  The scaled harmonic oscillator basis (SHO) is derived by a local
scaling-point transformation of the spherical harmonic oscillator radial wave
functions. The unitary scaling transformation produces a basis with improved
asymptotic properties. The SHO basis is employed in the solution of the
relativistic Hartree-Bogoliubov (RHB) equations in configurational space. The
model is applied in the self-consistent mean-field approximation to the
description of the neutron halo in Ne isotopes. It is shown that an expansion
of nucleon spinors and mean-field potentials in the SHO basis reproduces the
asymptotic properties of neutron densities calculated by finite element
discretization in the coordinate space. In the RHB description of neutron skins
and halos, SHO bases in two or three dimensions can be a useful alternative to
technically complicated solutions on a mesh in coordinate space.
