  We systematically investigate the neutron-skin thickness of neutron-rich
nuclei within a compressible droplet model, which includes several parameters
characterizing the surface tension and the equation of state (EOS) of
asymmetric nuclear matter as well as corrections due to the surface
diffuseness. Such a systematic analysis helps towards constraining the EOS
parameters of asymmetric nuclear matter and the poorly known density dependence
of the surface tension; the latter is estimated with help of available
experimental data for the neutron and proton density distributions and the
nuclear masses. Validity of the present approach is confirmed by calculating
realistic density distributions of Ca, Ni, Zr, Sn, Yb, and Pb isotopes within a
microscopic Skyrme-Hartree-Fock+BCS method for various sets of the effective
nuclear force. Our macroscopic model accompanied by the diffuseness corrections
works well in the sense that it well reproduces the evolution of the
microscopically deduced neutron-skin thickness with respect to the neutron
number for selected sets of the effective nuclear force. We find that the
surface tension of the compressible nuclear droplet is a key to bridging a gap
between microscopic and macroscopic approaches.
