Experimental System to Study the $\alpha$ Decay of $^{178}$Hf$^{m2}$

The nuclide $^{178}$Hf possesses a second isomer that is notable in its spin (I$^{\pi }$ = 16$^{+})$, lifetime (T$_{1/2}$~=~31 years) and excitation energy (E$_{m}$ = 2.446 MeV). It is this high excitation energy that permits $\alpha $ decay of the nucleus from the isomeric state, although the $^{178}$Hf nuclide is stable in its ground state. The $\alpha $ decay was detected (PRC 75, 057301, 2007) through the use of a track detector and the associated half-life was deduced to be (2.5 \underline {+} 0.5) $\times $ 10$^{10}$ years, compared with the previously-known half-life for IT decay of 31 years. The most probable decay sequence was predicted to be $\alpha $ decay with E$_{\alpha }$ = 3.91 MeV to the I$^{\pi }$ = 6$^{+}$ member of the $^{174}$Yb ground-state band. However, so far no spectroscopic study of this rare decay has been performed. An experimental system to accomplish this has been constructed using a silicon surface barrier (SSB) charged-particle detector and a high purity Germanium (HPGe) $\gamma $ detector, with the aim of recording both $\alpha $ decays and $\alpha -\gamma $ coincidences. The experimental design, instrumentation and preliminary testing will be discussed.