The $alpha$ particle preformation in the even-even nuclei from $^{108}$Te to $^{294}$118 and the penetration probability have been studied. The isotopes from Pb to U have been firstly investigated since the experimental data allow us to extract the m
icroscopic features for each element. The assault frequency has been estimated using classical methods and the penetration probability from tunneling through the Generalized Liquid Drop Model (GLDM) potential barrier. The preformation factor has been extracted from experimental $alpha$ decay energies and half-lives. The shell closure effects play the key role in the $alpha$ preformation. The more the nucleon number is close to the magic numbers, the more the formation of $alpha$ cluster is difficult inside the mother nucleus. The penetration probabilities reflect that 126 is a neutron magic number. The penetration probability range is very large compared to that of the preformation factor. The penetration probability determines mainly the $alpha$ decay half-life while the preformation factor allows us to obtain information on the nuclear structure. The study has been extended to the newly observed heaviest nuclei.
New recent experimental $alpha$ decay half-lives have been compared with the results obtained from previously proposed formulas depending only on the mass and charge numbers of the $alpha$ emitter and the Q$alpha$ value. For the heaviest nuclei they
are also compared with calculations using the Density-Dependent M3Y (DDM3Y) effective interaction and the Viola-Seaborg-Sobiczewski (VSS) formulas. The correct agreement allows us to make predictions for the $alpha$ decay half-lives of other still unknown superheavy nuclei from these analytic formulas using the extrapolated Q$alpha$ of G. Audi, A. H. Wapstra, and C. Thibault [Nucl. Phys. A729, 337 (2003)].
Theoretical decay half-lives of the heaviest odd-Z nuclei are calculated using the experimental Q value. The barriers in the quasimolecular shape path are determined within a Generalized Liquid Drop Model (GLDM) and the WKB approximation is used. The
results are compared with calculations using the Density-Dependent M3Y (DDM3Y) effective interaction and the Viola-Seaborg-Sobiczewski (VSS) formulas. The calculations provide consistent estimates for the half-lives of the decay chains of these superheavy elements. The experimental data stand between the GLDM calculations and VSS ones in the most time. Predictions are provided for the decay half-lives of other superheavy nuclei within the GLDM and VSS approaches using the recent extrapolated Q of Audi, Wapstra, and Thibault [Nucl. Phys. A729, 337 (2003)], which may be used for future experimental assignment and identification.
