Systematic study on proton radioactivity of spherical proton emitters within two-potential approach

In the present work we systematically study the half-lives of proton radioactivity for spherical proton emitters with Z $\ge$ 69 based on two-potential approach. While the nuclear potential of the emitted proton-daughter nucleus is adopted by a parameterized cosh type, the parameters of the depth and diffuseness for nuclear potential are determined by fitting experimental data of 32 spherical proton emitters. In order to reduce the deviations between experimental half-lives and calculated ones, we propose a simple analytic expression for formation probability of proton radioactivity with the same orbital angular momentum l. The results indicate that the formation probability can be simply described by a formula of A${}_d^{1/3}$. Moreover, the linear relationship between the formation probability and the fragmentation potential also exists. The calculated half-lives can well reproduce the experimental data.