The variation of $E(2_1^{+})$ of ${}^{134–140}\mathrm{Sn}$ calculated with empirical SMPN interaction has striking similarity with that of experimental $E(2_1^{+})$ of even-even ${}^{18–22}\mathrm{O}$ and ${}^{42–48}\mathrm{Ca}$, showing clearly that $N=84$–88 spectra exhibit the effect of gradually filling up the $\nu (2f_{7/2})$ orbital, which finally culminates in a new shell closure at $N=90$. Realistic two-body interaction CWG does not show this feature. Spin-tensor decomposition of SMPN and CWG interactions and variations of their components with valence neutron number reveals that the origin of the shell closure at ${}^{140}\mathrm{Sn}$ lies in the three-body effects. Calculations with CWG3M, which is obtained by including a simple three-body monopole term in the CWG interaction, predict decreasing $E(2_1^{+})$ for ${}^{136,138}\mathrm{Sn}$ and a shell closure at ${}^{140}\mathrm{Sn}$.

• Received 11 October 2009

DOI:https://doi.org/10.1103/PhysRevC.81.064328