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Most of the spectra of neutron star low mass X-ray binaries (NS LMXBs), beingthem persistent or transient, are characterized by the presence of a strongthermal Comptonization bump, thought to originate in the transition layer (TL)between the accretion disk and the NS surface. The observable quantities whichcharacterize this component dominating the emission below 30 keV, are thespectral index alpha and the rollover energy, both related to the electrontemperature and optical depth of the plasma. Starting from observationalresults on a sample of NS LMXBs in different spectral states, we formulate theproblem of X-ray spectral formation in the TL of these sources. We predict astability of the thermal Comptonization spectral index in different spectralstates if the energy release in the TL is much higher than the intercepted fluxcoming from the accretion disk. We use an equation for the energy balance andthe radiative transfer diffusion equation for a slab geometry in the TL, toderive a formula for the thermal Comptonization index alpha. We show that inthis approximation the TL electron temperature kTe and optical depth tau_0 canbe written as a function of the energy flux from the disk intercepted by thecorona (TL) and that in the corona itself Qdisk/Qcor, in turn leading to arelation alpha=f(Qdisk/Qcor), with alpha ~ 1 when Qdisk/Qcor <<1. We show thatthe observed spectral index alpha for the sample of sources here consideredlies in a belt around 1 +/- 0.2 a part for the case of GX 354--0. Comparing ourtheoretical predictions with observations, we claim that this result, which isconsistent with the condition Qdisk/Qcor <<1, can give us constraints on theaccretion geometry of these systems, an issue that seems difficult to be solvedusing only the spectral analysis method.

On the stability of the thermal Comptonization index in neutron star low-mass X-ray binaries in their different spectral states