Nuclear structure anomalies arising from the use of Bonn interactions and possible resolutions

Although the tensor interaction in the first order does not affect the single-particle splitting for closed LS shell nuclei, e.g., ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, it causes the j=l-1/2 member of a spin-orbit pair to come towards or even below the j=l+1/2 member for an open shell. With the bare Bonn A interaction, the splitting ${\mathrm{\epsilon }}_{\mathit{p}1/2}$-${\mathrm{\epsilon }}_{\mathit{p}3/2}$ is 4.2 MeV for an ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ core but is -3.0 MeV for a closed ${\mathit{p}}_{3/2}$ core of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. In large space shell-model calculations, this single-particle energy inversion leads to too high an occupancy of the ${\mathit{p}}_{1/2}$ orbit and pushes the wave functions of the low-lying states too much towards the LS limit. This manifests itself in too low a magnetic dipole transition rate from the ground state ($0_1^{+}$) to the $1_1^{+}$, T=1 state. Various mechanisms are investigated in attempts to cure this problem including the relativistic effects of the Dirac-Brueckner-Hartree-Fock approach, also the effects of core polarization on the effective interaction and finally the effects of changing the meson masses in the nuclear medium as parametrized in the Hosaka-Toki interaction. The Dirac effects tend to increase the spin-orbit interaction while the change of the meson masses yields a weaker effective tensor force. Both effects improve the results of the nuclear structure calculations. The core polarization graphs involving phonon exchange also improve the results but other graphs, e.g., particle-particle ladders and hole-hole diagrams work in the opposite direction.