Chicago Manual of Style Online
”Item in a commercial database
For items retrieved from a commercial database, add the name of the database and an accession number following the facts of publication. In this example, the dissertation cited above is shown as it would be cited if it were retrieved from ProQuest’s database for dissertations and theses.
Choi, Mihwa. “Contesting Imaginaires in Death Rituals during the Northern Song Dynasty.” PhD diss., University of Chicago, 2008. ProQuest (AAT 3300426).”
Thus, maybe?:
Moore, Carole Elizabeth. “Queen Emma and the Role of Women in Anglo-Saxon Society”. PhD diss., University of California, Santa Barbara, 1973. ProQuest (AAT 7511496.)