Microscopic calculations of nuclear incompressibility from cluster radioactivity

In the present work, based on the framework of the two-potential approach, we systematically investigate the incompressibility of nuclear matter $K$ from cluster radioactivity by considering the sum of an attractive double-folding potential and a repulsive Gaussian potential as the total nuclear potential of nucleon-nucleon interactions. The strength of the repulsive Gaussian core caused by the Pauli exclusion principle can be obtained by reproducing the cluster radioactivity experimental half-lives of 28 trans-lead nuclei ranging from $^{221}\mathrm{Fr}$ to $^{242}\mathrm{Cm}$. The incompressibility of nuclear matter can be calculated in the case of completely overlapped densities inside the potential barrier, which is related to the curvature of the nuclear matter equation of state. The obtained values for the incompressibility of nuclear matter range from 202.13--247.54 MeV. In addition, the influences of isospin asymmetry $\ensuremath{\delta}$ and the effective number of the valence particles ${N}_{p}{N}_{n}$ on the incompressibility of nuclear matter from cluster radioactivity are also discussed. The results show that the incompressibility of nuclear matter $K$ is linear to product of isospin asymmetry and the effective number of the valence particles ${N}_{p}{N}_{n}\ensuremath{\delta}$. At the same time, the estimated incompressibility of symmetric nuclear matter deduced from the results obtained for different asymmetric nuclei is $K(\ensuremath{\delta}=0)=251.14$ MeV.