Why is it Difficult to Detect a Millisecond Pulsar in Neutron Star X-ray Binaries?

We explain why it is possible to detect directly X-ray emission from near the surface of the neutron star (NS) in SAX J1808.4-3658 but not in most other low-mass X-ray binaries (LMXBs), with the exception that emission from the surface can be seen during bursts events. We show that the X-ray emission from SAX J1808.4-3658 mostly originates in the Comptonization process in a relatively optical thin hot region (with an optical depth $\tau_0$ around 4 and temperature is around 20 keV). Such a transparent region does not prevent us from detecting coherent X-ray pulsation due to hot spots on the NS surface. When the characteristic scattering time in the region is of order of inverse rotational frequency omega or higher then the amplitude of the harmonic oscillation decays exponentially with (tau_0 x omega). We give a precise model for the loss of modulation, such suppression of the QPO amplitude due to scattering can explain the disappearance of kHz QPOs with increasing QPO frequency. We also formulate general conditions under which the millisecond X-ray pulsation can be detected in LMXBs. We demonstrate that the observed soft phase lag of the pulsed emission is a result of the downscattering of the hard X-ray photons in the relatively cold material near the NS surface. In the framework of this downscattering model we propose a method to determine the atmosphere density in that region from soft-lag measurements.