A windowless hydrogen gas target for the measurement of 7Be(p, $ \gamma$ )8B with the recoil separator ERNA

Using the Coulomb and proximity potential model (CPPM) we have investigated the cluster decays of the isotopes ^212-240Pa, ^219-245Np, ^228-246Pu, ^230-249Am and ^232-252Cm leading to doubly magic ²⁰⁸Pb and its neighboring nuclei, which are not experimentally detected but which may be detectable in the future. It is found that most of the decays are favourable for experimental measurements (i.e., $T_{1/2}<10^{30}$ s) and this observation will serve as a guide to future experiments. Our study reveals the role of doubly magic ²⁰⁸Pb daughter nuclei and near doubly magic nuclei in the cluster decay process. In order to make a comparison with CPPM we also calculated the logarithmic half-lives using the Universal formula for the cluster decay (UNIV) by Poenaru et al., the Universal Decay Law (UDL) and the Scaling Law of Horoi et al., and they are found to be in good agreement. The Geiger-Nuttall plots of $log_{10}(T_{1/2})$ versus $Q^{-1/2}$ for various clusters from different isotopes of heavy parent nuclei have been studied and are found to be linear.