Defense Secretary Harold Brown and the new Energy Secretary, James R. Schlesinger, may be headed for a fight over' who controls the nation's multibillion-dollar nuclear weapons research and production establishment.

Thanks to a series of rapid government reorganizations that swallowed up the old Atomic Energy Commission, the bomb builders now have come to rest as part of Schlesinger Department of Energy.

But Brown, in letters last April to President Carter and the Senate Governmental Affairs Committee on the energy department organization, said he wanted "leftoperation "should be transferred to the Department of Defense."

He aded, "I would like to have the opportunity to review various management alternatives with the new Secretary of Energy."

Brown, an aide said recently, would not discuss when he plans to talk with Schlesinger about the weapons program.

A spokeman for Schlesinger said there would be a review of how the weapons program worked in the new department. "Somewhere down the road."

He added that an assistant secretary of energy for national security matters had been established by the energy Department legislation. Moving the weapons operation to Defense, he said, would take legislation.

More than a bureaucratic fight over bodies is involved. Schlesinger, a former Defense Secretay himself with strong, controversial views about strategic and tactical nuclear weapons, could use his department's responsibility for the nuclear porgrams "as a springboard back into national security matters," a key Capital Hill aide involved in defense matters said recently.

Carter seriously considered Schlesinger for Defense Secretary but chose Brown instead after some Democrats protested hiring the former Nixon-Ford Cabinet officers.

Brown, according to Pentagon sources, believes the time has come to bring the nuclear weapons program into the Defense Department for better planning.But, said one official, he is aware of Schlesinger's potential defense role as long as he controls the nuclear bomb builders.

The government-owned nuclear weapons operation is made up of thLos Alamos, N.M., and Livermore, Calif., research laboratories, test sites in New Mexico and Nevada, production plants in seven other states and 30,000 employees.

For the next fiscal year, Congress has approved $1.4 billion for nuclear weapons research, testing and nuclear weapoms research, testing and producton. And, $500 million will be spent for production of plutonium and other materials for use in nuclear weapons.

Since the first debates on the Atomic Energy Act in 1946, there has been a running controversy over whether civilian or the military establishment ought ot controlresearch and production in the nuclear weapons field.

The compromise written into the act established a civilian agency, the Atomic Energy Commission, run by civilian commissioners.

But, within the AEC a division of military applications was established to be run by a military man on active duty.

In addition, a military liaison committee was established made up of representatives of the military services, headed by a civilian appointed by the President.

The military committee recommended research and production program to the AEC. If they were turned down, the committee, through the Defense Secretary, could appeal that decision to the President.

When the AEC was abolished in 1974, its military applications division, as the nuclear weapons establishment was called, went into the Energy Research and Development Administration.

When ERDA, this year, became Department of Energy, the weapons program went with it.

At that time, however, a study was ordered to see if the weapons operation should go to Defense or another independent agency reporting directly to the President. The latter course would continue the idea of civilian agency rather than military control over the nuclear bomb-building process.

Completed in 1976, the study expanded on the three alternatives - shifting to Defense, creating a new agency and what the Ford administration chose, keeping the program within ERDA.

One military critic of the present situation put it this way. "Under the AEC, weapons was half the program. Under ERDA it was one-sixth. Under DOE it will be one-tenth. it isn't getting the attention it deserves."

This year, for the first time, the House and Senate Armed Services committees got their first close look at the nuclear weapons program since the demise of the Joint Atomic Energy Committee.

The Senate committee, in its report, hinted that co-ordination between ERDA and the Pentagon was not close enough. The committee cut more than $10 million from nuclear weapons production, saying the ERDA request did not reflect what the Pentagon believed could be done.

A Capitol Hill aide involved in the nuclear review said rencently he believed the Livermore and Los Alamos nuclear laboratories would be the focus of future investigations because of the freewheeling way they operate.