Abstract
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 $\ensuremath{\nu}(2{f}_{7/2})$ 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 $^{140}\mathrm{Sn}$.
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