  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.
