Alpha decay studies near $^{100}$Sn

Nuclei around the exotic doubly-magic $^{100}$Sn can provide key information to, and serve as rigorous tests of, the nuclear shell model. In particular, the energy splitting between neutron single-particle orbits in this region, the $\nu d_{5/2}$ - $\nu g_{7/2}$, can be extracted from the low-energy excited states in the odd-N Sn isotopes, ideally from $^{101}$Sn. Identification and examination of these nuclei is aided by the presence of an island of alpha and proton radioactivity for nuclei with Z $>$ 50 near $^{100}$Sn. The isotopes $^{109}$Xe and $^{105}$Te were identified at the Holifield Radioactive Ion Beam Facility using the Recoil Mass Spectrometer through the observation of the characteristic alpha decay chain $^{109}$Xe $\rightarrow$ $^{105}$Te $\rightarrow$ $^{101}$Sn. The efficient identification of the fast $^{105}$Te alpha decay was enabled through the use of digital signal processing using advanced pulse shape analysis alogrithms. The unique double alpha decay pulse provided an ideal tag to observe gamma-ray emission from the excited states of both $^{105}$Te and $^{101}$Sn at approximately 150 and 172 keV, respectively. Both excited states in $^{105}$Te and $^{101}$Sn were populated through alpha decay. The observation of the first excited state in $^{101}$Sn provides the $\nu d_{5/2}$ - $\nu g_{7/2}$ energy splitting. Using the experimental value in shell model calculations suggests an ordering of single particle states in $^{101}$Sn that contradicts previous expectations. The possibility of reaching the $^{108}$Xe $\rightarrow$ $^{104}$Te $\rightarrow$ $^{100}$Sn alpha decay chain will also be discussed.