President Carter has postponed his expected decision on producing neutron artillery shells and Lance missile warheads partly because of sharp criticism of the new tactical nuclear weapons that has developed in West Germany, according to informed government sources.

A debate over the weapons, which are planned for possible use on West German territory, has been raging in that country and has taken on political significance for chancellor Helmut Schmidt government.

Opposition to the neutron weapons has also been fanned throughout Europe by a concerted communist party campaign in countries on both sides of the Iron Curtain.

The President, a White House source said yesterday, "wants to consult with our allies," before announcing his decision on the weapon.

Carter, a White House spokesman said last month, was to disclose his final production decision shortly after Aug. 15, the date a Defense Department Energy Research and Development Administration report on the weapons was due at the White House.

Yesterday a Carter aide said the report had been received, "but the President needs time to review it."

A presidential decision, the aide said, is not expected now until September.

Neutron weapons are the first tactical nuclear shells and warheads that kill enemy troops through enhanced radiation rather than by heat and blast.

Because the neutron shells and warheads cut down on blast and heat, proponents argue they cause less collateral damage off the immediate battlefield.

The larger proposed neutron 8-inch shell, however, also would deliver a radiation dose one mile from ground zero large enough to kill, within 60 to 90 days, almost half the people exposed to it. The others who took such a dose would become temporarily ill and, after recovery, be more likely than those not exposed to get leukemia or some other form of cancer in later years.

During the Senate debate on the funds for production of the neutron weapons, proponents argued the neutron weapons, since they would create less physical destruction in Europe, could be used in West Germany and on the territory of other NATO allies.

Up to that point, the general public understanding in Europe had been that tactical nuclear weapons deployed with NATO forces were to be used in East Germany or other Communist countries.

Disclosure of the neutron weapons and the idea they would be used in NATO, rather than Warsaw Pact, countries set off the present debate.

It has been acrimonious, in part because NATO Commander Gen. Alexander M. Haig said the allies had already given the neutron weapons "enthusiastic support."

President Ford last November approved production of neutron shells for the 20-mile-range 8-inch howitzer and the warhead of the 56-mile-range Lance missile. His decision, however, was classified and thus kept secret from the public.

When news stories on the new neutron weapons first appeared in June, however, both President Carter, his White House aids and NATO governments said they had not known about the planned shells and warheads.

Pentagon officials have said they wanted to take development of neutron weapons secret from Soviet and other Communist governments until they were produced and deployed to NATO forces in Europe.

Under current planning, that deployment - if the President decides to go ahead - would not take place until 1979.

According to Pentagon officials, NATO military commanders and defense ministers from the NATO countries were told last year about the neutron weapons as part of a U.S. program to modernize the tactical nuclear weapons in Europe.

Those same Pentagon officials said no strong opposition to the U.S. plan was voiced at the time.

In July, Egon Bahr, executive secretary of Schmidt's ruling Socialist Democratic Party, wrote in the party's newspaper that production of the neutron weapons was "a symbol of mental perversion."

Other West German figures and publications have also weighed in with criticism of the weapons. But the more conservative Christian Democratic Party in West Germany has generally shown support for the weapons.

In addition to the foreign policy implications of the neutron weapons, President Carter is reportedly weighing these other factors:

The present nuclear 8-inch shells are 20 years old, have no sophisticated security devices, are slow in loading and possess a short, nine-mile range. Their power, said to range from less than one kiloton to between five and ten kilotons, is not enough to be totally effective against new Soviet tanks, which have been designed to withstand blast and thermal effects.

Because neutron weapons cause less collateral blast damage, opponents say, military commanders would be more likely to recommend their use - thereby lowering the present nuclear threshold.

A U.S. decision to go ahead with neutron weapons, could affect negotiations with the Warsaw Pact countries on reducing European military forces.