Prior Restraint Hypo

Here is a hypo I am borrowing from Profs. Ides and May:

"Modern Mercenary, a monthly periodical, is about to publish an article entitled "Five Easy Steps to Making Your Own Thermonuclear Device." The author of the piece, G.I. Jones, is a nuclear physicist who gathered...his information from nonclassified sources....Although the government doubts that Jone's article will lead to the basement construction of nuclear weapons, government experts claim that publication will possibly provide sufficient information to allow a medium-sized nation[such as, perhaps, Iran] to move faster in developing a thermonuclear weapon."

Assume that federal law authorizes injunctive relief against anyone who publishes scientific data concerning weapons of mass destruction "with reason to believe such data will be utilized to injure the United States or to secure an advantage to any foreign nation." Would it be constitutional for a federal court to enjoin Modern Mercenary from publishing the above-described article?