Formation region of emitted α and heavier particles inside radioactive nuclei

We investigate the formation distance(R0)from the center of the radioactive parent nucleus at which the emitted cluster is most probably formed.The calculations are performed microscopically starting with the solution to the time-independent Schr?dinger wave equation for the cluster-core system,using nuclear potentials based on the Skyrme-SLy4 nucleon-nucleon interactions and folding Coulomb potential,to determine the incident and transmitted wave functions of the system.Our results show that the emitted cluster is mostly formed in the pre-surface region of the nucleus,under the effect of Pauli blocking from the saturated core density.The deeperα-formation distance inside the nucleus allows less preformation probability and indicates a more stable nucleus for a longer half-life.Furthermore,theα-particle tends to be formed at a slightly deeper region inside the nuclei,with larger isospin asymmetry,and in the closed shell nuclei.Regarding the heavy clusters,we observed that the formation distance of the emitted clusters heavier thanα-particle increased via increasing the isospin asymmetry of the formed cluster rather than by increasing its mass number.The partial half-life of a certain cluster-decay mode increased with increase of either the mass number or the isospin asymmetry of the emitted cluster.

Constraints on the nuclear symmetry energy and its density slope from theαdecay process

We study the impact of the nuclear symmetry energy and its density dependence on the α-decay process.Within the framework of the preformed cluster model and the energy density formalism, we use different parameterizations of the Skyrme energy density functionals that yield different equations of state（EOS）. Each EOS is characterized by a particular symmetryenergy coefficient（asym） and a corresponding density-slope parameter L. The stepwise trends of the neutron（proton） skin thickness of the involved nuclei with both asym and L do not clarify the oscillating behaviors of the α-decay half-life Tα with these quantities. We find that the change of the skin thickness after α-decay satisfactorily explains these behaviors. The presented results provide constraints on asym centered around an optimum value asym = 32 MeV, and on L between 41 and 57 MeV. These values of asym and L, which indicate larger reduction of the proton-skin thickness and less increase in the neutron-skin thickness after an α-decay,yield a minimum calculated half-life with the same extracted value of the α-preformation factor inside the parent nucleus.

Influence of proton-skin thickness on the α decays of heavy nuclei

We investigate the effect of proton-skin thickness on the α decay process. We consider 188 neutrondeficient nuclei belonging to the isotopic chains from Te（Z = 52） to Pb（Z = 82）. The calculations of the half-life are carried out in the framework of the preformed cluster model, with the Wentzel-Kramers-Brillouin penetration probability and assault frequency. It is shown that the proton-skin thickness（？p） of the daughter nucleus gives rise to a total α-daughter nucleus interaction potential of relatively wide deep internal pocket and a thinner Coulomb barrier of less height. This increases the penetration probability but decreases the assault frequency. The overall impact of the proton-skin thickness appears as a decrease in the decay half-life. The proton-skin thickness decreases the stability of the nucleus. The half-lives of the proton-skinned isotopes along the isotopic chain decrease exponentially with increasing the proton-skin thickness, whereas the Qα-value increases with ？p. α-decay manifests itself as the second favorite decay mode of neutron-deficient nuclei, next to the β＋-decay and before proton-decay. It is indicated as main, competing, and minor decay mode, at 21%, 7%, and 57%, respectively, of the investigated nuclei.