Evolution of Nuclear Shells due to the Tensor Force

The monopole effect of the tensor force is presented, exhibiting how spherical single-particle energies are shifted as protons or neutrons occupy certain orbits. An analytic relation for such shifts is shown, and their general features are explained intuitively. Single-particle levels are shown to change in a systematic and robust way, by using the $\pi +\rho$ meson exchange tensor potential, consistently with the chiral perturbation idea. Several examples are compared with experiments.

Figure 1

(a) Schematic picture of the monopole interaction produced by the tensor force between a proton in $j_{>,<}=l\pm 1/2$ and a neutron in $j_{>,<}^{\prime }=l^{\prime }\pm 1/2$. (b) Exchange processes contributing to the monopole interaction of the tensor force.

Figure 2

Intuitive picture of the tensor force acting two nucleons on orbits $j$ and $j^{\prime }$.

Figure 3

Triplet-even potential due to the tensor force for various interaction models.

Figure 4

Proton (neutron) ESPE as a function of $N$ ($Z$). Lines in (a)–(c) show the change of ESPE’s calculated from the $\pi +\rho$ tensor force. Points represent the corresponding experimental data. (a) Proton ESPE’s in Ca isotopes relative to $1{\mathrm{d}}_{3/2}$. Points are from 13. (b) Proton ESPE’s in Ni isotopes; calculations only. See 19 for related experimental data. (c) Neutron ESPE’s in $N=51$ isotones relative to $2d_{5/2}$; points are from 21. (d) Proton ESPE’s in Sb isotopes; points are from 18. Lines include a common shift of ESPE as well as the tensor effect (see the text).