When presidents fall out

President and ex-presidents sometimes fall out. Truman and Eisenhower had that problem. And now so do Reagan and Carter. The campaign left their relationship quite bruised. But, according to associates of both men, the two have moved even farther apart as time has gone on.

Jimmy Carter is unamused over what he sees as less than considerate treatment from Reagan. He'd like to be consulted, particularly on matters where his background of experience, as in the Mideast, might provide information that the President would otherwise not have.

Carter had not hit it off too well with Ford either. But, at least in the early years of his presidency, he talked with Ford fairly frequently, using him as an adviser.

Also, Carter saw to it that Ford was kept well briefed on foreign affairs. Here again Carter faults Reagan for not keeping him similarly briefed. He felt especially uninformed when he attended Sadat's funeral. Both Nixon and Ford had been briefed on the Mideast. He had not.

Carter was asked by Reagan for support on the AWACS sale - and he gave it to him. It was at that time, last fall, that Carter also met with Reagan in the White House. And it looked for a while as though these adversaries were in the process of burying the hatchet.

But it didn't happen. Reagan and his aides felt that Carter, in his later meeting with the press, was excessively critical of the President. They did not like some of his words. Their perception is that Carter intensely dislikes the President and can't keep from showing it.

So the rift is widening. And it all sounds petty. It is preventing the government and the American people from benefiting from the experience - and in this case, very recent experience - of a man who for four years was at the center of global events.

This is not to say that Carter, a president retired by the voters, should be in a controlling advisory position. But he should be permitted to have his views presented to the President, along with the two other former presidents, Messrs. Ford and Nixon, on the critical issues of the day.

Carter may very well have had access to information that no one else knows about. Also, as a former president, he has earned the right to be listened to with respect by an incumbent president.

Asked if Carter had been consulted by the President on the Falklands crisis, a Carter associate who had just talked to him said, ''No, he has not.''

In recent days the Reagan people have been less than enchanted over the report that Carter is planning a trip to the Mideast to meet with leaders and help push the peace process forward. A Reagan spokesman said, ''We know nothing about it.'' But there is anxiety within the White House that Carter might be meddling in foreign affairs.

According to a source close to Carter, the former President would be pleased to act as an official special emissary or trouble-shooter in the Mideast. He would have found such an appointment a natural one. But, short of being asked by the President for help of this nature, Carter will not do anything to suggest he is acting in any official capacity. If he does visit the Mideast, he will make it clear that he is there only as a private citizen.

Carter does, however, intend to become more visible in the days ahead. Those who have talked with him recently say that he has come out of the ''low'' period following his electoral defeat, which he at first read as a public rejection of both himself and his presidency. He is perking up, ready to leave little Plains where he has in effect been hiding from public view.

Last weekend Carter, who now thinks that he and his presidency are being vindicated by events, came to Washington to address the Montgomery County Democratic Party's annual spring fund-raiser. And he is thinking of addressing the Democratic Party's midterm conference in Philadelphia in late June.

But Reagan and Carter remain far apart. It seems so needless and, in terms of the national interest, so wasteful of experience and talent.