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We examine ,;he experimental data on partial half lives for alpha decay of heavy even-even nuclei. When presented in the traditional form of Geiger-Nuttall plots for various isotopic sequences, these data dearly indicate the existence af &Iferent linear relations for neutron numbers N above and helow the magic value of 126. We present a simple cluster model, employing three fixed parameters, which is able to give an excellent account of all these half lives. In particular, it can reproduce the values for all even-even nuclei having 76 < Z < 100 to within a factor of approximately two. An important feature of the model is that it envisages preformed alpha particles in the parent nuclei t o be moving in orbits with a large value of a global quantumnumber. The discontinuity in the Geiger-Nuttall plots at N = 126 is then naturally explained by an increase of this global quantum number as the alpha particle is forced into a higher orhit by the shell closure.