  The neutron drop is firstly investigated in an axially symmetric harmonic
oscillator (ASHO) field, whose potential strengths of different directions can
be controlled artificially. The shape of the neutron drop will change from
spherical to oblate or prolate according to the anisotropy of the external
field. With the potential strength increasing in the axial direction, the
neutron prefers to occupy the orbital perpendicular to the symmetry axis. On
the contrary, the neutron likes to stay in the orbital parallel to the symmetry
axis when the potential strength increases in the radial direction. Meanwhile,
when the potential strength of one direction disappears, the neutron drop
cannot bind together. These investigations are not only helpful to simulate the
properties of neutrons in finite nuclei but also provide the theoretical
predictions to the future artificial operations on the nuclei like the
ultracold atom system, for a deeper realization of quantum many-body systems.
