  Recent observations and theoretical investigations of neutron stars indicate
that their atmospheres consist not of hydrogen or iron but possibly other
elements such as helium. We calculate the ionization and dissociation
equilibrium of helium in the conditions found in the atmospheres of magnetized
neutron stars. For the first time this investigation includes the internal
degrees of freedom of the helium molecule. We found that at the temperatures
and densities of neutron star atmospheres the rotovibrational excitations of
helium molecules are populated. Including these excitations increases the
expected abundance of molecules by up to two orders of magnitude relative to
calculations that ignore the internal states of the molecule; therefore, if the
atmospheres of neutron stars indeed consist of helium, helium molecules and
possibly polymers will make the bulk of the atmosphere and leave signatures on
the observed spectra from neutron stars. We applied our calculation to nearby
radio-quiet neutron stars with B_{dipole}~10^{13}-10^{14} G. If helium
comprises their atmospheres, our study indicates that isolated neutron stars
with T_{BB}~10^6 K such as RXJ0720.4-3125 and RXJ1605.3+3249 will have He^+
ions predominantly, while isolated neutron stars with lower temperature
(T_{BB}~5x10^5 K) such as RXJ1856.5-3754 and RXJ0420.0-5022 will have some
fraction of helium molecules. If helium molecules are abundant, their
spectroscopic signatures may be detected in the optical, UV and X-ray band.
(Abridged)
