Linkage among the neutron-skin thickness of ²⁰⁸Pb and nuclear symmetry energy using heavy particle radioactivity

The nuclear symmetry energy (NSE) is a linchpin in deciphering the behavior of matter in a wider domain extending from the characteristics of exotic nuclei to those of neutron stars in the cosmos.
Therefore, it is crucial to utilize potential probes to constrain the NSE and its slope parameter L($\rho_{0}$). In this work, we put forth the heavy particle radioactivity (HPR) as a probable bridge among the slope of NSE (L($\rho_{0}$)) and neutron-skin thickness of $^{208}Pb$ ($R_{skin}^{208}$), which serves to put constrain on the L($\rho_{0}$) value. The NSE and its slope parameter are determined from the single nucleon potential of asymmetric nuclear matter exploiting the analytical relationship between these quantities. The isovector/symmetry potential component of the single nucleon potential is derived through HPR for varying $R_{skin}^{208}$ by employing the heavy particle/cluster densities and core densities from the relativistic mean field model in conjunction with M3Y nucleon-nucleon interaction. It facilitates in constraining the L($\rho_{0}$) value and neutron skin of finite nuclei using HPR as a linkage, where heavy cluster and core densities of standard Fermi form are considered. The constrained value of L($\rho_{o}$) is 48 $\pm$ 9 MeV, which aligns with other estimations derived from nuclear mass measurements, dipole polarizability measurements and astrophysical data.