Optimum orientation versus orientation averaging description of cluster radioactivity

Abstract

Background:The deformation of the nuclei involved in the cluster decay of heavy nuclei affect seriously their half-lives against the decay. Purpose:We investigate the description of the different decay stages in both the optimum orientation and the orientation-averaged pictures of the cluster decay process. Method:We consider the decays of 232,233,234 U and 236,238 Pu isotopes. The quantum mechanical knocking frequency and penetration probability based on the Wentzel-Kramers-Brillouin approximation are used to find the decay width. Results:We found that the orientation-averaged decay width is one or two orders of magnitude less than its value along the non-compact optimum orientation. The difference between the two values increases with decreasing the mass number of the emitted cluster. Correspondingly, the extracted preformation probability based on the averaged decay width increases with the same orders of magnitude compared to its value obtained considering the optimum orientation. The cluster preformation probabilities (S c ) obtained in the two considered schemes give more or less comparable agreement with the Blendowske-Walliser (BW) formula based on the preformation probability of ( ) obtained from the orientation-averaging scheme. All the obtained results, including those obtained in the optimum-orientation scheme, deviate substantially from the BW law based on obtained using the optimumorientation scheme. Conclusion:In order to account for deformations of the participating nuclei, it is more relevant to calculate the decay width by averaging over the different possible orientations of the participating deformed nucleus, rather than considering the corresponding non-compact optimum orientation.

Influence of proton-skin thickness on the ${{\alpha }}$ decays of heavy nuclei

“…( 16) and ( 17)) are determined from the condition V T (r,θ)| r=R i (θ) =Q α . The orientation-independent [18] R 3 , located at the far tail region of the long-range Coulomb potential V C (r,θ), can be obtained in terms of the atomic number of the daughter nucleus (Z d ) and the angular momentum carried by the α-particle ( ) as [16],…”

“…The stability of nuclei is principally governed by the released energy and the change of the ground state properties from parent to daughter nuclei. For instance, the isospin asymmetry [13] and incompressibility [14] of nuclei, their deformation [15,16], and the closed shell effect [17,18] are essential factors affecting a possible decay mode. Also, the presence of unpaired nucleons in open shells [18,19], the spin and parity assignments of these unpaired nucleons [20,21], and the collective vibrational excitations [22] influence the com-peting decay modes.…”

Constraints on the nuclear symmetry energy and its density slope from the ${\boldsymbol{\alpha }}$ decay process

“…2 but yield narrower investigated range of L, from L (Skz1)=27.67 MeV to L(Ska45s20)=66. 21 MeV. The uncertainties in the Q α -value [71] and in the experimental half-life [72] are both taken into account in the extracted values of S α .…”

“…For instance, the α-decay process has been used to probe the nuclear incompressibility [12], the neutron and proton shell closures of finite nuclei [13,14,15], and the spin-parity configuration [16,17,18] of their ground-and isomeric states. Also, it has been used to investigate the collective vibrational and rotational excitations [19] of nuclei and their deformations [20,21]. It was found that considering the neutron-skin thickness of the daughter nucleus reduces the calculated half-life against α [22] and cluster [23] decays.…”

Change in neutron skin thickness after cluster-decay

“…The correlations between nuclear structure and the α and heavier cluster decay modes have been confirmed by dozens of studies [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Accurate knowledge of nuclear density distributions is essential to understand the fundamental properties of nuclear matter and the nature of nuclear force.…”