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The level structure of neutron rich $^{93,94,95}$Sr were studied via the \dtsr{94,95,96}, one neutron pickup reactions at TRIUMF. Excited states were populated when $^{94,95,96}$Sr beams of 5.5 AMeV bombarded a 0.5 mg/cm$^2$ CD$_2$ target. The de-exciting $\gamma$-rays and outgoing charged particles were detected by using the TIGRESS and SHARC arrays, respectively. The level scheme was contructed by using both E$_x$ vs E$_{\gamma}$ and E$_{\gamma}$ vs E$_{\gamma}$ matrices. Three excited states were observed in $^{93}$Sr and $^{95}$Sr, respectively. A total of ten excited states were observed in $^{94}$Sr of which four states were newly identified in the present experiment. Angular distribution measurements suggest spin and parity assignments for the 1880 (0$^+$), 2294 (0$^+$) and 2415 (3$^+$) keV levels and constrain the other five levels 2615, 2705, 2921, 3077 and 3175 keV in $^{94}$Sr. In this work no $\gamma$-ray transitions were observed from the 1880 and 2294 keV levels directly to the ground state. This is consistent with spin and parity assignments of the 1880 and 2294 keV levels as 0$^+$. The spectroscopic factors were calculated by fitting DWBA calculations to experimental angular distribution data and taking into consideration $\gamma$-decay branching ratios. Shell model calculations were carried out to understand the present experimental observations by using updated interaction and appropriate truncation schemes. The calculation was performed by using an updated NuShellX code and $glek$ interaction. The single-particle energies of the interaction were adjusted in such a way that the calculated and experimentally observed energy levels were in good agreement in the $N$ $\sim$ 56 and $Z$ $\sim$ 38 region. In the present calculations the valence [$1d_{5/2}$], [$2s_{1/2}$], [$1d_{3/2}$] and [$0g_{7/2}$] orbitals were included for neutrons outside the $N$ = 50 inert core. The proton degrees of freedom were varied systematically so that the effect of the proton valence space on the calculated levels could be studied. The calculated energy levels and spectroscopic factors that were predicted are in reasonable agreement with the experimental findings. This suggests that the low-energy states are predominantly neutron configurations with minor contributions from excitations between the proton [$1p_{3/2}$] and [$1p_{1/2}$] orbitals.