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.
Longitudinal ternary and binary fission barriers of $^{36}$Ar, $^{56}$Ni and $^{252}$Cf nuclei have been determined within a rotational liquid drop model taking into account the nuclear proximity energy. For the light nuclei the heights of the ternar
y fission barriers become competitive with the binary ones at high angular momenta since the maximum lies at an outer position and has a much higher moment of inertia.
The coefficients of different mass formulae derived from the liquid drop model and including or not the curvature energy, the diffuseness correction to the Coulomb energy, the charge exchange correction term, different forms of the Wigner term and di
fferent powers of the relative neutron excess $I=(N-Z)/A$ have been determined by a least square fitting procedure to 2027 experimental atomic masses. The Coulomb diffuseness correction $Z^2/A$ term or the charge exchange correction $Z^{4/3}/A^{1/3}$ term plays the main role to improve the accuracy of the mass formula. The Wigner term and the curvature energy can also be used separately for the same purpose. The introduction of an $|I|$ dependence in the surface and volume energies improves slightly the efficiency of the expansion and is more effective than an $I^4$ dependence. Different expressions reproducing the experimental nuclear charge radius are provided. The different fits lead to a surface energy coefficient of around 17-18 MeV and a relative equivalent rms charge radius r$_0$ of 1.22-1.23 fm.
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)].
The efficiency of different mass formulas derived from the liquid drop model including or not the curvature energy, the Wigner term and different powers of the relative neutron excess $I$ has been determined by a least square fitting procedure to the
experimental atomic masses assuming a constant R$_{0,charge}$/A$^{1/3}$ ratio. The Wigner term and the curvature energy can be used independently to improve the accuracy of the mass formula. The different fits lead to a surface energy coefficient of around 17-18 MeV, a relative sharp charge radius r$_0$ of 1.22-1.23 fm and a proton form-factor correction to the Coulomb energy of around 0.9 MeV.
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.
