattering, obtaining a set of equations that satisfy two- and three-body unitarity and are Lorentz invariant with regard to both the space and the spin variables. We use all the pion-nucleon S and P-wave channels and the two nucleon-nucleon S-wave channels as input, to give a good description of the data for pion kinetic energies in the region from 142 MeV up to 512 MeV.

The one-pion-exchange potential in the three-body model of nucleon-nucleon scattering

Abstract We derive the one-pion-exchange potential in the three-body model of nucleon-nucleon scattering in which the nucleon is treated as a bound state of a pion and a nucleon, and show that it has the same form as the usual Yukawa OPEP derived from field theory, except that its range is energy dependent and it becomes complex above the pion-production threshold.

Completeness relation for energy-dependent separable potentials

We point out that the eigenfunctions of energy‐dependent separable potentials, which are commonly used in the relativistic three‐body problem, form a complete set of states. The completeness property is important, since it is necessary in order to satisfy the optical theorem, and consequently to conserve probability. We show that there exists a large family of energy‐dependent separable potentials whose eigenfunctions form a complete set. Although the eigenfunctions of these potentials are not mutually orthogonal, it is shown that in general they are linearly independent.

THE CONTRIBUTION OF PION ABSORPTION WITH TWO NUCLEON EMISSION TO THE PION NUCLEUS OPTICAL POTENTIAL

Abstract Four terms in the pion-nucleus optical potential which arise from pion absorption with two nucleon emission are calculated using a model in which the nucleon is treated as a bound state of a pion and a nucleon. The contribution of these terms to the reaction cross section of carbon is considered. Two of the terms give rise to a negative reaction cross section, but it is shown that the sum of the four is positive definite. We find that the absorption reaction cross sections are very sensitive to the off-shell behavior of the free pion-nucleon T -matrix.