The least known but most bitter competition for defense business these days is carried on between the nation's two government-owned nuclear weapon laboratories.

Battling between Los Alamos Scientific Laboratory in New Mexico and Lawrence Livermore Laboratory in California over which will design the newest bomb or missile warhead -- as they are now doing for the new landbased MX and submarine-based Trident II intercontinental ballistic missiles (ICBM) -- has been going on for more than 25 years.

The U.S. nuclear weapons development process encourages a competitive phase in every warhead program when each lab designs and often tests candidate devices.

In the current next-generation ICBM competition, which has been underway almost four years, each lab has some 12 separate candidate warheads covering a spectrum of warheads per missile, yields, effects and costs. And more are about to be tested.

Like civilian defense contractors, each lab also has a crew of liaison people -- called "salesmen" by scientists. Some are former military men and all deal with the Pentagon and the Department of Energy, keeping up on the desires of the services and promoting their own weapon designs.

Over the past few years, the intensity of the lab competition has increased, fueled in part by the future prospect of a nuclear test ban and declining budgets for weapons development.

Two years ago, Livermore openly questioned whether the Los Alamos Mark 12A warhead for the Minuteman III missile would work as its designers said it would.

Last August, former Los Alamos scientists publicly called attention to some problems that had developed in Livermore's Polaris ICBM. A few months later, those same scientists found themselves criticized publicly for their own weapons failure.

In September, a Los Alamos scientist was so enraged that a Livermore design for the ground-launched cruise missile was approved for production rather than his own lab's that he wrote the General Accounting Office calling for an investigation.

During a recent interview, a scientist in the nuclear weapons field who knows the work of both labs said, "I worry about the ethics of the players" in the increasingly petulant atmosphere. "It is destructive to the needs of the country."

He says the labs are trying to influence weapons decisions by "overselling" the nuclear effects of their designs "in the struggle to be No. 1."

Not everyone holds that view. At the Pentagon, for example, a key nuclear weapons official said "emotionalism of the scientists drives competition in the labs" but that it has been "an up-and-down thing."

"In the main," he concluded, "it has not been unhealthy."

Within the competition there is a good deal of mutual, although touchy, cooperation. For example, each lab reviews and comments on the other's underground nuclear test proposals and results.

That, of course, has led to controversy.Los Alamos scientists refer to a "California kiloton" when Livermore claims a higher yield for its devices than the data seem to the New Mexico group to justify.

Los Alamos, the home of the first atomic bombs, nestles on a picturesque 7,300-foot-high plateau of the Jemez Mountains, 35 miles from the nearest city, Santa Fe. Its seclusion, initially based on World War II security needs, continues today and gives the town, with its 17,000 population, the air of a nuclear Shangri-La.

Spread over 31 square miles, it retains much of the campus quality so in keeping with its professorial founder, Dr. J. Robert Oppenheimer.

Livermore, on the other hand, in setting and atmosphere reflects the probing, aggressive, imaginative nature of its founder, Dr. Edward Teller.

Packed within one square mile in a fast-growing California suburban valley, Livermore is almost astride a four-lane freeway that puts San Francisco slightly over an hour away.

One weapons scientist summed up the commonly accepted difference between the two labs, saying Los Alamos takes the position "we're here to serve the nation if it needs us," while Livermore "believes it's God's work to build bigger and better warheads."

A Livermore official put it differently. "Our job is to improve weapons... You turn over the stockpile [by building all new weapons] because it pays off in a variety of ways."

Not far below the surface of today's feuding are the still deeply felt feelings over the titanic Oppenheimer-Teller battle in the late 1940s and early 1950s over the future of nuclear weapons development. All the participants know that Livermore was born in 1952 at Teller's insistence to battle Los Alamos as it was being run by Oppenheimer's chosen successor, Dr. Norris Bradbury.

Staffed initially by aggressive scientists in the Teller mode, such as Herbert York, Harold Brown and John Foster, by the early 1960s Livermore had taken over as designer of the prestigious strategic warheads -- the Minuteman land-based ICBM and the sub-based Polaris ICBM.

When the low-key Bradbury resigned from Los Alamos in 1970, its new director, Dr. Harold Agnew, appeared determined to reinstate Los Alamos to its old position.

He apparently succeeded. Los Alamos over othe past few years has won the design competition for the newest generation of strategic misslle warheads -- the Minuteman Mark 12A, the Trident and the air-launched cruise missile. All are about to go into production.

Livermore, on the other hand, ran into bad luck. During the same period it designed the neutron, or enhanced radiation, warhead for the Lance missile and 8-inch shell -- both of which have been delayed in their neutron form by President Carter.

Livermore also designed, primarily for the B1 bomber, the new B77 strategic bomb, which also was delayed by the Carter administration. It now is going forward, but in a less elaborate design.

Another Livermore nuclear weapon, the Standard missile for the Navy's shipboard Aegis system, has been permanently delayed.

There is a feeling at both labs that the MX and Trident II warheads may be the last major ICBM systems for a long time. Thus both labs have made a major effort to win them.

Most of the seven to nine underground nuclear tests that each lab has had in each of the last few years have been used for potential ICBM warheads.

In that period, the Air Force profile of the warhead it is seeking for the MX changed radically and often.

According to one lab official involved in the MX program, the Air Force has talked at one time of one warhead and at other times of up to 14 on each missile. It has suggested yields for warheads that ranged from 100 kilotons to 1 megaton. Once it was to be three warheads at 500 kilotons each.

At one point, when the Air Force was talking of 14 or more warheads per MX missile, a DOE study showed such aprogram would use up all the plutonium and most of the enriched uranium stocks. Accordingly, the reactors building weapons-grade plutonium accelerated production.

In November 1976, the Air Force requested designs that would use less, rather than more, nuclear materials.

Just before the 150-kiloton-threshold test ban treaty went into effect, Los Alamos tested a 500-kiloton candidate. In their tests since, both labs have had to be satisfied with explosions of lower yields.

Livermore has appeared confident that it would get the nod on the MX warhead -- a decision expected sometime next year. In its five-year projections, a slick report of its past and future workload, Livermore flatly stated it would get the MX.

Los Alamos officials say the award of the MX to Livermore would be no surprise to them. The Department of Energy has tended in the past to divide the workload. In return, however, Los Alamos would expect to get the Trident II.

The policy of parceling the work between the loboratories seems to lie behind recent decisions by DOE to give the ground-launched cruise missile (GLCM) to Livermore and the extended-range Pershing II missile to Los Alamos.

Both weapons are for deployment in Western Europe and meet a request from NATO allies for a medium-range missile that can reach the Soviet Union from West Germany.

Each lab reportedly also plans to add one of its specially designed warheads to its missile.

Livermore is talking about putting a reduced residual radiation (RRR) warhead on the GLCM. That warhead would be maninly blast with almost no radiation -- an effect desired because the device would be aimed at reinforced concrete buildings and airport runways and thus would have to hit the ground to be effective.

Los Alamos is considering putting an earth penetrator warhead on its Pershing ballistic missile. This exotic device would bury itself in the ground before exploding, causing a huge cratering effect. It, too, would be aimed at concrete buildings and runways.

The RRR and the earth penetrator represent another aspect of the lab competition -- new effects. Both labs use a certain amount of their money for exploring new and sometimes novel ideas for future weapons -- and then sell them to the military.

Los Alamos began work several years ago on insensitive high explosives (IHE). The work began after several airplane accidents where the explosives in nuclear bombs went off and spread nuclear materials around the accident sites.

The IHE Los Alamos developed will not go off even if a bomb containing it is dropped. Therefore, nuclear weapons using IHE are much safer in handling.

Los Alamos proposed IHE first, in its B61 tactical bomb design, and when the B77 strategic bomb competition was underway, even Livermore was using IHE for a component. Now IHE is used in all new, large nuclear warheads.

Not all new proposals get accepted.

Livermore has been pushing insertable nuclear components (INCs), devices that, when placed in a conventional Navy heavy gun round, for example, would change it into a nuclear weapon. Alerted by the Arms Control and Disarmament Agency about the arms control implications of such a device, the White House refused to permit Livermore to test the concept.

In its place, Livermore developed a different type of insertion mechanism, one that would be used only with nuclear weapons. It, too is an INC, but by keeping the nuclear component separate from the rest of the weapon it is more secure from theft.

Livermore also has worked out an automated computerized arming system for its INCs system, thereby eliminating, the designers say, any problems with human failures.

The Mrk 12A fight between the two laboratories illustrates what could become a serious future problem in the event of a comprehensive test ban -- two labs disagreeing, in this case, over the yield of a weapon, with no testing permitted to see which is right.

In the early 1970s the Pentagon decided it wanted to beef up the power of its Minuteman III ICBMs so they could destroy Soviet missile silos. At the same time, however, the Pentagon did not want to build a costly new missile -- only a new warhead with the same shape, weight and volume as the existing one.

From the labs, however, it wanted double the yield -- from 175 kilotons to 350 kilotons -- with roughly the same amount of nuclear material. (To give some sense of proportion, the bomb dropped on Hiroshima was 12.5 kilotons.)

Livermore, which designed the Mark 12 warhead for the Minuteman III, said the Pentagon's request couldn't be fulfilled. Los Alamos said it could.

It designed a weapon that Livermore critics said would not provide the double yield. The design was tested underground at full yield and, in the words of a Los Alamos scientist, "flopped."

Before a new version could be put together, the threshold test ban went into effect in May 1976. That limited both the United States and the Soviet Union to testing devices of less than 150 kilotons.

Los Alamos scientists maintained their revised warhead would make 350 kilotons. Livermore scientists said it wouldn't. It couldn't be tested.

Also irritating Livermore was that, in changing its design, Los Alamos added 35 pounds to the new warhead. That required the Air Force to redesign the nose cone and delayed the Mark 12A program several months, adding substantially to the cost.

As competitive as the labs had been in the past, neither had ever gone as far as to raise formal, serious doubts about the work of the other.

That was a step, however, that Livermore took on the Mark 12A. It formally questioned the Los Alamos device in a presentation to the Washington-based officials who ran the nuclear weapons program.

It also raised the issue in conversations with people on Capitol Hill and in the Pentagon.

As a result, something formal had to be done to settle the squabble between the two labs.

A special panel of scientists was established to come up with a certification of the Mark 12A. The panel was headed by Dr. John Foster, a former Livermore director.

Last year the panel certified the warhead at 350 kilotons, "plus or minus 10 percent," one source said.

The bad taste from the Mark 12A affair has lasted.

In a Livermore report to DOE before a test last summer of an experimental warhead for the MX missile, the lab wrote that its approach would lead to a better design than the controversial Los Alamos Mark 12A warhead.

The implications of a Mark 12A controversy in a period of a comprehensive test ban are obvious.

In a recent interview, Teller put his view succinctly: "Except for Livermore, they [Los Alamos] would have the final word... The laboratories need each other to keep each other honest."

Another measure of how sensitive scientists at the two labs are toward each other came up recently in what seemed to be a simple exchange of letters on the proposed comprehensive test ban treaty.

Bradbury, former director of Los Alamos, J. Carson Mark, former head of that lab's theoretical division, and Richare L. Garwin, a longtime consultant to Los Alamos, wrote Carter on Aug. 15 to argue that nuclear tests were not required to certify the reliability of weapons already in the stockpile.

In their letter, the three pointed to a problem in the past with the Polaris warhead that apparently required changing a component.

The Polaris warhead was designed by Livermore and at least one top administrator there bitterly noted in a later interview that Los Alamos scientists had not called attention to a problem in any Los Alamos-designed warheads -- "particularyly considering what happened on their watch," the Livermore man said. He refused to elaborate.

Elaboration did come, however. In a letter last month to The Washington Post, Rep. Jack Kemp (R-N.Y.) took issue with the Bradbury-Mark-Garwin letter. Kemp noted that during the 1958-1961 nuclear test moratorium, Bradbury and Mark had certified the yields of weapons "which were found not to work when testing was resumed."

Pressed recently, a Los Alamos official said the men had certified a bomb as having a 200-kiloton yield that was produced during the moratorium.The high explosive in the bomb had to be changed after it exploded, killing some workers. When it was later tested using a new high explosive, its yield turned out to be around 2 kilotons.

Behind all the feuding and fussing may be the reality that less money may be available for weapons as time goes on.

To survive now, both labs devote half their budgets, which both run nearly $300 million a year, to non-weapons activities such as energy and health research.

Agnew, who is retiring as Los Alamos director in March, recently said that 10 years from now if the two labs keep going both will be "cripples" without many good people between them. He wants to combine the weapons work in "one larger, integrated lab," with Los Alamos, naturally, being his preference.