Rearrangement terms

For density-dependent terms, the total energy obtained from the proton and neutron eigenvalues $\epsilon_i^{p,n}$ and kinetic energies $T^{p,n}$

$$E=\frac{1}{2}\left(T^{p}+T^{n}\right)+\frac{1}{2}\sum_{i}\left(\epsilon_{i}^{p}+\epsilon_{i}^{n}\right)+E_{RR}$$ (64)

includes the additional rearrangement term

$$E_{RR}=\frac{1}{2}\left(T^{p}+T^{n}\right)-\frac{1}{2}\sum_{... ...lon_{i}^{n}\right) +\int {\rm d}^3\vec{r}\, {\cal H}(\vec{r}).$$ (65)

For spherical symmetry the terms with density-dependent coupling constants in the Skyrme functional only involve the $\rho_\tau$ densities and for these a straightforward derivation gives

$$E_{RR}=-\frac{1}{2}\int {\rm d}^3\vec{r}\, \left(\frac{\part... ...\partial {\cal H}}{\partial\rho_{1}}\rho_{1}-2{\cal H}\right).$$ (66)