Gravitational Shapiro Phase Shift on Pulsars' period to detect Dark Matter

The Shapiro Phase Shift on Pulsars (SPSP) influence at low , but detectable level the pulsars' (PSR) periods and their derivatives. This effect may be already written in PSRs' time derivative deviation and in particular it may explain the presence of a few negative pulse derivatives among 558 known PSRs. We describe in detail the phenomenon and predict that the SPSP may play a role in period derivative deviations for just a few PSRs a year ( 0.5 - 5 ev / yr) at a positive period derivative 10^-14 - 10^-15 s/s level , leading to a plausible explanation to the puzzling negative pulse derivative of few PSRs' periods.