A new problem has crept up almost unnoticed in the gathering storm over the sale of AWACS radar planes to Saudi Arabia: There's a serious shortage of officers to man the planes.

Air Force officers apparently don't find much satisfaction or reward in working on one of the most sophisticated surveillance aircraft in the world, according to congressional spokesmen. The crews find the hours long and the pay inadequate. Besides, the typical AWACS officer spends 150 days a year away from home in places such as Iceland, Korea and Saudi Arabia.

The shortage is particularly acute among experienced weapons controllers--the captains, majors and lieutenant colonels who oversee the high-priced electronic gear aboard the planes.

The Air Force is required to have 379 supervisory personnel to man its 25 Airborne Warning and Control System planes, but can muster only 288, according to Sen. Barry Goldwater (R-Ariz.). It is required to have 32 field officers (majors or above), but has only 12.

It hasn't had much luck finding volunteers either. When the Air Force put out a call in 1980 for 78 mission commanders with the rank of major or higher, there were only 17 takers.

Goldwater says the situation "is now severe and will worsen," especially if Congress approves the sale of five AWACS planes to Saudi Arabia and U.S. officers are dispatched to train the Saudis.

The AWACS is basically a Boeing 707, similar to those used in passenger flights, with a huge radar dish on its roof and a belly full of sophisticated electronic gear. Eight enlisted men or women and nine officers are needed to operate each aircraft. Six of the officers are called weapon controllers and work at the rear of the plane overseeing surveillance equipment.

The controller shortage is blamed on several things. Part of it, according to Goldwater, is the old problem of keeping highly skilled people in the armed forces. As soon as these people are trained, "the electronics people are waiting right outside the school building with their hands to grab them at one, two and three times the pay they would have received if they stayed in the service," Goldwater said recently on the Senate floor.

But the AWACS crews have a couple of special problems. One is the time that crew members, all stationed at Tinker Air Force Base in Oklahoma, have to spend away from home.

Hard feelings also result from pay differentials on each plane. Simply put, the officers in the front of the plane are paid more than those in the back. Pilots and navigators in the cockpit get $306 a month in extra flight pay while controllers get $110 in hazardous duty pay.

The House moved to correct that recently by adopting an amendment to the military pay bill. Under the amendment, captains, majors, lieutenant colonels and colonels with from six to 18 years' experience would get an extra $400 a month in hazardous duty pay. The bill is now before a conference committee.

Goldwater introduced a similar amendment on the Senate floor, but withdrew it when senators complained they had never heard of the problem. Goldwater admitted he had learned of the shortages only 2 1/2 hours before the Senate was to vote on the military pay bill. "It's another example of the Pentagon screwing around until it is too late," he said.