Using all the RXTE archival data of Sco X-1 and GX 5-1, which amount to about 1.6 mega seconds in total, we searched for possible occultation events caused by Oort Cloud Objects. The detection efficiency of our searching approach was studied with simulation. Our search is sensitive to object size of about 300 m in the inner Oort Cloud, taking 4000 AU as a representative distance, and of 900 m in the outer Oort Cloud, taking 36000 AU as the representative distance. No occultation events were found in the 1.6 Ms data. We derived upper limits to the number of Oort Cloud Objects, which are about three orders of magnitude higher than the highest theoretical estimates in the literature for the inner Oort Cloud, and about six orders higher for the outer Oort Cloud. Although these upper limits are not constraining enough, they are the first obtained observationally, without making any model assumptions about comet injection. They also provide guidance to such serendipitous occultation event search in the future.
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