The United States, owner of the largest stockpile of atomic weapons in the world, could be running short of nuclear material to build the many new weapons the Pentagon thinks it may need in the coming years.

That question is now being studied by specialists in the Pentagon, the Department of Energy and the White House's National Security Council staff and budget office.

The problem is two-fold: Many new atomic missile warheads will be needed over the next decade for new weapons already being developed by the United States, and that number could increase dramatically if U.S.-Soviet talks on limiting such arms collapse entirely, which now seems a distinct possibility given the worsening superpower relations.

Such a situation would put considerable strain on U.S. plants that produce atomic explosives.

According to a memo circulating in the agencies concerned, "without remedial actions, there will be insufficient special nuclear material to support the build-up the Department of Defense claims it will need."

Furthermore, the memo points out, because it takes longer to set up facilities for producing nuclear material than it does to produce the missiles or other weapons that carry it, decisions may have to be made soon.

A variety of potential solutions are being studied. But if the answer is to build another huge nuclear reactor complex for turning out the special grade of plutonium that goes into atomic bombs and missiles, it could add several billion dollars more over the next 10 years to the cost of the next cycle in the arms race, informed sources say.

The United States is now believed to have more than 15,000 atomic weapons of all kinds -- bombs for big B52 bombers and smaller jets, warheads for thousands of large and small missiles, and atomic artillery shells.

Many of these weapons are old, built in the 1950s. The study is looking into whether the nuclear material from a few Polaris missile submarines, soon to be retired, can be used for newer missiles, or if some old battlefield nuclear weapons from Europe can be similarly transformed. Some of this has been done in the past. But how much is technically or tactically feasible for the new weapons coming along is not yet clear, specialists say.

The three reactors at the huge U.S. government plant along the Savannah River in South Carolina turn out the bulk of the plutonium used in weapons today. These reactors are said to be operating at less than full capacity and production could be increased somewhat. There are also two "reserve" reactors -- currently shut down -- at that plant. Another reactor at Hanford, Wash., currently producing plutonium for fuel, could produce weapons-grade material if a reprocessing facility there were reopened, sources say.

Officials estimate it would take about three years to get the reserve facilities started up again, at a cost of a few hundred million dollars each. It probably could double existing U.S. production capability, they say.

The concern is that this still won't be enough if the United States decides to match the surge expected in Soviet atomic weaponry if the strategic arms limitation process collapses.

The Soviets already have more ocean-spanning missiles than the United States does. Because many of the Soviet missiles are bigger than their American counterparts, they eventually could carry far more individual atomic bombs.

Intelligence estimates forecast that without a new SALT agreement, the Soviets could send about 14,000 atomic warheads toward the United States by 1989, just using their land-based missiles. The so-called "worst case" estimates are several thousand above that.

Even with SALT, however, the U.S. atomic arsenal is expanding more than is commonly recognized.

Current U.S. plans call for building the huge MX land-based missile, which can carry 10 or more individual atomic warheads, plus new Trident submarine missiles, new air-launched cruise missiles to be carried by B52 bombers, new ground-launched cruise missiles to be deployed in Europe and new 8-inch atomic artillery shells.

If SALT collapses, an expansion of the MX force undoubtedly will be proposed. However, some government studies show that the program that could be in for the biggest and most aggressive expansion would be the new air-launched cruise missile, for which Boeing recently won a big Air Force contract.

These missiles, about 20 of which can be carried aloft by a B52 and then aimed at targets 1,500 miles away, are the ones whose production could be most rapidly expanded. By using a modified version of one of the existing wide-bodied commercial jet airliners to carry the missiles, officials say studies show that about 6,000 of these jet-powered buzz bombs could be added to the force aboard 200 new planes in the next decade.

The new interagency study of nuclear production capabilities, which is supposed to be completed next month, also will look at the pace of new weapons programs and whether older weapons can be retired more rapidly as part of the effort to match plans with capacity.