Comparison of Pauli projection and supersymetric transformation methods for three-body nuclear structure and reactions

Abstract

Three-body Faddeev-type equations for bound, resonant, and scattering states in the systems of nuclear core and two nucleons are solved using the momentum-space framework. Two approaches for eliminating the Pauli-forbidden deeply-bound states are compared, projecting out those states by a nonlocal term in the potential, and by a supersymmetric transformation of the potential. While the former method is preferred by the experimental data for the deuteron-${}^4${He} scattering, the results for bound and resonant states do not indicate a clear superiority of a single method. Instead, systematic differences between them are found.

Figures (6)

• Figure 1: (Color online) The differential cross section and deuteron vector analyzing power $iT_{11}$ for the deuteron-${}^{4}\mathrm{He}$ elastic scattering at 17 MeV deuteron beam energy as functions of the c.m. scattering angle. Results of PP (solid curves), SS (dashed-dotted curves), and RC (dotted curves) models are compared. The experimental data are from Ref. gruebler:79a.
• Figure 2: (Color online) The fully exclusive differential cross section for the deuteron breakup in collision with the 15 MeV ${}^{4}\mathrm{He}$ nucleus. It is shown as a function of the arclength $S$ along the kinematical curve in a coplanar kinematical configuration with 17.1 and 50.5 deg polar angles of ${}^{4}\mathrm{He}$ and proton, respectively, and with 180 deg difference in their azimuthal angles. Curves are as in Fig. , and the experimental data are taken from Ref. koersner:77.
• Figure 3: (Color online) The semi-inclusive differential cross section for the ${}^{4}\mathrm{He}(d,p)$ reaction at 7.5 and 20 MeV deuteron beam energies as a function of the proton scattering angle in the c.m. frame. Curves are as in Fig. .
• Figure 4: (Color online) Ground-state binding energy of ${}^{19}\mathrm{B}$, ${}^{11}\mathrm{Li}$, ${}^{20}\mathrm{C}$, ${}^{16}\mathrm{C}$, and ${}^{18}\mathrm{O}$ nuclei, calculated including different number of angular momentum states. The predictions of SS and PP models are compared. The lines are for guiding the eye only.
• Figure 5: (Color online) Kinetic energy expectation value for ground state of ${}^{11}\mathrm{Li}$ and ${}^{16}\mathrm{C}$ nuclei, calculated including different number of angular momentum states. The predictions of SS and PP models are compared. The lines are for guiding the eye only.