Microscopic Description of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mi>α</mml:mi></mml:mrow></mml:math> Decay in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Po</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>212</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Ra</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>224</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math> Isotopes
F. Mercier, Jie Zhao, J.-P. Ebran, E. Khan, Tamara Nikšić, D. Vretenar
Abstract
A microscopic calculation of half-lives for both the $\ensuremath{\alpha}$ and $2\ensuremath{\alpha}$ decays of $^{212}\mathrm{Po}$ and $^{224}\mathrm{Ra}$ is performed, using a self-consistent framework based on energy density functionals. A relativistic density functional and a separable pairing interaction of finite range are used to compute axially symmetric deformation energy surfaces as functions of quadrupole, octupole, and hexadecapole collective coordinates. Dynamical least-action paths are determined, that trace the $\ensuremath{\alpha}$ and $2\ensuremath{\alpha}$ emission from the equilibrium deformation to the point of scission. The calculated half-lives for the $\ensuremath{\alpha}$ decay of $^{212}\mathrm{Po}$ and $^{224}\mathrm{Ra}$ are in good agreement with data. A new decay mode, the symmetric $2\ensuremath{\alpha}$ emission, is predicted with half-lives of the order of those observed for cluster emission.