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[Background] In our earlier work {\bf [Phys. Rev. C 104, 055804 (2021)]}, westudied the surface properties of a neutron star, assuming it as a huge finitenucleus containing protons, neutrons, electrons, and muons. For the first time,we reported these results of a neutron star for a few representative masses. Inthe present paper, we give a detailed study of these quantities to drawdefinite conclusions. [Method]To carry forward our earlier idea, the energydensity functional of the momentum space of neutron star matter is converted tothe coordinate space in a local density approximation. This functional is againused to derive the neutron star surface properties within the coherent densityfluctuation model using the weight function obtained from the density profileof the neutron star using the recently developed G3 and widely used NL3 andIU-FSU parameter sets in the context of relativistic mean-field formalism.[Results] The systematic surface properties of the neutron star, such asincompressibility, symmetry energy, slope parameter, and curvature coefficient,is calculated. The volume and surface components of the total symmetry energyare decomposed with the help of the $\kappa$ factor obtained from the volume tosurface ratio of the symmetry energies in the liquid drop limit of Danielewicz.The magnitude of the computed surface quantities increases with the neutronstar's mass. [Conclusion] The incompressibility $K^{\rm star}$, symmetry energy$S^{\rm star}$, slope parameter $L_{\rm sym}^{\rm star}$ and curvaturecoefficient $K_{\rm sym}^{\rm star}$ of the neutron stars with different massare analyzed and found to be model dependent. NL3 is the stiffest equation ofstate endue us with the higher magnitude of surface quantities as compared tothe G3 and IU-FSU forces.

Systematic study for the surface properties of neutron star