BOSTON (Reuters) - The U.S. Coast Guard will not reopen a search for a 54-year-old woman whose fishing boat sank last week, despite the discovery of her son alive on a life raft a week after the incident, officials said on Monday.

Authorities had searched 62,000 square nautical miles off New England, an area larger than the state of Georgia, after Linda Carman, 54, and Nathan Carman, 22, failed to return to their Rhode Island port from a fishing trip on their 31-foot (9.5 m) boat the "Chicken Pox" on Sept. 18.

A passing freighter found the younger Carman alive in a life raft on Saturday, within the search area Petty Officer Nicole Groll outlined to reporters on Monday.

He told rescuers he had searched for his mother but failed to find her.

"The search window will not be reopened," Groll said.

(Reporting by Scott Malone; Editing by Bernadette Baum)