When the 17-year-old Palestinian schoolgirl appeared in an alleway in West Beirut's Burj al Barajinah refugee camp, the first thing that struck the visitor was her prettiness: a soft, radiant face with large, limpid black eyes.

But when she began to speak it was the terror, not the beauty, that riveted the attention.

"We live in fear here," said the girl, who will be called Fatma to protect her identity. "Everyone is nervous and afraid. There is a great, great fear that after Shatila, we will be next."

There are good reasons for their fears. Burj al Barajinah, on the southern fringes of Moslem West Beirut, has been disarmed and remains unprotected, either by the Lebanese Army or the Israelis.

Not even President Reagan's announcement Monday that a new multinational peace-keeping force will be sent to Beirut has done much to still the terror of the people of Burj al Barajinah. They are terrified that before the international force can be deployed later this week the Christian militiamen who killed their friends and neighbors in Shatila may come here and try to do the same.

The Lebanese Army is supposed to be protecting Burj al Barajinah, and all of West Beirut, under the terms of the agreement negotiated by U.S. special envoy Philip C. Habib last month that led to the evacuation of the Palestine Liberation Organization troops who had been the camp's defenders for almost a decade.

The Lebanese Army, weak, demoralized and insecure, has balked at the assignment. Its soldiers did enter the camp two weeks ago to search for guns and ammunition left behind by the PLO, but after a few armed men fired at them, the soldiers left almost as quickly as they had come, leaving behind only a couple of lightly manned roadblocks north and south of the camp.

The Israeli occupation of West Beirut last week sent the camp into a frenzy of apprehension. "We have gone to the Army maybe 100 times to ask them to come in here and defend us," said a Palestinian matron. "All they did was ignore us."

Last Saturday, when word had already swept through the camp about the massacre at Shatila, within gunshot distance of Burj, Lebanese Army soldiers appeared in the camp again to ask all its residents to take any weapons they might still have to a nearby mosque for collection so the Israelis, or their Christian militia allies, would have no excuse to invade the camp.

"They said if everyone would turn over their weapons," Fatma recalled, "everything would be all right and they would protect us from the Israelis and Haddad's men [the Israeli-supported Christian militia of cashiered Lebanese Army Major Saad Haddad]. When the Lebanese Army came we made great welcome, we were so glad. The Lebanese Army is much better than the Israelis or Haddad."

According to dozens of Palestinians who gathered around a visitor to ask for him to intercede somehow to get protection for them, hundreds of guns were turned over to the Lebanese Army. "We are not from the PLO, but we have always had weapons to defend ourselves," said one 18-year-old youth as a dozen of his friends, all schoolboys, nodded in assent. "But we wanted Army protection, so we took the guns we had always kept to defend our families to the mosque and the Army took them away."

Once the camp was disarmed, the Lebanese Army simply left it as it was before, "defended" by a few dozen soldiers at the two roadblocks north and south of the camp entrance and by three-man patrols through its streets once or twice a day.

"We begged them to protect us," Fatma said, her voice quavering. "They said they couldn't fight Saad Haddad, they were not strong enough."

Disarmed and abandoned, the Palestinians of Burj al Barajinah, a camp of 10,451 registered refugees of families who fled Palestine in 1948 when the state of Israel was created, have the frightened look of a hunted people these days as reports have swept through the camp about the horrors of what happened to their friends and neighbors in Shatila.

Many have gone to Shatila, where several hundred bodies already have been recovered, and returned to Burj to add to the terror with their reports of the carnage.

Some have come back with exaggerated tales of seeing 70 men without heads. Others, more accurately, have talked of seeing women and children with their necks slit. All know that an unspeakable horror has descended around them and that it is a horror that could well come to them too.

"What do people do when they come back from Shatila?" a visitor asked Fatma's 58-year-old father. "They just come back and cry," he replied.

The father, whose name cannot be given lest it draw retribution, said that apparently erroneous reports of approaching Christian militiamen already had sent residents of the camp fleeing in panic twice. At night, he said, most people leave their homes and sleep away from the camp in neighboring residential districts, using garages, fields and cars as places to hide.

"Why do we live here?" Fatma asks helplessly. "We are not wanted. We are treated as if we are not people. Who says hello to us? Nobody."

Her father, who is trying to rebuild his refrigerator repair business, shattered by Israeli shells during the summer (as was his car and four now recemented rooms in his home), says quietly, "We want to go away from here, but where can we go?"