R. van Wageningen

Variational calculations on a simple triton model using a complete hyperspherical function basis

Abstract Variational calculations which have been performed for the three-boson model of the triton are reported. The trial function is constructed using a denumerable, complete and orthonormal set of functions. Each of these functions is the product of a hyperspherical harmonic and a hyperradial function. This leads to a standard matrix eigenvalue problem. Various forms for the radial dependence of the two-particle interaction, with and without repulsion near the origin, and with and without a 1 r singularity in the origin, are investigated. Using a particular set of hyperspherical harmonics and introducing a new set of hyperradial functions, a considerable improvement is achieved compared with other calculations using hyperspherical function bases. Our results also compare favorably with those obtained using different methods or other types of trial functions. From this comparison and by investigating the convergence of the energy and of the trial function we find that the quality of the results ranges from excellent for the simplest interactions to acceptable for the more sophisticated ones. A few results of physical interest are given.

Analytic T matrices for Coulomb plus rational separable potentials

The l=0 partial wave projected Coulomb off‐shell T matrix Tc,l=0 in momentum representation is obtained in closed form. Problems existing in the literature concerning the half‐ and on‐shell behavior of Tc and Tc,l are discussed and clarified by means of explicit formulas. The remaining derivations in this paper are based on Tc,l=0. We consider the class of N‐term separable potentials where the form factors are rational functions of p2 (in momentum representation). We prove that the l=0 T matrix corresponding to the Coulomb potential plus any such so‐called rational separable potential has a very simple form, namely, it can be written in terms of rational functions and the (simple) hypergeometric function with parameters (1, iγ; 1+iγ), where γ is the well‐known Coulomb parameter. Explicit analytic formulas are derived for a number of simple members of the class, the Yamaguchi potential being one of them. In this particular case the expressions of Zachary and of Bajzer are reproduced who used a method based...

Potential Effects in Nucleon-Deuteron Scattering

Abstract Nucleon-deuteron elastic scattering and break-up cross sections have been calculated using many different S-wave rank one separable potentials. A correlation between the different results and the intrinsic strength of the interaction has been found. A proper treatment of the high energy repulsion improves agreement with experiments. The Coulomb interaction has been included in an approximate way.

Low-lying levels of 12C and the three-alpha particle model

Abstract Energies and wave functions are calculated for the 0 + ground state and the 2 + and 0 + excited states of a system of three structureless alpha particles. The results are compared with the experimental levels of the 12 C nucleus.

Calculations of the triton binding energy for Reid's soft-core nucleon-nucleon interaction☆

Abstract The triton energy ET has been calculated variationally for Reids soft-core potential. The L · S - term and the 1D2, 3D2 states contribute - 2 MeV and +0.2 MeV resp. The odd-state contribution is negligibly small. Our results are compared with those of other authors.

Nucleon-deuteron breakup quantities calculated with separable interactions including tensor forces and P-wave interactions

Abstract Nucleon-deuteron breakup calculations at a nucleon bombarding energy of 22.7 MeV have been performed with separable interactions including a tensor force and P-wave interactions. Differential cross sections and a selection of polarization quantities have been computed for special regions of the phase space. The influence of a tensor force and P-wave interactions on the differential cross section is of the order of 20 %. Large discrepancies between theory and experiment occur for the vector analyzing powers, both for the kinematically complete and for the incomplete situation. The calculations show that there are kinematical situations in which the differential cross sections and the tensor analyzing powers are sufficiently large to make measurements feasible.

Nucleon-nucleon interaction and triton binding energy

Abstract The Hulthen and the generalized Bargmann potential, which are both in a certain sense equivalent to the Yamaguchi separable two-nucleon interaction, are shown to give a rather different triton binding energy. The implications of this result are discussed.

The off-shell sensitivity of the nucleon-deuteron breakup reaction

Abstract Nucleon-deuteron breakup cross sections have been calculated using a number of phase equivalent S-wave nucleon-nucleon interactions. These interactions are of a separable type and have been obtained by solving an inverse scattering problem. With these interactions the off-shell sensitivity of the nucleon-deuteron breakup reaction has been investigated in various regions of the three-body phase space. The results are presented in the form of “generalized Phillips plots” in which the breakup cross sections are plotted as a function of the doublet scattering length. We find that at low projectile energies there exists in general a strong correlation between the break up cross sections and the doublet scattering length. At higher energies large deviations occur, especially in those regions of phase space where destructive interference between the various three-body amplitudes is present. It is concluded that at higher energies the breakup reaction can give additional information about the off-shell behaviour of the nucleon-nucleon interaction.

The number of bound states of the Coulomb plus Yamaguchi potential

It is shown that certain assertions on the number of bound states of a Coulomb plus Yamaguchi potential which Zachary [J. Math. Phys. 12, 1379 (1971); 14, 2018 (1973)] claims to have proved are incorrect. We prove that there are always infinitely many bound states if the Coulomb part of the potential is attractive and that, in case the Coulomb part of the potential is repulsive, there is one bound state only if the Yamaguchi potential is sufficiently attractive.

Square-well potential and three-nucleon bound-state properties

Abstract The fact that several three-nucleon bound-state properties calculated with square-well potentials are very close to the corresponding values for repulsive-core potentials, is attributed to the comparatively strong attraction at large distances.