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The spectral properties of X–ray radiation produced in a static atmosphere around a neutron star accreting at very low rates are investigated. Previous results by Alme & Wilson (1973) are extended to the range $10^{-7}\leq L/L_{Edd}\leq 10^{-3}L\sim 10^{31}-10^{32} \ {\rm ergs, s^{-1}}$, expected from isolated neutron stars accreting the interstellar medium. The emergent spectra show an overall hardening with respect to the blackbody at the neutron star effective temperature in addition to a significant excess over the Wien tail. The relevance of present results in connection with the observability of low–luminosity X–ray sources is briefly discussed.

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