Unveiling the intruder deformed 0$^+_2$ state in $^{34}$Si
Résumé
The 0$^+_2$ state in $^{34}$Si has been populated at the {\sc Ganil/Lise3} facility through the $\beta$-decay of a newly discovered 1$^+$ isomer in $^{34}$Al of 26(1)~ms half-life. The simultaneous detection of $e^+e^-$ pairs allowed the determination of the excitation energy E(0$^+_2$)=2719(3)~keV and the half-life T$_{1/2}$=19.4(7)~ns, from which an electric monopole strength of $\rho^2$(E0)=13.0(0.9)$\times$10$^{-3}$ was deduced. The 2$^+_1$ state is observed to decay both to the 0$^+_1$ ground state and to the newly observed 0$^+_2$ state (via a 607(2)~keV transition) with a ratio R(2$^+_1$$\rightarrow$0$^+_1$/2$^+_1$$\rightarrow$0$^+_2$)=1380(717). Gathering all information, a weak mixing with the 0$^+_1$ and a large deformation parameter of $\beta$=0.29(4) are found for the 0$^+_2$ state, in good agreement with shell model calculations using a new {\sc sdpf-u-mix} interaction allowing \textit{np-nh} excitations across the $N=20$ shell gap.
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