Theoretical Study On Alpha Decay Half-lives To The Favored Band Of Daughter Nuclei

α-decay is a powerful tool to investigate the properties of unstable nuclei in the mass table, especially for the drip-line nuclei, closed-shell nuclei and superheavy nuclei. Extensive theoretical studies have been devoted to pursuing a quantitative description of α-decay half-lives by both phenomenological and microscopic methods. As early as1911, Geiger and Nuttall observed the linear dependence of the logarithm of α-decay half-life (logioTi/2) on the logarithm of the range of α-particle (proportional to decay energy Q), which is well known as the Geiger-Nuttall law. The first microscopic interpretation of this dependence was given by Gamow and by Condon and Guerney in the1920s, which proved the correctness of quantum mechanics for nuclear phenomena and led to the use of quantum mechanics on the nuclear many-body system. Up till the late1960s, the study of alpha decay had been an active field of research. Several decades has passed since that time, and again an appreciable amount of new data have been accumulated. In the "superheavy synthesis" experiments, most of the newly synthesized nuclei undergo α-decay (for quiet a few of these nuclei α-decay is the only decay process detected). Moreover, for these newly synthesized short-lived nuclei, α-decay data is almost the only kind of data that can be used to establish the proton number and neutron number of a specific nucleus. Among the empirical formulas for calculating α-decay half lives, the Viola-Seaborg formula is the most famous one. It was proposed in1966by Viola and Seaborg who got them by generalizing the Geiger-Nuttall law. Other forms of relations between log10T1/2and Q have also been proposed for the α-emitters in subsequent researches. Such analytical expressions are very useful for the experimentalists who need to evaluate the expected half-lives during the design of experiments and to rapidly check the measured decay energies and half-lives after experiments. In addition to the analytical formulas such as the V-S formula, semi-microscopic and microscopic approaches have been widely applied to calculate the half-lives of both α-decay and exotic cluster radioactivity, such as the shell model, the cluster model, the fission-like model and the mixed shell-and-cluster model and so on. However, most of α-decay studies are focused on the unhindered α-transitions where the angular momentum carried by the α-cluster is zero (L=0), i.e. the ground-state to ground-state transitions of eveneven nuclei. In contrast, the hindered α-transitions (L≠0) are relatively less studied because of the lack of accurate data and the difficulties in treating the angular momentum, especially for odd-A and odd-odd nuclei. In recent years, a large amount of new and more precise data on the fine structure of α-decay has been reported in experiments. Theoretically many interesting questions concerned with α-decay fine structure arise, for instance, do the data of hindered α-transitions with the same angular momentum L obey the Geiger-Nuttall law? Is there any accurate analytical expression for the evaluation as well as prediction of α-decay half-lives of the L≠0transitions? Our study focuses on the deformed alpha emitters. In the deformed region the collective model has been verified by a large amount of experimental data, and has been proved to be able to predict accurately the energy levels, the intensity of electric quadrupole and magnetic dipole transitions,β decay branching ratios, as well as early experimental data on α-decay branching ratios. Thus another question is: for the newly accumulated data on α-decays from heavy deformed nuclei, are the predictions given by the collective model still correct? To try to answer these questions, we firstly perform systematic analysis on the α-transitions to members of favored bands of both the even-even and odd-A nuclei and check the validity of the Geiger-Nuttall law for these transitions. More importantly, we propose two reliable and accurate expressions for the L≠0α-transitions. One of the expressions is got by simplifying the general formula given by the collective model, while the other is got by generalizing the Viola-Seaborg formula. The agreement between the experimental data and our expressions is remarkably well. It is expected that both expressions are helpful for the experimental studies on α-decay fine structure in future.