Giorgio Cattapan

A separable potential approach to nucleon-nucleus scattering with exact treatment of Coulomb interactions

Abstract A suitable, physically reasonable choice of separable nucleon-nucleus potential is made, which leads to very simple analytic expressions for the form factors in the Coulomb-state representation. This allows one to take account of Coulomb effects in an exact and simple way. The model is applied to the analysis of the elastic scattering of nucleons by 4 He, 12 C and 16 O targets. A good fit of the experimental phase shifts is obtained with almost the same values of the potential parameters for neutron-nucleus and proton-nucleus elastic scattering.

The role of the Δ in nuclear physics

Abstract We review the properties of Δ , and the role it plays in Nuclear Physics. We try to assess what has been ascertained up to now, and what remains to be clarified about this hadron, which represents the outstanding structure in the medium-energy pion–nucleon interaction. We consider the free Δ first, with particular emphasis on those aspects which may give information on the internal hadron structure, such as the isospin mass splittings in the Δ multiplet, and the electromagnetic fingerprints of deviation from spherical symmetry. We then discuss the N – Δ interaction, both under the point of view of meson-exchange models, and under a microscopic quark-model perspective. In so doing, we review the present status of the meson–nucleon and meson– Δ coupling constants and form factors, whose knowledge is a prerequisite for a description of nuclei in terms of effective hadronic degrees of freedom. We discuss also the coupled-channel approach to the NN – NΔ system, and how it compares with relativistic treatments grounded on Quantum Field Theory. We then consider light nuclei, where the percentage of Δ components in the nuclear wave function, and Δ contributions to meson-exchange currents can be studied in a quantitative way, with a minimum of uncertainties due to nuclear-structure effects. Finally, we discuss Δ propagation in finite nuclei and nuclear matter. To this end, we try to give an update presentation of classical subjects, such as the effective Δ interaction in the nuclear environment, medium effects and quenching phenomena, where Δ -hole excitations and nuclear-structure effects are strictly intertwined.

A multichannel quasi-separable potential approach to nucleon-nucleus scattering

A quasi-separable potential model for two-body multichannel scattering is developed. Spin and Coulomb effects are taken into account. By a suitable choice of the separable nuclear interactions we arrive at simple analytic expressions for the transition amplitudes. Our model is applied to the study of the n-12C and p-12C scattering processes. Effects arising from the excitation of the target nucleus are well reproduced.

On the coupled-channel calculation of the optical potential with full inclusion of coupling effects

Abstract We develop a method for a coupled-channel calculation of the optical potential in which the multichannel Greens function is evaluated exactly. The quantum-mechanical coupled-channel problem is solved by expanding the multichannel interactions in terms of coupled sturmians. Closed-and open-channel effects are straightforwardly included by the use of energy-dependent basis functions. An application in the framework of a schematic multichannel model is developed.

Asymptotic properties of bound states in coupled quantum wave guides

We investigate the motion of bound-state poles in two quantum wave guides laterally coupled through a window. The imaginary momentum ik at the bound-state poles is studied as a function of the size a of the window. Both bound and virtual states appear as a spans the whole range from 0 up to +∞. We are able to find simple scaling laws relating the critical value of the window size at which the nth bound state appears to the number n of bound states, in the limit of large n. A similar relation is also provided for the slope and the second derivative of the pole trajectories in the (k, a) plane. These relations are characterized by an extremely high numerical accuracy. We also evaluate the exact value of the first two derivatives for a = 0.

Spin observables for thepd↔π+treaction around theΔresonance

The proton analyzing power Ay0 and the deuteron tensor analyzing power T20 are evaluated for the pd pi+ t process, in the energy region around and above the Delta resonance. These calculations extend a previous analysis of the excitation function and differential cross-section, based on a model embodying one-- and two-body p-wave absorption mechanisms and isobar excitation. The three-nucleon bound state and the pd scattering state are evaluated through Faddeev techniques for both the Bonn and Paris potentials. The spin variables exhibit a greater sensitivity to the number of included three-nucleon partial waves than the cross-sections, while the role played by the initial-- or final-state interactions appears to be small. The results for the tensor analyzing power at backward angles show a non-negligible dependence on the potentials employed, consistently with what has been previously found for the cross-sections. The calculation of spin observables gives a clear indication that other reaction mechanisms (presumably s-wave two-body absorption) have to be included in the model, in order to reproduce the experimental data below the Delta-resonance, in analogy with the simpler pp pi+ d process.

{pi}NNN-NNN problem: Connectedness, transition amplitudes, and quasiparticle approximation

In this paper we review the present status of the {pi}NNN-NNN problem. In particular, we reconsider the chain-labeled approach recently proposed by us, and identify a class of graphs, previously overlooked, which prevents the kernel of the corresponding {pi}NNN-NNN equations from being connected. We propose some approximate schemes, yielding connected-kernel equations. A generalization of the residue method allows us to relate the transition amplitudes for the coupled {pi}NNN-NNN system to the chain-labeled formalism. The quasiparticle approach is extended to the present situation, where emission/absorption of particles is allowed. The open problems for the {pi}NNN-NNN system in light of the present and of previous approaches are finally discussed. {copyright} {ital 1997} {ital The American Physical Society}

Spin observables for the pd pi+ t reaction around the a Delta resonance

The proton analyzing power Ay0 and the deuteron tensor analyzing power T20 are evaluated for the pd pi+ t process, in the energy region around and above the Delta resonance. These calculations extend a previous analysis of the excitation function and differential cross-section, based on a model embodying one-- and two-body p-wave absorption mechanisms and isobar excitation. The three-nucleon bound state and the pd scattering state are evaluated through Faddeev techniques for both the Bonn and Paris potentials. The spin variables exhibit a greater sensitivity to the number of included three-nucleon partial waves than the cross-sections, while the role played by the initial-- or final-state interactions appears to be small. The results for the tensor analyzing power at backward angles show a non-negligible dependence on the potentials employed, consistently with what has been previously found for the cross-sections. The calculation of spin observables gives a clear indication that other reaction mechanisms (presumably s-wave two-body absorption) have to be included in the model, in order to reproduce the experimental data below the Delta-resonance, in analogy with the simpler pp pi+ d process.

Theory of coupled pi -trinucleon systems.

We derive the dynamical equations which couple the four-body ([pi][ital NNN]) system to the underlying three-nucleon system. Our treatment can be considered the proper generalization of the Afnan-Blankleider equations for the coupled [ital NN]-[pi][ital NN] system. The resulting connected-kernel equations resemble in structure the Yakubovski[hacek i]-Grassberger-Sandhas equations for the standard four-body problem, but involve 24 chain-labeled components (rather than the usual 18 ones) and, within the scheme where the Hilbert space is truncated to states with at most one pion, allow for a consistent evaluation of reaction amplitudes involving [pi] absorption/production.

An Algebraic Approach to Multichannel Scattering by Negative-Energy Weinberg States

The single and multichannel scattering problem for elastic and inelastic collisions between two composite particles is solved by resorting to basis sets of negative-energy Sturmian functions referring to auxiliary potentials which allow an easy solution of the Sturmian eigenvalue equation. By means of these functions the original coupling potentials are approximated with finite-rank interactions. The coupled-channel equations can be then reduced to sets of algebraic linear equations which can be solved by standard matrix-inversion techniques. For illustrative purposes, our formalism is applied to the elastic neutron-alpha scattering. The results of these preliminary calculations are encouraging and show a fast convergence of the method in the whole energy region we have considered (0÷20 MeV).