Resumo
New estimates of partial $\alpha$-decay half-life,$T_{\!1/2}$, for $^{156\mbox{--}162, 174, 176}$Hf isotopes by a semi-empirical, one-parameter model are given. The used model is based on the quantum mechanical tunneling mechanism through a potential barrier, where the Coulomb, centrifugal and overlapping components to the barrier have been considered within the spherical nucleus approximation.
This approach enables to reproduce, within a factor 2, the measured $T_{\!1/2}$ of ground-state to ground-state (gs--gs) $\alpha$-transitions for the artificially produced $^{156\mbox{--}162}$Hf isotopes.
Half-life predictions for $\alpha$-transitions from the ground-state of $^{159, 161}$Hf isotopes to the first gamma-excited level of $^{155, 157}$Yb isotopes are reported for the first time.
The model also provides $T_{\!1/2}$-values of $(2.43\pm 0.28)\times 10^{16}$~a and $(1.47\pm 0.19)\times 10^{20}$~a for the naturally occurring $^{174}$Hf and $^{176}$Hf isotopes, respectively, in quite good agreement with a number of estimates by other authors.
In addition, the present methodology indicates that $^{174, 176}$Hf isotopes exhibit $\alpha$-transition to the first gamma-excited level of their daughter Ytterbium isotopes which half-lives are found $(0.9\pm 0.1)\times 10^{18}$~a and $(0.72\pm 0.08)\times 10^{22}$~a, respectively, with a chance of being measured by improved $\alpha$-detection and $\alpha$-spectrometry methods available nowadays.