Among the cases brought by federal prosecutors last year was that of You Xiaorong, a researcher who left a job in Atlanta in which she researched BPA-free coatings for beverage cans used by the Coca-Cola Company. The indictment asserts that Dr. You, who is known as Shannon, was offered a Thousand Talents award “based on the secrets she stole.” She is alleged to have transferred trade secrets worth $120 million, uploading files to her Google drive and taking photographs of industrial laboratory equipment. Ms. You has pleaded not guilty.

Many investigations of academics are still in progress, but some accusations have been made public. Officials at M.D. Anderson Cancer Center in Houston and at the National Institutes of Health, for example, found emails and documents that they say revealed flagrant violations by some academic scientists, such as grant reviewers who sent confidential grant proposals detailing research plans to colleagues in China. In other cases, the N.I.H. said, researchers were getting patents or starting companies in China based on research carried out at a United States university with support from the federal government.

Dr. Mulvenon said explicit transgressions are thought to be only a part of the problem of keeping valuable United States technology safe.

It is, he said, a gray area. “It’s not a case of them stealing technology by infiltrating a computer,” he said “What we are seeing is them relieving the rest of the world of technology by means that are not necessarily illegal.”

He added, “We can’t say, ‘We don’t want to do research with the Chinese.’”

Peter Zeidenberg, a lawyer who is representing two dozen Chinese and Chinese-American scientists who are under investigation, noted that prosecutors in most of the cases have not alleged any technology transfers, and were focused instead on the scientists’ failure to disclose grants.

“They’re taking an unbelievably heavy-handed approach to this,” said Mr. Zeidenberg, a partner in the Washington, D.C., firm Arent Fox. “There is no compliance training on these forms. It’s just a form you get every year. Until very recently, nobody paid any attention this stuff. Now they’re cracking the whip and they’re treating these people like felons.”

Scores of Western scientists have applied for Thousand Talents grants over the years. In interviews, several described their decision as straightforward: China had money available.