Collectivity of the 2p-2h proton intruder band of ${}^{116}\mathrm{Sn}$

The half-life of the $4_2^{+}$ state of the $2\mathrm{p}-2\mathrm{h}$ proton intruder band of ${}^{116}\mathrm{Sn}$ has been measured with the fast-timing technique. The lifetime of $T_{1/2}=29\left(10\right)$ ps leads to a transition probability $B\left(E2;4_2^{+}\to 2_2^{+}\right)=40\left(13\right)$ Weisskopf units, which is in very good agreement with the large $B\left(E2;2_2^{+}\to 0_3^{+}\right)$ value measured previously and provides strong support for the $0_3^{+}$ state as the bandhead of the intruder configuration and for the shape coexistence in the semimagic ${}^{116}\mathrm{Sn}$ nucleus. IBM-2 calculations with mixing reproduce the experimental data very well, giving insight into the degree of mixing between the different states.

Figure 1

Systematics of the Sn isotopes showing the half-lives or the limits of half-lives of the $0_2^{+}$ (red), $0_3^{+}$ (blue), and $4_2^{+}$ (green) states. The half-lives are taken from Refs. [36, 37] and from this work.

Figure 2

The projections of the FIPPS Ge and the fast-timing ${\mathrm{LaBr}}_3\gamma$-ray spectra from triple-$\gamma \gamma \gamma$ coincidences of the ${}^{115}\mathrm{Sn}(n_{\mathrm{th}},\gamma ){}^{116}\mathrm{Sn}$ reaction. While the Ge spectrum is generated using the ${\mathrm{LaBr}}_3-\mathrm{Ge}$-Ge events, the ${\mathrm{LaBr}}_3$ spectrum is from the fast-timing ${\mathrm{LaBr}}_3-{\mathrm{LaBr}}_3-\mathrm{Ge}$ events. The Ge spectrum is scaled by a factor of 0.5 for illustrative comparison with the ${\mathrm{LaBr}}_3$ spectrum.

Figure 3

The mirror-symmetric mean time-walk characteristics of the FIPPS fast-timing array with 16 ${\mathrm{LaBr}}_3$ detectors.

Figure 4

Doubly gated Ge and ${\mathrm{LaBr}}_3$ coincidence spectra generated using gates as indicated and illustration of the determination of the relative full-energy peak to Compton-background ratio, P/B. The spectra were derived from triple Ge-${\mathrm{LaBr}}_3-\mathrm{Ge}$ and respective Ge-${\mathrm{LaBr}}_3-{\mathrm{LaBr}}_3$ coincidences with a coincidence window of 250 ns.

Figure 5

The experimental time distribution of the $0_3^{+}$ state of ${}^{116}\mathrm{Sn}$ using the 1201–734-keV $\gamma -\gamma$ cascade and the following 1293-keV $\gamma$ ray employing the FIPPS Ge detectors as a trigger. The data are time-walk corrected and the reference time is $t_0=0$. The experimental centroid is determined using Eq. (1) and is indicated by the vertical line. The results are discussed in the text.

Figure 6

Interpolation of the time response $C_{\mathrm{BG}}$ of the Compton background at $E_{\mathrm{decay}}=734$ keV (upper panel) and at $E_{\mathrm{feeder}}=1201$ keV (lower panel). The data are corrected for the time walk as derived from Fig. 3 and are fitted using a second-order polynomial. The green lines represent the 1 $\sigma$ uncertainty bands obtained by analyzing the correlation matrices.

Figure 7

Doubly gated coincidence $\gamma$-ray spectra generated to investigate the quality of the spectrum around the 467-keV FEP and the peak-to-background ratio (P/B) of the ${\mathrm{LaBr}}_3$ spectrum.

Figure 8

The Ge(2112 keV)-triggered time-difference distribution between the 467- and 417-keV transitions feeding and and deexciting the $4_2^{+}$ state of ${}^{116}\mathrm{Sn}$. The result is time-walk-corrected relative to $t_0=0$.

Figure 9

Comparison of the absolute $B\left(E2\right)$ transition probabilities of the normal and intruder configurations identified experimentally in ${}^{116}\mathrm{Sn}$ with the predictions of the $sd$ IBM-2 with mixing. Additional low-spin states are shown up to 3 MeV. The experimental data were taken from Refs. [33, 34, 36]. The transitions deexciting the experimental $6_1^{+}$ state are drawn with gray color to emphasize that only the $\gamma$-ray branching ratio is measured, not the absolute $B\left(E2\right)$ values as in the case of the other transitions.