When Jeane Kirkpatrick, a professor at Georgetown University and a lifelong Democrat, wrote a magazine article last year criticizing President Carter, one response she received was a warm, complimentary letter from Ronald Reagan.

The Republican candidate said he wanted to meet her, and after they got together, Kirkpatrick said, she found she liked him very much. By the time Reagan defeated Carter in last week's presidential election, Kirkpatrick had become one of Reagan's most visible foreign policy advisers and an articulate partisan on his behalf. She now is on the president-elect's transition team, and may be named to an important job, in his administration, though she says she isn't seeking one.

"It represented a really big step for me [to support Reagan]," said Kirkpatrick, 52, who had worked ardently for Hubert Humphrey in three presidential campaigns. "But I did it wholeheartedly. I had just become totally dismayed with Jimmy Carter."

Though Kirkpatrick's political odyssey was longer than most, she was far from alone this year at Georgetown University. For Georgetown was a leading center of ideas and advisers for Reagan's presidential campaign. It now may be an important source of talent when he moves into the White House.

"At least Harvard is being pushed out," said the wife of one Georgetown professor. "They've always been number one."

In the informal sweepstakes of which university supplies the most manpower for the new administration Georgetown may not be number one either. Indeed, Stanford University in Reagan's home state of California had more members of his preelection advisory committees than any other college.

But the 15 listed from Georgetown were second to the 22 from Stanford. No other university came close, and some of those involved at Georgetown see that as a further sign of the university's ascension to the academic big leagues.

"Georgetown University used to be as good as the Washington arts were 20 years ago, the kind of level that Cleveland wouldn't spit at," said Edward N. Luttwak, an expert in strategic studies who was educated at the London School of Economics and John Hopkins University. "Now Georgetown's standards have increased immeasurably. I think it's going places, and I got on board the ship. There were others who launched the ship."

Luttwak, who has been advising Reagan since his first choice, Sen. Howard Baker (R-Tenn.), dropped out of the presidential race last spring, said the Republican president-elect also turned to Georgetown because of the university's relatively large collection of conservative academics whose outlook is compatible with his own.

Georgetown has been a relatively conservative school since its inception," Luttwak said. "That's probably less true now than it used to be, but the people who have the ideas now -- right or wrong -- are the conservatives, across the board in domestic and foreign policy, and the others have to respond to them."

"I think there's a human, institutional tendency for a clustering of people with a like point of view," said Robert Kupperman, a senior fellow at the Georgetown Center for Strategic and International Studies (CSIS). "There's no party line, but Brookings and Harvard have tended to be liberal, and Georgetown has tended to be politically right of center. I wouldn't call it a bastion of Republicanism. It's broadening itself all the time. But it's natural that Reagan would find a lot of people to work for him here.

Indeed, in foreign and defense policy Georgetown contributed more members of Reagan's advisory panels than any other university. Stanford, however, was far more heavily represented on the domestic issues side, and also provided the two top managers of the candidate's domestic policy groups, Martin Anderson and Darrell Trent. Many of the Stanford advisers came from the university's traditionally conservative think tank, the Hoover Institution.

Georgetown's own think, the Center for Strategic and International Studies (CSIS), produced about two-thirds of university's Reagan advisers. The center occupies three floors of an office building at 18th and K streets NW -- far from the main Georgetown campus and relatively close to the White House.

The most prominent of them, former Secretary of State Henry Kissinger, carries the title of counsellor at the center and has his office there. He became an adviser to Reagan after the Republican convention in Detroit. But many others at CSIS had joined the Reagan effort well before that.

Luttwak, 38, who has written a book on the strategy of the Reagan Empire as well as analyses of current defense capability, said that he had some doubts about Reagan at first. "But when I met him we had a short but deadly serious conversation and he had impressed the hell out of me on the substantive issues."

Luttwak said he asked Reagan "a very tricky question" about how he could square the support he was getting from ideological libertarians with what Luttwak believes is the need for a draft in order to field an effective army.

Luttwak said Reagan replied that the United States cannot have military conscription until a president studies the issue and builds support for it, otherwise "you would just have a revolt on your hands." He said Reagan told him another problem with an immediate draft was that the military's cadre of noncommissioned officers has deterriorated so much that a flood of draftees could create a breakdown even worse than the present situation.

"These were very subtle observations," Lutwak said. "From that moment on I knew that everything I had been reading about [Reagan] was very misleading."

Luttwak said he hasn't met Reagan again, but was called on regularly during the campaign to supply paragraphs and short texts for the candidate's "speech-writing machine."

Robert G. Neumann, vice chairman of CSIS and a former U.S. ambassador to Afghanistan and Morocco, served as the head of Reagan's Middle East advisory group and briefed the candidate several times at Reagan's rented estate near Middleburg, Va.

Another scholar at the center, Chester A. Crocker, headed Reagan's task force on Africa. Ray S. Cline, a former deputy director of the CIA who now is executive director for world power studies at CSIS, was on the intelligence advisory group.

The two Georgetown economists who served as Reagan advisers were Lev Dobriansky, 62, a long-time Republican stalwart, and Paul Craig Roberts, 41, who used to be a staffer for a Republican congressman and an editorial writer for the Wall Street Journal before coming to Georgetown last summer.

Roberts takes credit for writing the original Kemp-Roth bill in 1976, which serves as the basis for Reagan's current tax cut proposals.

Would he like to work in Reagan's new administration?

"I really don't know," Roberts said. "You give up a lot when you're in the government."