Novel Features of Nuclear Forces and Shell Evolution in Exotic Nuclei

Novel simple properties of the monopole component of effective nucleon-nucleon interactions are presented, leading to the so-called monopole-based universal interaction. Shell structures are shown to change as functions of $N$ and $Z$, consistent with experiments. Some key cases of this shell evolution are discussed, clarifying the effects of central and tensor forces. The validity of the present tensor force is examined in terms of the low-momentum interaction $V_{\mathrm{lowk}}$ and the $Q_{\mathrm{box}}$ formalism.

Figure 1

Monopole matrix elements of various forces for (a)–(d) $pf$ and (e)–(h) $sd$ shells. In (b),(d),(f),(h), the tensor-force effect is subtracted from the others, and results from a Gaussian central force are shown.

Figure 2

Diagrams for the $V_{\mathrm{MU}}$ interaction.

Figure 3

Single-particle energies calculated by $V_{\mathrm{MU}}$ interaction. The dashed lines are obtained by the central force only, while the solid lines include both the central force and the tensor force. Some states, e.g. $f_{7/2}$ in (b), are hole states.

Figure 4

Tensor forces in AV8’ interacton, in low-momentum interactions obtained from AV8’, and in the third-order $Q_{\mathrm{box}}$ interaction for (a) $T=0$ and (b) $T=1$.