Coulomb Excitation of ${}^{104}\mathrm{Sn}$ and the Strength of the ${}^{100}\mathrm{Sn}$ Shell Closure

A measurement of the reduced transition probability for the excitation of the ground state to the first $2^{+}$ state in ${}^{104}\mathrm{Sn}$ has been performed using relativistic Coulomb excitation at GSI. ${}^{104}\mathrm{Sn}$ is the lightest isotope in the Sn chain for which this quantity has been measured. The result is a key point in the discussion of the evolution of nuclear structure in the proximity of the doubly magic nucleus ${}^{100}\mathrm{Sn}$. The value $B(E2;0^{+}\to 2^{+})=0.10(4)$ $e^2{b}^2$ is significantly lower than earlier results for ${}^{106}\mathrm{Sn}$ and heavier isotopes. The result is well reproduced by shell model predictions and therefore indicates a robust $N=Z=50$ shell closure.

Figure 1

Identification plot for the ${}^{104}\mathrm{Sn}$ secondary beam. The $x$ axis is the $A/Q$, where $A$ is the mass and $Q$ is the charge of the nuclei, obtained from a time of flight measurement, and the $y$ axis is the nuclear charge $Z$, obtained from a $\Delta E$ measurement.

Figure 2

$\Delta E-E$ plot for the ions after the ${}^{197}\mathrm{Au}$ target. The $x$ axis is the total energy deposited in the LYCCA CsI, and the $y$ axis is the energy loss in the LYCCA DSSSD.

Figure 3

Doppler corrected energy spectra for ${}^{104}\mathrm{Sn}$ (upper panel), and for ${}^{112}\mathrm{Sn}$ (lower panel). The $E2$ transition of interest is visible at 1260 and 1257 keV for ${}^{104}\mathrm{Sn}$ and ${}^{112}\mathrm{Sn}$, respectively. The dashed line represents an extrapolation of the background used in the analysis.

Figure 4

Experimental $B(E2;0^{+}\to 2^{+})$ values for ${}^{104–114}\mathrm{Sn}$ from Coulomb excitation and LSSM results for ${}^{100–114}\mathrm{Sn}$. The data were measured at REX-ISOLDE [10, 12], MSU [11], GSI-DSA [29], IUAC [28], GSI [9, 45], and in the study for this Letter. The ${}^{112}\mathrm{Sn}$ reference point is taken from Ref. 28, the ${}^{114}\mathrm{Sn}$ value from Ref. 45 and compared to data from Doppler line shape analysis [29]. LSSM results with a ${}^{80}\mathrm{Zr}$ core are shown for truncation $t_{\pi }=4$, $t_{\nu }=2$ and seniority truncation for neutrons in ${}^{100–106}\mathrm{Sn}$ (solid red line). LSSM calculations for ${}^{102–114}\mathrm{Sn}$ with a ${}^{90}\mathrm{Zr}$ core (dashed blue line) are taken from Ref. 9. The shaded bar represents the averaged value for ${}^{106–114}\mathrm{Sn}$ Coulomb excitation data.