We report on unusually very hard spectral states in three confirmed neutron-star low-mass X-ray binaries (1RXS J180408.9-342058, EXO 1745-248, and IGR J18245-2452) at a luminosity between ~ 10^{36-37} erg s^{-1}. When fitting the Swift X-ray spectra (0.5 - 10 keV) in those states with an absorbed power-law model, we found photon indices of Gamma ~ 1, significantly lower than the Gamma = 1.5 - 2.0 typically seen when such systems are in their so called hard state. For individual sources very hard spectra were already previously identified but here we show for the first time that likely our sources were in a distinct spectral state (i.e., different from the hard state) when they exhibited such very hard spectra. It is unclear how such very hard spectra can be formed; if the emission mechanism is similar to that operating in their hard states (i.e., up-scattering of soft photons due to hot electrons) then the electrons should have higher temperatures or a higher optical depth in the very hard state compared to those observed in the hard state. By using our obtained Gamma as a tracer for the spectral evolution with luminosity, we have compared our results with those obtained by Wijnands et al. (2015). We confirm their general results in that also our sample of sources follow the same track as the other neutron star systems, although we do not find that the accreting millisecond pulsars are systematically harder than the non-pulsating systems.
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