Alpha Decay for Uranium Isotopes

Both the transfer matrix approach and the Wentzel Kramers Brillouin(WKB) approximation are used to calculate the penetrability of \alpha decay for uranium isotopes. It is found that the penetrability obtained with WKB approximation is about 40% smaller than the accurate result obtained with the transfer matrix approach, and a parabolic relationship between this underestimation and the decay energy can be observed. Based on the cluster model, the half-lives of \alpha decay for uranium isotopes are calculated in which the transfer matrix approach is used to obtain the penetrability. In addition, the influences of potential depth V_0, the diffuseness parameter a, and the global quantum number G on the calculated half-life are also investigated. Furthermore, with considering an isospin-dependent potential depth parameter, the \alpha decay half-lives of uranium isotopes can be fairly well reproduced by the cluster model.