Both the valence nucleons (holes) and the isospin asymmetry dependencies of the preformation probability of an α-cluster inside parents radioactive nuclei are investigated. The calculations are employed in the framework of the density-dependent cluster model of an α-decay process for the even-even spherical parents nuclei with protons number around the closed shell Z 0 = 82 and neutrons number around the closed shells Z 0 = 82 and Z 0 = 126. The microscopic α-daughter nuclear interaction potential is calculated in the framework of the Hamiltonian energy density approach based on the SLy4 Skyrme-like effective interaction. Also, the calculations based on the realistic effective M3Y-Paris nucleon-nucleon force have been used to confirm the results. The calculations then proceed to find the assault frequency and the α penetration probability within the WKB approximation. The half-lives of the different mentioned α decays are then determined and have been used in turn to find the α spectroscopic factor. We found that the spectroscopic factor increases with increasing the isospin asymmetry of the parent nuclei if they have valence protons and neutrons. When the parent nuclei have neutron or proton holes in addition to the valence protons or neutrons, then the spectroscopic factor is found to decrease with increasing isospin asymmetry. The obtained results show also that the deduced spectroscopic factors follow individual linear behaviors as a function of the multiplication of the valence proton (N p ) and neutron (N n ) numbers. These linear dependencies are correlated with the closed shells core (Z 0 , N 0 ). The same individual linear behaviors are obtained as a function of the multiplication of N p N n and the isospin asymmetry parameter, N p N n I . Moreover, the whole deduced spectroscopic factors are found to exhibit a nearly general linear trend with the function N p N n /(Z 0 + N 0 ).

Proton and neutron density profiles of 760 nuclei in the mass region of are analyzed using the Skyrme energy density for the parameter set SLy4. Simple formulae are obtained to fit the resulting radii and diffuseness data. These formulae are useful to estimate the values of the unmeasured radii, and especially in extrapolating charge radii values for nuclei which are far from the valley of stability or to perform analytic calculations for bound and/or scattering problems. The obtained neutron and proton root-mean-square radii and the neutron skin thicknesses are in agreement with the available experimental data and previous Hartree-Fock calculations.

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ABSTRACT:The ground-state spin and parity of a formed daughter in the radioactive -emitter is expected to influence the preformation probability of the  and daughter clusters inside it. We investigate the  and daughter preformation probability inside odd-A and doubly-odd radioactive nuclei when the daughter and parent are of different spin and/or parity. We consider only the ground-state to ground-state unfavored decays. This is to extract precise information about the effect of the difference in the ground states spin-parity of the involved nuclei far away any influences from the excitation energy if the decays are coming from isomeric states. The calculations are done for 161 -emitters, with and , in the framework of the extended cluster model, with WKB penetrability and assault frequency. We used a Hamiltonian energy density scheme based on Skyrme-SLy4 interaction to compute the interaction potential. The  plus cluster preformation probability is extracted from the calculated decay width and the experimental half-life time. We discussed in detailed steps the effect of angular momentum of the emitted -particle on the various physical quantities involved in the unfavored decay process and how it is finally increases the half-life time. We found that if the ground states spin and/or parity of parent and daughter nuclei are different, then the preformation probability of the -cluster inside parent is less than it would be if they have similar spin-parity. We modified the formula that gives the preformation probability in terms of the numbers of protons and neutrons outside the shell closures of parent, to account for this hindrance in the preformation probability for the unfavored decays between ground states.2

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