To identify PDS in the Solar Orbiter density time series, we followed a spectral analysis procedure based on the multitaper method. First, we estimated the adaptive MTM power spectral density over running linearly de-trended six-, twelve- and eighteen-hour intervals with a 5 minutes sliding window. Then, we identified periodic variations in the time series at frequency values at which both the normalized spectrum and an additional statistical test for phase coherence (harmonic F-test) exceed the corresponding 90% confidence threshold. The combination of the MTM and the harmonic F-test is a robust approach that has been extensively tested and employed to identify PDSs in in situ measurements and remote-sensing observations. In order to determine the exact duration of each PDS event, we used the continuous wavelet transform and the Morlet wavelet as mother wavelet. We calculated the wavelet power of the total ion density time series in each of the six-, twelve- and eighteen-hour intervals identified as containing a PDS via the MTM method. Then, we isolated the time periods in which the power at the corresponding PDS frequency exceeded the 75th percentile of the power during the six-, twelve- and eighteen-hour interval (again at the same frequency as identified with the MTM method). Note that we examined the average power in the +-0.15 mHz range in order to account for the frequency uncertainty. Finally, in order to avoid any dubious detections, we required the duration of each PDS to be at least twice its period. This criterion produced a list of 29891, 38478 and 37974 PDS events for the six-, twelve- and eighteen-hour interval, respectively. CK received support from the ESA Archival Research Visitor Programme. S.D. was also supported by NASA Grant 80NSSC21K0459.