The alpha-decay half-lives of even-even nuclei from Sm to Th are systematically studied based on the transfer matrix method. For the nuclear potential, a type of cosh-parametrized form is applied to calculate the penetration probability. Through a least-squares fit to experimental half-lives, we optimize the parameters in the potential and the a preformation factor P-0. During this process, P-0 is treated as a constant for each parent nucleus. Eventually, the calculated half-lives are found to agree well with the experimental data, which verifies the accuracy of the present approach. Furthermore, in recent studies, P-0 is regulated by the shell and paring effects plus the nuclear deformation. To this end, P-0 is here associated with the structural quantity, i.e., the microscopic correction of nuclear mass (E-mic). In this way, the agreement between theory and experiment is greatly improved by more than 20%, validating the appropriate treatment of P-0 in the scheme of E-mic.

Although significant progress has been made in the synthesis of superheavy nuclei, the experimental knowledge of them is still very limited while the alpha decay chain is the main tool used to identify newly produced superheavy nuclei. Previously, we have extracted nuclear charge radii of superheavy nuclei via the experimental alpha decay data. As a further step, the density dependent cluster model is improved by introducing the difference between the density distributions of protons and neutrons. Besides, the important quantity, i.e., the alpha preformation factor, is connected with the microscopic correction of nuclear mass during this procedure, to perform a more reasonable description of the alpha decay process. It is found that the present deduced nuclear charge radii of heavy nuclei are in a better agreement with the measured values as compared to those in our previous evaluations. Subsequently, the nuclear radii of heavier even-even isotopes with Z = 98-116 are probed, accompanied by the consistency with the empirical evaluations. Moreover, the effect of the depressed density at the center of superheavy nucleus on the final extracted nuclear radius plus the decay lifetime is discussed, which appears to be different from the case of lighter nuclide.

The seniority symmetry is known to be partially conserved in two special cases in the (9/2)(4) system, which can lead to striking features in the corresponding structure and electromagnetic transition properties. However, it is still quite difficult to derive those kind of solvable states, in general, especially towards higher- j orbits. We have developed a novel and effective way to confront this challenge by starting from the m scheme and making use of the angular momentum projection method. It also allows us to explore another special family of seniority conserving states in the midshell besides the specific case of the (9/2)(4) configuration. Moreover, we have studied systemically all states in single- j systems up to j = 15/2 and derived the analytic expressions for the eigenvalues of all solvable states with a focus on those in j = 9/2 and j = 11/2. Such studies can also be useful for the experimental search of relevant states and for the understanding of their electromagnetic transition properties.