n this study, the effect of the surface symmetry energy on the neutron skin thickness and division of it into the bulk and surface parts are investigated by determination of the symmetry energy coefficient asym(A) of finite nuclei. We demonstrate the importance of the isospin asymmetry distribution in the symmetry energy coefficient of finite nuclei at the surface region. We attempt to find out how different surface symmetry energies may affect alpha decay half-life. The Skyrme interactions are used to describe the neutron and proton density distributions and to calculate the symmetry energy coefficient asym(A) of four nuclei and the surface symmetry energy. The chosen Skyrme interactions can produce the binding energy and root-mean-square charge radii of both mother and daughter nuclei. We single out the spherical isotones of N = 126 named 208Pb, 210Po, 212Rn and 214Ra for daughter nuclei and explore the dependence of the bulk and surface contributions on the surface symmetry energy. The half-life of mother nuclei, i.e., 212Po, 214Rn, 216Ra and 218Th, is employed to investigate the extent to which it is affected by different surface symmetry energies. The calculated half-lives show a downward tendency for different surface symmetry energies which can be caused by various neutron skin thicknesses.
