As I understand it, the surface of a neutron star is an iron shell.
"Current models indicate that matter at the surface of a neutron star is composed of ordinary atomic nuclei crushed into a solid lattice with a sea of electrons flowing through the gaps between them. It is possible that the nuclei at the surface are iron, due to iron's high binding energy per nucleon. It is also possible that heavy elements, such as iron, simply sink beneath the surface, leaving only light nuclei like helium and hydrogen. If the surface temperature exceeds 10^6 kelvins (as in the case of a young pulsar), the surface should be fluid instead of the solid phase that might exist in cooler neutron stars (temperature <10^6 kelvins)."
Reading a little further into the wiki, the depth of atomic matter is controlled by the neutron drip line. Since neutron stars have a maximum mass, this is likely a feature that they all exhibit.
At the beginning of the neutron drip, the pressure in the star from neutrons, electrons, and the total pressure is roughly equal. As the density of the neutron star increases, the nuclei break down, and the neutron pressure of the star becomes dominant. When the density reaches a point where nuclei touch and subsequently merge, they form a fluid of neutrons with a sprinkle of electrons and protons. This transition marks the neutron drip, where the dominant pressure in the neutron star shifts from degenerate electrons to neutrons.
I suppose you meant neutrons instead of atoms.
Atoms do not exist in a neutron star. At least, non in any significant quantity.