A. Kievsky

A High-precision variational approach to three- and four-nucleon bound and zero-energy scattering states

The hyperspherical harmonic (HH) method has been widely applied in recent times to the study of the bound states, using the Rayleigh–Ritz variational principle, and of low-energy scattering processes, using the Kohn variational principle, of A = 3 and 4 nuclear systems. When the wavefunction of the system is expanded over a sufficiently large set of HH basis functions, containing or not correlation factors, quite accurate results can be obtained for the observables of interest. In this review, the main aspects of the method are discussed together with its application to the A = 3 and 4 nuclear bound and zero-energy scattering states. Results for a variety of nucleon–nucleon (NN) and three-nucleon (3N) local or non-local interactions are reported. In particular, NN and 3N interactions derived in the framework of the chiral effective field theory and NN potentials from which the high-momentum components have been removed, as recently presented in the literature, are considered for the first time within the context of the HH method. The purpose of this review is twofold. The first is to present a complete description of the HH method for bound and scattering states, also including detailed formulae for the computation of the matrix elements of the NN and 3N interactions. The second is to report accurate results for bound and zero-energy scattering states obtained with the most commonly used interaction models. These results can be useful for comparison with those obtained by other techniques and are a significant test for different future approaches to such problems.

Critical comparison of experimental data and theoretical predictions for N-d scattering below the breakup threshold

Abstract The theoretical approaches for studying N-d processes using realistic, semi-phenomenological NN potentials have matured considerably during the last few years. Accurate calculations of scattering observables are now feasible. Recently, high-quality measurements of N-d scattering at energies below the deuteron breakup threshold became available. Therefore, a detailed comparison between theory and experimental data can now be performed. In this paper the various sets of experimental data for the N-d differential cross section, and the vector and tensor analyzing powers are examined in a critical way in the incident nucleon energy range from 1 to 3 MeV. In order to identify possible inadequacies of the interaction models adopted, phase-shift analyses were performed and compared to the theoretical parameters.

Polarization observables in p - d scattering below 30-MeV

Differential and total breakup cross sections as well as vector and tensor analyzing powers for

Study of bound and scattering states in three-nucleon systems

p\ensuremath{-}d

The three-nucleon bound state with realistic soft- and hard-core potentials

scattering are studied for energies above the deuteron breakup threshold up to

Variational description of the helium trimer using correlated hyperspherical harmonic basis functions

{E}_{\mathrm{lab}}=28 \mathrm{MeV}.

Calculation of the alpha-particle ground state within the hyperspherical harmonic basis

The

Phenomenological spin orbit three-body force

p\ensuremath{-}d

Neutron H-3 and proton He-3 zero energy scattering

scattering wave function is expanded in terms of the correlated hyperspherical harmonic basis and the elastic S matrix is obtained using the Kohn variational principle in its complex form. The effects of the Coulomb interaction, which are expected to be important in this energy range, have been rigorously taken into account. The Argonne AV18 interaction and the Urbana URIX three-nucleon potential have been used to perform a comparison to the available experimental data.

Spectra of helium clusters with up to six atoms using soft-core potentials

Abstract A variational technique to describe the ground state and scattering states below the break-up threshold for a three-nucleon system is developed. The method consists in expanding the wave function in terms of correlated harmonic hyperspherical functions suitable to handle the large repulsion contained in the nuclear potential at short distances; three-body forces have also been considered. The inclusion of the pp Coulomb repulsion in the p-d processes does not cause any particular problem, since no partial wave decomposition of the interaction is performed. Accurate numerical results are given for ground state properties and scattering lengths, phase shifts and mixing parameters at three different energies of the incident nucleon. The agreement with other available results and with experimental analyses is highly satisfactory.