Since Radiohead’s new album is finished (and due out Saturday!), the band’s members now have some free time on their hands. Guitarist Jonny Greenwood will spend his R&R scoring another film, as The Playlist reports that Greenwood has committed his talents to Lynne Ramsay‘s upcoming drama, We Need To Talk About Kevin.

Based on a 2003 novel by Lionel Shriver, the film tells the story of a mother (Tilda Swinton) of a teenage boy who went on a high-school killing spree tries to deal with her grief — and feelings of responsibility for her child’s actions — by writing to her estranged husband (John C. Reilly). Scottish director Lynne Ramsay, best known for the films such as Ratcatcher and Morvern Callar, will oversee the project.

According to IMBD, the film is due out sometime in 2011. There is no word on if and when the soundtrack will receive release. While we wait for additional details, be sure to pick up Greenwood’s other recent film score, Norwegian Wood, when it hits U.S. stores March 8th via Nonesuch.