We report on a search for pulsars at the positions of eight low-mass white dwarfs and one higher-mass white dwarf with the 100-m Effelsberg Radio Telescope. These systems have orbital parameters suggesting that their unseen companions are either massive white dwarfs or neutron stars. Our observations were performed at 1.36 GHz, reaching sensitivities of 0.1-0.2 mJy. We searched our data accounting for the possible acceleration and jerk of the pulsar signals due to orbital motion, but found no significant pulsar signals. Considering our result jointly with 20 non-detections of similar systems with the Greenbank Radio Telescope, we infer $f_{rm NS}leq 0.10$, for the fraction of NSs orbiting these white dwarfs. We discuss the sensitivity of this result to the underlying assumptions and conclude with a brief discussion on the prospects of targeted surveys for discovering millisecond pulsars.
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