We review the recent application of the so-called finite range simple effective interaction (SEI)
to study the Ni and Cu isotopes with neutron numbers $N=40$ to $N=50$.
Recent experiments performed in neutron-rich Cu isotopes have revealed a crossing between the
$3/2^-$ and $5/2^-$ spin-parity of the ground state and first excited state in $^{75}$Cu.
In contrast to the common situation with Skyrme and other effective forces, where a tensor
interaction needs to be added to account for this crossing and the crossing of the 2$p_{3/2}$ and 1$f_{5/2}$ proton
single-particle levels in Ni isotopes, we find that SEI can reproduce the experimental crossing
without the necessity of adding a tensor interaction.
We also study with SEI the correlation of the charge radii differences in mirror nuclei pairs with the neutron skin thickness
and with the slope $L$ of the symmetry energy.
By comparing the SEI predictions with the measured charge radii difference in four mirror pairs
and with the NICER astrophysical constraint for the radius of 1.4\,M$_{\odot}$ neutron stars,
we obtain the constraint $L\approx70$--100 MeV.
This range for $L$ is discussed in light of the recent PREX-2 and CREX data on the neutron skin thickness.