Adopting different neutron and proton density distributions the cluster decay half-lives have been investigated using double-folding potentials with constant and nuclear asymmetry dependent sets of the parameters of nuclear densities. Two adopted asymmetry dependent sets of the parameters are fitted based on the microscopic calculations and calculated based on the neutron skin/halo-type nuclei assumption and employing experimental rms charge radii. The bulk agreement between theory and experiment has been obtained for entire sets of parameters using calculated cluster preformation probability. The very little differences between skin and halo-type assumption have been observed. However, the notable role of the asymmetry parameter has been seen in relatively large differences between the skin and skin-type with zero thickness.
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