In the present work, combining with the Geiger-Nuttall law, a two-parameter empirical formula is proposed to study the two-proton (2p) radioactivity. Using this formula, the calculated 2p radioactivity half-lives are in good agreement with the experimental data as well as the calculated ones obtained by Goncalves et al. ([Phys. Lett. B 774, 14 (2017)]) using the effective liquid drop model (ELDM), Sreeja et al. ([Eur. Phys. J. A 55, 33 (2019)]) using a four-parameter empirical formula and Cui et al. ([Phys. Rev. C 101: 014301 (2020)]) using a generalized liquid drop model (GLDM). In addition, this two-parameter empirical formula is extended to predict the half-lives of 22 possible 2p radioactivity candidates, whose the 2p radioactivity released energy Q2p>0, obtained from the latest evaluated atomic mass table AME2016. The predicted results have good consistency with ones using other theoretical models such as the ELDM, GLDM and four-parameter empirical formula.

In this study, based on the Gamow-like model, we systematically analyze two-proton ( ) radioactivity half-lives of nuclei near or beyond the proton drip line. It is found that the calculated results can reproduce experimental data well. Furthermore, using this model, we predict the half-lives of possible radioactivity candidates whose radioactivity is energetically allowed or observed but not yet quantified in the latest table of evaluated nuclear properties, i.e., NUBASE2016. The predicted results are in good agreement with those from other theoretical models and empirical formulas, namely the effective liquid drop model (ELDM), generalized liquid drop model (GLDM), Sreeja formula, and Liu formula.

In the present work considering the contributions of the daughter nuclear charge and the orbital angular momentum taken away by the emitted proton, we propose a two-parameter formula of new Geiger-Nuttall law for proton radioactivity. A set of universal parameters of this law is obtained by fitting 44 experimental data of proton emitters in the ground state and isomeric state. The calculated results can reproduce the experimental data well. For a comparison, the calculations performed using other theoretical methods, such as UDLP proposed by Qi et al. [Phys. Rev. C 85, 011303(R) (2012)], the CPPM-Guo2013 analyzed by our previous work [Deng et al., Eur. Phys. J. A 55, 58 (2019)] and the modified Gamow-like model proposed by us [Chen et al., J. Phys. G: Nucl. Part. Phys. 96, 065107 (2019)] are also included.Meanwhile, we extend this new Geiger-Nuttall law to predict the proton radioactivity half-lives for 51 ≤ Z ≤ 91 nuclei, whose proton radioactivity is energetically allowed or observed but not yet quantified in NUBASE2016.

In the present work we systematically study α decay half-lives of Z > 51 nuclei using the modified Gamow-like model which includes the effects of the centrifugal potential and electrostatic shielding. For the case of even-even nuclei, this model contains two adjustable parameters: the parameter a related to the screened electrostatic barrier and the radius constant r 0 , while for the case of odd-odd and odd-A nuclei, it is added a new parameter i.e. hindrance factor h which is used to describe the effect of an odd-proton and/or an odd-neutron.Our calculations can well reproduce the experimental data. In addition, we use this modified Gamow-like model to predict the α-decay half-lives of seven even-even nuclei with Z = 120 and some un-synthesized nuclei on their α decay chains.

In the present work we systematically study the half-lives of proton radioactivity for 51 ≤ Z ≤ 83 nuclei based on the Gamow-like model with a screened electrostatic barrier. In this model there are two parameters while considering the screened electrostatic effect of Coulomb potential with the Hulthen potential i.e. the effective nuclear radius parameter r 0 and the screening parameter a. The calculated results can well reproduce the experimental data. In addition, we extend this model to predict the proton radioactivity half-lives of 16 nuclei in the same region within a factor of 2.94, whose proton radioactivity are energetically allowed or observed but not yet quantified. Meanwhile, studying on the proton radioactivity half-life by a type of universal decay law has been done. The results indicate that the calculated half-lives are linearly dependent on Coulomb parameter with the same orbital angular momentum.Systematic study of proton radioactivity based on Gamow-like model with a screened electrostatic barrier2 been identified between Z = 51 and Z = 83 [5,6]. As an important decay mode of unstable nuclei, proton radioactivity is an useful tool to obtain spectroscopic information because the decaying proton is the unpaired proton not filling its orbit and to extract important information about nuclear structure lying beyond the proton drip line, such as the coupling between bound and unbound nuclear states, the shell structure [7] and so on. There are a lot of models and empirical formulas having been proposed to deal with the proton radioactivity such as the effective interactions of densitydependent M3Y (DDM3Y) [8,9], the single-folding model [9][10][11], the distorted-wave Born approximation [12], Jeukenne, Lejeune and Mahaux (JLM) [8], the generalized liquid-drop model [13-15], the finite-range effective interaction of Yukawa form [16], the R-matrix approach [18], the Skyrme interactions [19], the relativistic density functional theory [20], the phenomenological unified fission model [21, 22], the twopotential approach (TPA) [5] which is also successfully applied to the α decay and cluster radioactivity [23-28], the Coulomb and proximity potential model (CPPM) [29], a simple empirical formula proposed by Delion et al. [30] and so on. For more details about different theories of proton radioactivity, the readers are referenced to Ref. [17].Recently, Budaca et al. used a simple analytical model based on the WKB approximation considering the screened effect of emitted proton-daughter nucleus Coulomb interaction with the Hulthen potential to systematically study the half-lives of proton radioactivity for 41 nuclei with Z ≥ 51 [31]. The results indicate that the difference between the outer turning point radii corresponding to pure Coulomb and Hulthen barriers increases with the proton number Z increasing. Whereas the penetration probability is sensitive to the outer turning point radii. In 2016, Zdeb et al. [32] calculated the half-life of proton radioactivity with a Gamow-like model, which has much deeper ...