Can the UN peace-keeping forces in southern Lebanon keep peace?

Invading Israeli forces made short work of the 7,000-man United Nations peace-keeping force in Lebanon, calling into question the future effectiveness of this ''buffer'' and diminishing the likelihood the UN could patrol the area when the fighting ends.

''At least you could have shot in the air like when our people approach you, '' Palestine Liberation Organization (PLO) chairman Yasser Arafat complained to a UN official the day after the Israelis pushed into Lebanon.

''What could I tell him?'' the official lamented. ''It would have been impossible to stop the Israelis. But still it is very embarrassing to us after all the work we have done in securing the agreement of the PLO to allow us to deploy in the south.''

A Norwegian soldier with the UN force was killed when the Israelis invaded. There have been no other known casualties among members of the UN force -- formally called the United Nations Interim Force in Lebanon (UNIFIL).

Unifil had been expecting the invasion for some time, and sources say they had no clear option in the midst of the invasion but to stand aside.

Gen. William Callahan, the UN force commander, complained in a letter June 8 to Gen. Rafael Eitan, Israel's chief of staff, of being stalled by the Israelis on June 6 at Israel's northern command headquarters. He said he was told of the invasion only 28 minutes before it began and that he ''strongly objected and protested against such wrong and unacceptable a course of action.'' The protest was to no avail.

Forty-eight hours later, the general said, ''Israeli vehicles in an endless stream continue to pass through and occupy numerous UNIFIL positions in utter disregard of the function of the force as laid down by the mandate of the UN Security Council.''

General Callahan's letter of protest was seen here as an attempt to reduce damage to the image of the UN forces following the Israeli invasion.

Lebanese, Palestinian, Israeli, and UN officials doubted the force could have stopped or seriously delayed the invading Israelis. Many feel it is unlikely the UN will play a future role in Lebanon.

A UN official complained June 8 that the delicate negotiations that led to the deployment of UNIFIL batallions in 1978 - and to the recent expansion of the force by 1,000 men -- would be extremely difficult to repeat, given the UN's inability to stop the Israelis.

The PLO sees the UN as a one-sided peace-keeper, stopping Palestinian infiltrations of Israeli-held territory but doing little to stymie the Israelis.

The 1978 UNIFIL mandate established the force to pursue three objectives: (1) confirm the withdrawal of Israeli forces following the ''Litani operation,'' (2) restore peace and security in the region, and (3) assist the Lebanese government in assuring the return of authority to the area.

Observers here say it will be difficult for the UN to fill the void if and when the Israelis complete their military operations against the PLO. Cognizant of this, Israeli strategists have recently been talking of setting up a ''multinational peace-keeping force,'' similar to the one operating in the Sinai along the Israeli-Egyptian border. An Israeli suggestion that UNIFIL might be greatly expanded to patrol almost all of the captured Lebanese territory would get little support in Beirut.

''At this point,'' a UN official told the Monitor, ''the UN's Security Council resolutions (calling for immediate Israeli withdrawal) are being ignored and we are being criticized here for ineffectiveness. It will be hard for the UN to reestablish itself as a peace-keeper after this is all over.''