After an overview of actual possibilities of standard Shell Model calculations, we will focus on correlations and cross shell excitations in the isotopic chains of Silicon, Nickel and Tin.
Emphasis will be put on E2 response, for the description of the most exotic isotopes in the vicinity of 42Si, 78Ni and 132Sn.
Shell evolution far from stability at N=28, N=50 and N=82, as well as
connections with tensor components of the effective interaction
will be discussed.
In particular, we will report on the results of a quantitive analysis of the role played by different components of the in-medium NN interaction in the shell evolution.
Based on the analysis of a well-fitted realistic interaction in $sdpf$ shell model space,
we reveal the role played by the different terms in the variation
of the N=16, N=20$ and N=28 shell gaps in neutron-rich nuclei. We will discuss some other regions of the nuclear chart and compare with available data. Finally, comparison of the spin-tensor content of the microscopically derived effective interaction and a well-adjusted one can shed light on the renormalization procedure and the effect expected from the three-nucleon interaction.