What psychoanalytic theory would be appropriate to apply to Henry James' Turn of the Screw for a final research paper I am working on? I would like to focus my paper on the central character, the governess.
As a graduate student, the main issue you will encounter in trying to apply psychoanalytic theory to Henry James' Turn of the Screw is that this story has been subject to various forms of psychoanalytic criticism ever since the appearance of Edmund Wilson's seminal essay "The Ambiguity of Henry James" in 1934. If you search through the MLA bibliography using "psychoanalysis" and "Henry James" as search terms, you will find a quite massive bibliography on the topic.
While the earliest forms of psychoanalytic treatment of James' work followed a Freudian path, more recent criticism has tended to be Lacanian, in both its structuralist and post-structuralist incarnations. Although Jungian readings are slightly less common, several do exist, often influenced by Northrop Frye. The difficulty with any of these approaches on a graduate level is that they require mastering an extensive bibliography of previous work and, for that reason, it is difficult to make an original contribution.
A possibility closer to the leading edge of contemporary criticism would be using evolutionary psychology, which is a far newer discipline, and has only recently been exploited by literary critics. To do this, you would look at the ways the governess reacts to various circumstances in terms of how such types of reactions or psychological mechanisms could have contributed to individual survival or reproductive success. For example, you could examine how the governess reacts to the children (despite her not being genetically related to them) in terms of how such reactions help humanity survive as a species.