Structure of the Lightest Tin Isotopes

We link the structure of nuclei around ${}^{100}\mathrm{Sn}$, the heaviest doubly magic nucleus with equal neutron and proton numbers ($N=Z=50$), to nucleon-nucleon ($NN$) and three-nucleon ($NNN$) forces constrained by data of few-nucleon systems. Our results indicate that ${}^{100}\mathrm{Sn}$ is doubly magic, and we predict its quadrupole collectivity. We present precise computations of ${}^{101}\mathrm{Sn}$ based on three-particle–two-hole excitations of ${}^{100}\mathrm{Sn}$, and we find that one interaction accurately reproduces the small splitting between the lowest $J^{\pi }=7/2^{+}$ and $5/2^{+}$ states.

Figure 1

Ground-state energies per nucleon $E/A$ for selected closed-shell nuclei computed with the closed-shell IMSRG [38] using the interactions of Ref. [45] in comparison with experiment (black horizontal lines).

Figure 2

Panel (a) shows low-lying states in ${}^{100}\mathrm{Sn}$ computed with the chiral interaction $1.8/2.0(\mathrm{EM})$ in the EOM-CCSD and EOM-CCSD(T) approximations and compared to LSSM calculations based on phenomenological interactions [6]. Panel (b) shows the EOM-CCSD results for the $B(E2)$ transition strength in ${}^{100}\mathrm{Sn}$ with the interactions as indicated, and the experimental data for all other even tin isotopes. The full (dashed) line is taken from LSSM as reported in Ref. [6] (Ref. [12]). Panel (c) shows the energy of the $J^{\pi }=2_1^{+}$ states in even tin isotopes, with coupled-cluster results for ${}^{100,102}\mathrm{Sn}$ [labeled as in panel (b)] and VS-IMSRG results for ${}^{100-110}\mathrm{Sn}$ with interactions as indicated, and data for ${}^{102-132}\mathrm{Sn}$ (black circles). The shapes illustrate the absence or presence of collectivity.

Figure 3

Panel (a) shows the energy splitting between the lowest $J^{\pi }={7/2}^{+}$ and ${5/2}^{+}$ states in light odd-mass tin isotopes. Data are black circles for isotopes with definite (full) and tentative spin assignments (open symbols). Theoretical results are from coupled cluster (full) and VS-IMSRG (open symbols) for the interactions as indicated. Panel (b) shows the correlation between the neutron separation energy $S_n$ and the energy splitting between the lowest $J^{\pi }={7/2}^{+}$ and ${5/2}^{+}$ states for the interactions and computational method as labeled (symbols with error bars and an encompassing blue uncertainty band) compared to data (vertical and horizontal green lines). Panel (c) shows the low-lying levels in ${}^{101}\mathrm{Sn}$ based on the chiral interaction $1.8/2.0(\mathrm{EM})$ computed with various coupled-cluster equation-of-motion (EOM) methods, the VS-IMSRG, and compared to data.

Figure 4

Ground and first excited states in ${}^{101}\mathrm{Sn}$ and ${}^{105}\mathrm{Te}$ obtained in VS-IMSRG for the $1.8/2.0(\mathrm{EM})$ and $2.0/2.0(\mathrm{EM})$ interactions, with spins $J^{\pi }=5/2^{+}$ (red) and $J^{\pi }=7/2^{+}$ (black).