Washington ? Ariel Sharon has never made a secret of his negotiating strategy for the Palestinians: Pound them, then pound them harder, until they give up. Now the Israeli prime minister must figure out how to live with the appalling success his approach is producing. So must President Bush.

Sharon’s recent and still sketchy plan to withdraw from the Gaza Strip and some settlements on the West Bank is not an admission of failure or a strategic retreat by a warrior forever on the offensive. Far from it.

As Sharon intended when he took power in 2001, Yasser Arafat’s Palestinian Authority is broken beyond repair and Arafat is a pariah. Moreover, Palestinian cities are imploding under a wave of internal crime and brutality as Arafat’s CIA-equipped militias sell off or donate their weapons and protection to ordinary criminals, as well as to the terrorists of Hamas and Hezbollah. The smoldering ruins of Gaza and Nablus will soon be hardly worth occupying.

Sharon’s original vision of destroying Arafat’s authority as a way of stemming Palestinian suicide bombers and other murderers of Israeli civilians may not have encompassed that exact result. But a fratricidal collapse and anarchy in some places were clearly visible, probable outcomes of the strategy he chose. If today’s atomization of Palestinian society is not what Sharon wanted, it is something he did nothing to prevent.

It is a strategy, of course, that Arafat made possible, if not inevitable, through his support for terrorism and his flagrant corruption. Arafat’s undercutting of Mahmoud Abbas as prime minister last summer effectively derailed the U.S.-supported “road map” process and left the Palestinians to Sharon’s mercies.

But peace efforts were stirring back to life in the wake of the surprise and confusion generated by Sharon’s announcement that he was considering a partial Israeli disengagement: Unless the Palestinians quickly agreed to negotiate on his terms, Sharon said, he would close 21 Israeli settlements in Gaza and withdraw Israeli troops from the territory, while reducing and presumably consolidating settlements in the West Bank.

Critics immediately portrayed the disengagement idea as one more pressure tactic or as a diversion by Sharon to draw attention from the mounting political scandals surrounding him at home. Whatever his intent, Sharon provided the Bush administration with a small opening to forge the missing link in its diplomatic strategy for the region.

That means making sure that unilateral withdrawals are not used as a substitute or end point for the road map — that the process does not stop with a symbolic Israeli disengagement. The White House also will be looking for ways to link renewed Israeli-Palestinian peace talks to its Greater Middle East Initiative to encourage reform and democracy in the Arab world.

U.S. officials have made these points repeatedly to Sharon’s team in an intensive set of diplomatic contacts over the past three weeks.

The impetus for that effort came from Sharon’s failure to answer this practical question: Who will be in charge in Gaza when Israel pulls out? Leaving that wretched territory to its own devices would let the religious killers of Hamas and Hezbollah give new meaning to the concept of a breeding ground for terrorism.

Western diplomats have begun exploring with Egypt an important security role in Gaza if Sharon does withdraw. At a minimum, Egyptian troops would police the Gaza border to prevent arms smuggling to terror groups. Ideally, they would move into the territory to support dissident Fatah forces fighting Hamas and Hezbollah in a power struggle.

Egyptian help will not come easily or for free. And it will create its own problems, especially for the Gazans, who were once under Egyptian administration. But in starting a bargaining process over how Egypt can help bring about Israeli withdrawal, President Hosni Mubarak will perhaps be drawn into the larger U.S.-sponsored negotiation on political reform in the Arab world that he has thus far refused to countenance.

Long shot? Sure. But that is the interesting part about what has happened since Sharon sprang his daring idea. It initially elicited cries of dismay not only from Israeli settlers, but also from Arafat and his European supporters, who urged Bush to force Sharon to shut up about unilateral moves. One European Union official gravely said: “This withdrawal is just a land grab.”

That reaction was wrong, as Arafat admitted on Thursday by finally welcoming the withdrawal idea publicly. The Bush team is right to pursue the small opening Sharon offered, and to try to enlarge it into a moment for unfreezing minds in and about the Middle East.