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The first ever search for $alpha$ decays to the first excited state in Yb was performed for six isotopes of hafnium (174, 176, 177, 178, 179, 180) using a high purity Hf-sample of natural isotopic abundance with a mass of 179.8 g. For $^{179}$Hf, also $alpha$ decay to the ground state of $^{175}$Yb was searched for thanks to the $beta$-instability of the daughter nuclide $^{175}$Yb. The measurements were conducted using an ultra low-background HPGe-detector system located 225 m underground. After 75 d of data taking no decays were detected but lower bounds for the half-lives of the decays were derived on the level of $lim T_{1/2}sim 10^{15}-10^{18}$~a. The decay with the shortest half-life based on theoretical calculation is the decay of $^{174}$Hf to the first $2^+$ 84.3~keV excited level of $^{170}$Yb. The experimental lower bound was found to be $T_{1/2}geq 3.3times 10^{15}$ a.
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A search for $alpha$ decay of naturally occurring osmium isotopes to the lowest excited levels of daughter nuclei has been performed by using an ultra-low-background Broad-Energy Germanium $gamma$-detector with a volume of 112 cm$^3$ and an ultra-pure osmium sample with a mass of 118 g at the Gran Sasso National Laboratory of the INFN (Italy). The isotopic composition of the osmium sample has been measured with high precision using Negative Thermal Ionisation Mass Spectrometry. After 15851 h of data taking with the $gamma$-detector no effect has been detected, and lower limits on the $alpha$ decays were set at level of $lim T_{1/2}sim 10^{15}-10^{19}$ yr. The limits for the $alpha$ decays of $^{184}$Os and $^{186}$Os to the first excited levels of daughter nuclei, $T_{1/2}(^{184}$Os$)geq 6.8times10^{15}$ yr and $T_{1/2}(^{186}$Os$)geq3.3times10^{17}$ yr (at 90% C.L.), exceed the present theoretical estimates of the decays half-lives. For $^{189}$Os and $^{192}$Os also decays to the ground states of the daughter nuclei were searched for due to the instability of the daughter nuclides relative to $beta$ decay.
The first ever search for $2varepsilon$ and $varepsilonbeta^+$ decay of $^{174}$Hf was realized using a high-pure sample of hafnium (with mass 179.8 g) and the ultra low-background HPGe-detector system located 225 m underground. After 75 days of data taking no indication of the double beta decay transitions could be detected but lower limits for the half-lives of the different channels and modes of the decays were set on the level of $lim T_{1/2}sim 10^{16}-10^{18}$ a.
Negative results obtained in AMS searches by Dellinger et al. on mostly unrefined ores have led them to conclude that the very heavy long-lived species found in chemically processed samples with ICP-SFMS by Marinov et al. are artifacts. We argue that it may not be surprising that results obtained from small random samplings of inhomogeneous natural minerals would contrast with concentrations found in homogeneous materials extracted from large quantities of ore. We also point out that it is possible that the groups of counts at masses 296 and 294 seen by Dellinger et al. could be, within experimental uncertainties, due to $^{296}$Rg and $^{294}$eka-Bi in long-lived isomeric states. In such case, the experiments of Dellinger et al. lend support to the experiments of Marinov et al.
We provide first evidence that under certain conditions, 1/2-spin fermions may naturally behave like a Grover search, looking for topological defects in a material. The theoretical framework is that of discrete-time quantum walks (QW), i.e. local unitary matrices that drive the evolution of a single particle on the lattice. Some QW are well-known to recover the $(2+1)$--dimensional Dirac equation in continuum limit, i.e. the free propagation of the 1/2-spin fermion. We study two such Dirac QW, one on the square grid and the other on a triangular grid reminiscent of graphene-like materials. The numerical simulations show that the walker localises around the defects in $O(sqrt{N})$ steps with probability $O(1/log{N})$, in line with previous QW search on the grid. The main advantage brought by those of this paper is that they could be implemented as `naturally occurring freely propagating particles over a surface featuring topological---without the need for a specific oracle step. From a quantum computing perspective, however, this hints at novel applications of QW search : instead of using them to look for `good solutions within the configuration space of a problem, we could use them to look for topological properties of the entire configuration space.
Evidence for the existence of long-lived neutron-deficient isotopes has been found in a study of naturally-occurring Th using iductively coupled plasma-sector field mass spectrometry. They are interpreted as belonging to the recently discovered class of long-lived high spin super- and hyperdeformed isomers.
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