There is a tragic inevitability to the breakdown of the year-old, American-arranged cease-fire in southern Lebanon. Palestinians know--the world knows--that the Israelis have an Achilles heel: they cannot abide the murder of their people. That gives an extraordinary power to the lone gunman and, beyond that, to the tacticians of terrorism. Someone setting out to kill Israelis can be reasonably sure that the response will be not long in coming and that it will entail an impressive display of state power, with all the tangled military and political consequences that such displays always bring.

Last Thursday in London, an Arab assailant fired a bullet through the head of the Israeli ambassador. This created a certain embarrassment for the PLO. It claims to represent all Palestinians, even those not under its direct military control, but, depending on the circumstances, it tends to be selective about which acts of Palestinian violence it accepts responsibility for.

In this instance, it denied responsibility for shooting Ambassador Shlomo Argov, saying, cynically, that the shooting "served Israeli and not Palestinian interests." In Beirut, meanwhile, the PLO's No. 2 official, Salah Khalaf, speaking after Israeli planes had retaliated for the London shooting by bombing Palestinian guerrilla positions in Lebanon, dropped all pretense of civilized demeanor and declared: "We will hit civilian targets in northern Israel." Heavy shelling of border settlements followed, and then came Israel's strike north for the stated purpose of ensuring that Palestinian units will no longer be able to fire long-range artillery shells into Israel.

Unquestionably, the Israelis have a right of self defense. The British have just gone 8,000 miles to protect their people; the Israelis yesterday went only eight. The question of proportionate response may yet arise, as it usually does when armies operating by one logic move against guerrillas operating by another. In the current circumstances, however, the Palestinian provocation is so brazen that it will take an exceptionally disproportionate response to revive the question.

Much fuss will be made if the Israeli military stays in southern Lebanon. But then, the Lebanese authorities, in their outrage, may see the situation more clearly than do many of their fellow Arabs. Increasingly, the Lebanese are coming to the position that the undigested and undisciplined Palestinian presence is the root cause of Lebanon's agony. The Israelis should certainly get out of Lebanon promptly. So should the PLO's forces and their patrons in the Syrian army.

In time, one hopes, a new cease-fire will be installed, and then there will be an argument over which of poor Lebanon's numerous foreign occupiers should depart. The core problem--the problem of Israeli-Palestinian coexistence--will remain. Among both Israelis and Palestinians now, the leadership and the dominant popular mood seem to give priority to military confrontation over political compromise. At least as long as that situation holds, they will both continue to suffer the bitter fruits of their terrible, unnecessary feud.