President Carter's decision to put the neutron "bomb" in cold storage has created a dangerous leadership crisis not only in the Western alliance he is supposed to lead but at the bewildered highest levels of his won administration as well.

"As of March 23, every top official in this administration, and many just under the top, favored full speed ahead on the neutron," one middle-level official appointed by the president told us. Yet, on that day, Carter decided to cancel the enhanced radiation warhead designed to spare both civilians and structures while immobilizing enemy tanks. There was no significant new consultation with senior advisers.

Why did he take that step, by which, whatever his intention, he seems to have succumbed to Soviet pressure and abandoned his March 17 Wake Forest pledge to demand tit-for-tat concessions from Moscow? Nobody is sure. Explanation range from failure of the neutron warhead to meet the president's technical-engineering standards to his emotional quest for a nuclear-free world.

Some administration offcials feel political pressure will force Carter to order production. But even so, an attempt to trace what happened finds disconcerting answers: Although the decision-making process is chaotic, blame attaches directly to the president, not to his aides.

The only high official who had publicly expressed concern over the neutron warhead was U.N. Ambassador Andrew Young, whose jurisdictional connection is dim. Everybody else of importance argued forcefully for the warhead, even if only as a bargaining chip. That included Defense Secretary Harold Brown, Secretary of State Cyrus Vance and National Security Adviser Zbigniew Brzezinski.

Young's public opposition was mild. But privately, just before he and Carter sojouned to Latin America and Africa, Young told the president: This is a terrible, terrible weapon. How can we go to the special U.N. session on disarmament with this on our hands?

But Young is not perceived by close Carter-watchers as the only influence. Hamilton Jordan, Carter's political aide who is now privy to every presidential decision in foreign-military policy, is privately regarded as "the missing link" in the chain of advice that routed the Vance-Brown-Brzezinski regulars. "It's heart-breaking," one official who blames Jordan told us. "The whole government was going the other way."

In the background was the Soviet propaganda campaign. European heads of state - and particularly left and center-left parliamentarians - were warned that a go-ahead would have ominous results on Soviet conduct in Western Europe.

Soviet President Leonid Brezhnev sent personal letters to President Valery Giscard d'Estaing of France and other NATO heads of state that were quickly forwarded to Carter. The presumption is that those dire warnings had an effect on the president.

Moscow's propaganda campaign peaked when the Kremlin-controlled World Peace Council held an anti-neutron "conference" in Washington Jan. 25. Several congressmen who fought appropriations for the neutron last September were invited to the first Washington rally of that Helsinki-based council (though we find no record of any having attended). The Soviet propaganda campaign is under direct control of Politburo member Boris Ponomarev, who visited Washington this year.

The effect of that campaign was described last week by Sen. Sam Nunn (D-Ga.) as Moscow's "most successful" propagandizing in postwar history. At least it probably escalated Young's concern over how a neutron go-ahead would affect President Carter's scheduled appearance at the United Nations next month.

Some Carter insiders feel that the president, as in the coal strike, failed to focus on the neutron issue until far too late, giving the impression he was for production but not entirely committing himself. An almost exact parallel can be found in the astonished reaction within the administration last summer when, contrary to expectations, he canceled the B1 bomber.

According to one highly credible theory, Carter did not truly come to grips with the neutron until just before his Latin American trip. He made the decision in the near isolation of his inner White House staff, falb bergasting his foreign-and military-policy makers and undermining his European allies.

The last effort to switch Carter's position came on the long Air Force One ride back to Washington from Liberia. Vance and Brzezinski huddled with the president, pressing him to change his mind.

But what finally persuaded him to announce his decision last Friday to "defer" production - instead of cancel it outright - was not those advisers but the firestorm of criticism in The New York Times, The Washington Post and other influential papers.

That leaves the president facing disorder, disillusionment and incredulity among the men he named to guide his national security apparatus. That witches' brew of discontent could prove even more disabling to him than the wreckage of the neutron policy now strewn across Western Europe.