An empirical formula for the half-lives of ground state and isomeric state one proton emission
Abstract.An empirical formula for the half-life estimates for the one proton transition from ground state and isomeric states of 44 proton emitters is presented. The experimental data of the logarithm of the half-life corresponding to different $\ell$ℓ-values, viz., $ \ell=0$ℓ=0 (8-emitters), $\ell =2$ℓ=2 (14-emitters), and $ \ell =5$ℓ=5 (19-emitters), of different proton emitters are separately fitted as a function of the charge number of the daughter and Q -value. The slopes and the intercept values from the obtained relations are found to vary linearly with the $\ell$ℓ-values for the choices of a particular power value of 0.8 on the $ Z_{1}$Z1 dependence. A linear relation of the slopes and intercepts is obtained as a function of $\ell$ℓ, thus resulting in a simple formula involving only four parameters applicable to different $\ell$ℓ-values. The proton emitters with $\ell =3$ℓ=3 (3-emitters) are not considered for the fitting. The obtained four parameter formula is applied to estimate the half-lives of the proton emitters with ℓ = 3. The predictions of the formula are found to be in good agreement with the experimental data for the proton emitters with $\ell = 3$ℓ=3. Our calculated values are compared with the available theoretical as well as empirical estimates of the experimentally known proton emitters. Further, the redictions for most possible proton emissions reported earlier are also compared with our calculations using the proposed formula. Because of the good overall agreement with the experimental data as well as with other theoretical/model predictions, this proposed formula may serve as a handy tool for planning new experiments.