  Half-life of proton radioactivity of spherical proton emitters is studied
within the scheme of covariant density functional (CDF) theory, and for the
first time the potential barrier that prevents the emitted proton is extracted
with the similarity renormalization group (SRG) method, in which the spin-orbit
potential along with the others that turn out to be non-negligible can be
derived automatically. The spectroscopic factor that is significant is also
extracted from the CDF calculations. The estimated half-lives are found in good
agreement with the experimental values, which not only confirms the validity of
the CDF theory in describing the proton-rich nuclei, but also indicates the
prediction power of present approach to calculate the half-lives and in turn to
extract the structural information of proton emitters.
