  We developed a new model for the X-ray spectral fitting \xspec package which
takes into account the effects of both thermal and dynamical (i.e. bulk)
Comptonization. The model consists of two components: one is the direct
blackbody-like emission due to seed photons which are not subjected to
effective Compton scattering, while the other one is a convolution of the
Green's function of the energy operator with a blackbody-like seed photon
spectrum. When combined thermal and bulk effects are considered, the analytic
form of the Green's function may be obtained as a solution of the diffusion
Comptonization equation. Using data from the BeppoSAX, INTEGRAL and RXTE
satellites, we test our model on the spectra of a sample of six persistently
low magnetic field bright neutron star Low Mass X-ray Binaries, covering three
different spectral states. Particular attention is given to the transient
powerlaw-like hard X-ray (> 30 keV) tails that we interpret in the framework of
the bulk motion Comptonization process. We show that the values of the best-fit
delta-parameter, which represents the importance of bulk with respect to
thermal Comptonization, can be physically meaningful and can at least
qualitatively describe the physical conditions of the environment in the
innermost part of the system. Moreover, we show that in fitting the thermal
Comptonization spectra to the X-ray spectra of these systems, the best-fit
parameters of our model are in excellent agreement with those of COMPTT, a
broadly used and well established XSPEC model.
