The question was put to Stuart E. Eizenstat, President Carter's chief domestic policy adviser: what is the president's current thinking on the future of nuclear power in the United States, and has it changed since the accident at Three Mile Island?

Eizanstat paused before answering. "The findings of the Kennedy Commission will be important in making that determination," he said.

Ask that question around the White House these days and the response is likely to be pretty much the same. The president has appointed a special commission, headed by Dartmouth College President John Kemeny, to investigate the March 28 Three Mile Island accident and make recommendations on improving the safety of nuclear reactors.

Until the commission reports, in about six months, White House officials say, Carter is necessarily withholding judgment on the issue.

But, in fact, there is nothing in the president's worse nuclear power plant accident to suggest any fundamental change in his long-held view that there is a necessary role for nuclear power in the United States' energy future.

There has, however, been a standing in Carter's rhetoric on the issue since Three Mile Island, a tacit recognition that nuclear power could blossom into a major presidential campaign issue next year.

California Gov. Edmund G. (Jerry) Brown Jr., who is considered almost certain to challege Carter for the Democratic presidential nomination next year, has firmly staked out an antinuclear position. It was Brown who earlier this month addressed 65,000 people at an antinuclear-power rally at the Capitol, where the main theme was a demand to shut down existing nuclear reactors and not bulid any new ones.

Meanwhile, Sen. Edward M. Kennedy (d-Mass.), potentially the president's most formidable rival next year, has assumed at least half an antinuclear position. The day after Brown addressed the protesters on Capitol Hill, Kennedy called for an immediate moratorium on the construction of new nuclear power plants and an examination of the future of operating plants "on a case-by-case basis."

This has left Carter somewhere uncomfortably closer to the position by nuclear advocates, with an energy secretary, James R. Schlesinger Jr., who is as firmly identified in the public mind with pro-nuclear forces as actress Jane Fonda is with the opposition.

Since the accident at Three Mile Island, the president's strongest statement on the subject of nuclear power was his assertion, in response to the demands of antinuclear activits, that it is "out of question" ot consider shutting down all operating reactors.

But more often than not, Carter's statements on the subject since the accident have been a throwback to his 1976 campaign-style shetoric on so many other issues, in which he has appeared to suggest a softening of his position without really doing so.

The question was put to him directly on May 4 at a news conference in Des Moines. In light of findings on the likely health impact of the Three Mile Island accident, he was asked, "Have you begun to rethink your attitude about light water reactors?"

Carter replied: "I am deeply concerned about it, and, as you know, have appointed a special presidential commission to look into the cases of the accident, to see what mistakes may have been made in the design or the operation of the plant, to make more effective the Nuclear Regulatory Commission and also to make sure that, if we have a repetition at any time of a similar accidnet, that there be better coordination between private, local, state and federal officials.

"Obviously," he continued, "nuclear reactor safety is the preeminent concern, and I believe that this is an opinion shared by Americans throughout our nationa. It is not a new concern for me . . . But I think we have a proper degree, now, of commitment through this commission, which will report very expeditiously, commensurate with a broad range of their discussions and investigations in six months, to prevent any further accidents of this kind."

The questioner persisted, asking, "Do you still consider yourself a strong supporter of the concept of nuclear energy?"

"I have always thought that nuclear power should be used as a last resort in the evolution of energy," the president replied. "But I also recognize that when you use what oil is available and what coal is available and what solar energy is available, up until now we have seen a need to use nuclear power.

"We now get about 12 percent, I think, of our electricity from nuclear power . . . And it would not be advidable to terminate this peremptorily."

One White House aide argues that Carter should not make any formal pronouncements of his views about nuclear power until after the Three Mile Island commission reports its findings. To do so, he said, would tend to prejudice the commission's findings in advance.

But within the president's often convoluted answers to the questions asked him in Des Moines, there is a statment of his basic belief, a reiteration of a nuclear engineer's fundamental faith in the safety of nuclear reactors.

"I think we have a proper degree, now, of commitment through this commission . . . to prevent any further accidents of this kind," he said.

No one in the White House or the Energy Department disputes that this represents Carter's basic position and that it is not likely to change unless the Kemeny Commision comes up with unexpectedly disturbing findings about the long-range implications of the Three Mile Island accident.

Coupled with the president's repeated warnings about U.S. energy dependence, Carter woudl seem inevitably headed toward continued support of nuclear power, even if Three Mile Island had changed the political atmosphere and will probably slow the growth of nuclear energy.

"We have taken a position that nuclear will have a role-it will be a factor in our energy future," Eixenstat said. "How much of a factor and whether it will be accelerated is very much on open question."

"Jim's view," a Schlesinger aide at the Energy Department added, "is that nuclear has a role, and given what we're up against it is going to have a role." Since Three Mile Island, he added, there has been no pressure on Schlesinger from the White House to alter that view or his often outspoken comments on the subject.

Al least one Carter political operative recently lamented the president's failure to confront Brown and other antinuclear crusaders on the issue, to lay out bluntly the country's bleak energy options if the United States abruptly turns its back on atomic power.

But in the White House, the prevailing attitude is one of caution, to take comfort and cover beneath the umbrella affored by appointment of the Three Mile Island commisson.

Since the accident, White House officials have decided to delay introduction in Congress of legislation, long supported by the president, that would streamline the licensing procedures of the NRC, in effect cutting the time it takes to get new nuclear power plants licensed, built and operating.

But the decision to delay, one aide said, represented not any fundamental policy shift but a recognition of politiocal reality and the impossibility of gaining passage of such a measure so soon after Three Mile Island.

The administration has also established a task force, composed of aides from Eizenstat's staff, the Energy Department and the Office and Management and Budget, that will attempt to produce a concise statement on nuclear power before the commission reports in October.

Whatsever the task force produces, White House officials say they believe the key moment politically for the president will come when the commission reports.

The Carter aides remain uncertain of how important nuclear power may be as an issue in 1980. Potentially, they say, the antinuclear movement could have enormous impact, even it it is not likely ever to reach the intensity of the antiway movement of the 1960s that toppled Lyndon B. Johnson.

But it is not clear, one Carter adviser said, whether nuclear power is the kind of issue tha people will vote on, or just protest on a bright Sunday afternoon in spring.

As long as the commission is studying the issue, Carter can avoid, as he has so far, any hard and fast pronouncements on nuclear power. But come October, the commission report is likely to crystalize the issue and renew the debate started by Three Mile Island, just four months before the first presidential primary in New Hampshire.

It is then, a Carter adviser said, that the president will have "his maximum opportunity to position himself on the issue."