We report on a quantitative study of the evolution of the nuclear shell structure, in particular, effective single-particle energies (ESPEs), based on the spin-tensor decomposition of an effective two-body shell-model interaction. While the global trend of the ESPEs is mainly due to the central term of the effective interaction, variations of shell gaps invoke various components of the in-medium NN force. From a detailed analysis of a well-fitted realistic interaction in the sdpf shell-model space, two most important contributions for the evolution of the N = 20 and N = 28 shell gaps are confirmed to be the central term and the tensor term. The role of the latter is dominant to explain the energy shift of spin-orbit partners. Spin-tensor analysis of microscopic effective interactions in sd, pf, and gds shell-model spaces, contrasted with that of the phenomenologically adjusted ones, shows no evidence of amplification of the tensor component contribution; however, it points toward the neglect of three-body forces in the present microscopic interactions
