An empirical formula for the half-lives of ground state and isomeric state one proton emission

New Geiger-Nuttall law for two-proton radioactivity *

“…The exponent on the orbital angular momentum l taken away by the emitted proton, β is 1, which is obtained by fitting 44 experimental data of the proton radioactivity in the ground state and isomeric state. Combined with Sreeja et al works [36,55] and our previous work [44], it is interesting to validate whether a two-parameter form of empirical formula is suitable to investigate the 2p radioactivity or not. In this work, due to the experimental data of 2p radioactivity nuclei with orbital angular momentum l = 0 were not observed in experiments, we choose the experimental data of true 2p radioactivity nuclei ( 19 Mg, 45 Fe, 48 Ni, 54 Zn and 67 Kr) with l = 0 and the predicted 2p radioactivity half-lives of 7 nuclei with l = 0 (1 case with l = 1, 4 cases with l = 2 and 2 cases with l = 4) extracted from Goncalves et al work [33] as the database.…”

“…where a and b represent the two isotopic chaindependent parameters of this formula. Later, the G-N law was widely applied to study the half-lives of α decay [46][47][48][49], cluster radioactivity [50][51][52] and proton radioactivity [53][54][55]. However, relative to α decay and cluster radioactivity, the proton radioactivity half-life is more sensitive to the centrifugal barrier, it leads to the linear relationship between the half-life of the proton radioactivity and the released energy Q p only exists for the proton radioactivity isotopes with the same orbital angular momentum l taken away by the emitted proton [44,53,55].…”

New Geiger-Nuttall law for proton radioactivity

“…Where ξ = Z 0.8 d / Q p is taken from Ref. [31]. In this circumstance, the Root Mean Square(RMS) deviation of the empirical estimates with respect to the experimental value are found to be 0.301, 0.648, 0.238 and 0.138 corresponding to l = 0, 2, 3 and 5.…”

“…Committed to extend this linear relationship to all available proton emitters, Budaca [13] and Sreeja et al . [31] employ the Brown-type empirical formula [33] to determine the contribution of the charge of the daughter nucleus Z d i.e. a particular power value of dependence on Z d .…”

“…To verify the information of proton radioactivity half-life, Sreeja et al . [31] follow the Browntype empirical formula to propose a new formula with including orbital angular momentum l dependence, it is expressed as…”