Empirical formulas for proton decay half-lives: Role of nuclear deformation and Q-value

Two empirical formulas for the proton decay half-lives including nuclear deformation are proposed. The formula with parameter set I gives the logarithm of the proton decay half-lives as an explicit function of the orbital angular momentum with eight adjustable parameters, whereas that with set II represents the logarithm of the reduced half-lives as an implicit function of the angular momentum with seven adjustable parameters. Experimental data for the half-lives of 44 proton emitters in the ground state or isomeric state were used to obtain the parameters. The experimental and calculated Q values were used. Different sets of parameters were obtained for the ground state transition, isomeric state transition, and all transitions for both deformed and spherical nuclei. The best agreement with experimental data was observed for set I for deformed proton emitters with experimental Q values.