  The macroscopic model for a neutron star (NS) as a perfect liquid drop at the
equilibrium is formulated for derivations of the particle number density
$\rho$, equation of state (EoS) for the pressure $P=P(\rho)$, and the NS mass
expressions, $M=M(R)$. We use the leptodermic approximation $a/R<<1$, where $a$
is the crust thickness of the effective NS surface (ES), and $R$ is the mean
radius of the ES curvature. Within the approximate Schwarzschild metric
solution to the general relativity theory equations for the spherically
symmetric systems, the macroscopic gravitation is taken into account in terms
of the total separation energy and incompressibility in the simplest form as
expansion of a gravitational potential $\Phi(\rho)$ in powers of
$\rho-\overline{\rho} $, where $\overline{\rho}$ is the saturation density, up
to second order. Density distribution $\rho$ across the ES in the normal
direction to the ES was obtained analytically for a general form of the energy
density $\mathcal{E}(\rho)$ in the leading order of parameter $a/R \ll 1$. For
the typical crust thickness, $a \sim 1$ km, and effective radii, $R\sim 10$ km,
one finds the leading expression for the density $\rho$. NS masses are
analytically calculated as a sum of the volume and surface terms, $M(R)=M_{\rm
V}+M_{\rm S}$, taking into account the radial curvature of the Schwarzschild
metric space, in reasonable agreement with recently measured masses,
$M=(1.4-2.0) M_\odot$, and radii, $R=10-14$ km, for several neutron stars. The
energy tension coefficient is derived with accounting for the Schwarzschild
metric correction. We derive the simple macroscopic equation of state,
$P=P(\rho)$, with the surface correction. The analytical and numerical
solutions to Tolman-Oppenheimer-Volkoff equations for the pressure are in good
agreement with the volume part of our EoS.
