Exact estimate of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math>-decay rate and semiclassical approach in deformed nuclei

We compare the quantum mechanical procedures to estimate the total $\ensuremath{\alpha}$-decay width from deformed nuclei in the laboratory and intrinsic systems of coordinates. Our analysis shows that the total half-life estimated in the intrinsic frame by neglecting the rotational motion of the core (adiabatic approach) is one order of magnitude smaller at ${\ensuremath{\beta}}_{2}=0.3$ than the corresponding value in the spherical case. A similar calculation in the laboratory system of coordinates by considering the core motion (giving the correct theoretical estimate) predicts a reduction by only a factor of 2. The widely used ``angular WKB'' (Wentzel-Kramers-Brillouin) semiclassical procedure provides decay widths which are comparable to the adiabatic approach. We propose a new and very simple semiclassical ``angular momentum WKB'' procedure to evaluate the decay width in deformed nuclei. It provides decay widths very close to the ones obtained by the exact laboratory coupling channels procedure.