New lifetime measurement for the $2_1^{+}$ level in ${}^{112}\mathrm{Sn}$ by the Doppler-shift attenuation method

Levels in the ${}^{112}\mathrm{Sn}$ nucleus have been excited by inelastic scattering with ${}^{35}\mathrm{Cl}$ projectile at $E_{\mathrm{lab}}=195\mathrm{MeV}$. The Doppler affected $\gamma$-ray peak arising from the decay of the $2_1^{+}$ level has been analyzed, using updated methodologies, to extract the level lifetime and corresponding electric quadrupole ($E2$) transition probability, $B(E2;0_{\mathrm{g}.\mathrm{s}.}^{+}\to 2_1^{+})$. The present result is discrepant with respect to the results reported from existing lifetime measurements, but in compliance with independent systematic measurements of the low-lying $E2$ transition strengths in the stable even-mass Sn isotopes, by pure Coulomb excitation as well as heavy-ion induced inelastic collisions. The transition probability also confirms an enhancement in collectivity for the $2_1^{+}$ level, and is found to be in good agreement with generalized seniority model (GSM) as well as state-of-the-art Monte Carlo shell model (MCSM) calculations. Within the realm of the MCSM scheme, the enhancement is understood in terms of oblate deformations for both the $0_{\mathrm{g}.\mathrm{s}.}^{+}$ and $2_1^{+}$ states in ${}^{112}\mathrm{Sn}$ arising due to strong proton-core excitations and enhanced proton-neutron interactions. In addition, limits for the lifetime of the $3_1^{-}$ level and the $E1$ transition probability, $B(E1;3_1^{-}\to 2_1^{+})$, have been obtained.

Figure 1

Experimental $\gamma$-ray spectrum showing transitions in ${}^{112}\mathrm{Sn}$ in coincidence with the $2_1^{+}\to 0_{\mathrm{g}.\mathrm{s}.}^{+}$ transition. Various $\gamma$ rays of ${}^{112}\mathrm{Sn}$, namely, (a) 76 keV, (b) 263 keV, (c) 302 keV, (d) 378 keV, (e) 510 keV (509 keV as seen in Ref. [31], with some admixture from the 511 keV annihilation $\gamma$ ray), (f) 664 keV, (g) 805 keV, (h) 894 keV, (i) 934 keV, (j) 991 keV, (k) 1097 keV, (l) 1264 keV, and (m) 1278 keV, which were also observed in previous measurements on neutron scattering [31] and/or fusion-evaporation [37], have been marked in the spectrum. The $2_1^{+}$ state is fed through such parallel decay paths, marked with different colors. The $3_1^{-}\to 2_1^{+}$ transition is seen with a Doppler broadened line shape, unlike the other stopped peaks.

Figure 2

Experimental Doppler broadened $\gamma$-ray peak of the 1097-keV ($3_1^{-}\to 2_1^{+}$) transition in ${}^{112}\mathrm{Sn}$ spectra gated with the $2_1^{+}\to 0_{\mathrm{g}.\mathrm{s}.}^{+}$ transition (gated from below), and corresponding fits obtained using the lineshape code. The dashed lines represent deconvoluted fit of the additional stopped peaks in the fitting range (please see text for details). The dotted lines represent the exclusive transition line shape, while the solid lines show the total fit.

Figure 3

Experimental Doppler broadened $\gamma$-ray peak of the 1257-keV ($2_1^{+}\to 0_{\mathrm{g}.\mathrm{s}.}^{+}$) transition in ${}^{112}\mathrm{Sn}$ spectra gated with the $3_1^{-}\to 2_1^{+}$ transition (gated from above), and corresponding fits obtained using the lineshape code. The dashed lines represent deconvoluted fit of the additional stopped peaks in the fitting range (please see text for details). The dotted lines represent the exclusive transition line shape, while the solid lines show the total fit.

Figure 4

Typical calculated relative population distribution of the scattered ${}^{112}\mathrm{Sn}$ recoils in their $3_1^{-}$ excited state as a function of laboratory scattering angle ${\theta }_{\mathrm{rec}}^{\mathrm{LAB}}$ and kinetic energy $E_{\mathrm{rec}}$, in the ${}^{35}\mathrm{Cl}+{}^{112}\mathrm{Sn}$ system at $E_{\mathrm{lab}}=195\mathrm{MeV}$.

Figure 5

Systematic plot of $B(E2;0_{\mathrm{g}.\mathrm{s}.}^{+}\to 2_1^{+})$ values for the stable even-mass Sn isotopes using the data obtained from several recent measurements [4, 5, 11, 13, 14, 28, 34], and the one from the present measurement for the ${}^{112}\mathrm{Sn}$ isotope. The dashed and solid lines represent the GSM [23] and the MCSM [26] calculations, respectively.

Figure 6

$T$ plot of the $0_{\mathrm{g}.\mathrm{s}.}^{+}$ state in ${}^{112}\mathrm{Sn}$ coordinated by the intrinsic moments, $Q_0$ and $Q_2$.

Figure 7

$T$ plot of the $2_1^{+}$ state in ${}^{112}\mathrm{Sn}$ coordinated by the intrinsic moments, $Q_0$ and $Q_2$.