Penetration factor in deformed potentials: Application to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>decay with deformed nuclei

Abstract

A new averaging process of the calculation of \ensuremath{\alpha}-decay half-lives for heavy and superheavy nuclei is studied in the framework of a deformed density-dependent cluster model. The potential between a spherical \ensuremath{\alpha} particle and a deformed daughter nucleus is calculated numerically from the double-folding model by the multipole expansion method. The nuclear potential is calculated at each \ensuremath{\alpha}-particle emission angle applying the Bohr-Sommerfeld condition at each case. The penetration factors and the half-lives for all the emission angles are evaluated with the new averaging process and compared with older values based on a fixed value of the nuclear potential depth. Finally, the half-lives of 83 even-even heavy nuclei in the atomic-number range 82--118 are calculated by the two methods and compared with their experimental values and the corresponding half-lives of the spherical daughter nuclei.