"We Are Scared," the bedsheet banners at Brown University were screaming this week -- scared, said the backers of Referendum No. 1, of nuclear war. They were demanding that the school stock cyanide "suicide pills for optional student use exclusively in the event of nuclear war." I take literally their statement of fear of the nuclear nightmare, though I suspect their claim of a right to university-assisted suicide is primarily for dramatic effect, an attempt to goad those in authority into doing something to avoid the awful prospect.

There is another group of frightened Americans who wave no banners and make no dramatic demands. They don't know what to demand. I speak of parents whose fear is for the safety of their small children. The special nature of their fer is that it has nothing to do with enemies, of whom the children have none, or even strangers, whom they can be taught to avoid. It is the fear that their babies will be abused -- and perhaps permanently scarred -- by those entrusted with their care.

Peace activists believe the thing they fear can be forestalled through international negotiations. Frightened parents have no one to negotiate with, no one to look to for practical help, not even a suspect -- until it's too late. Just last week, a 48-year-old Bronx minister was indicted on charges of sexually asaulting five boys and a girl in a day-care center at his church. This past summer saw molestation charges brought against the founder and six teachers of a suburban Los Angeles nursery school. Thirty children at a city-run day-care center in New York told authorities they had been sexually abused. It goes on and on, and no one knows what to do.

Abuse by strangers is hard enough to take. But in that case we at least can demand extra police patrols and tak special pain to remind our children to avoid people they don't know. But when our children are abused by people we trust, in institutions we have specially chosen or even in our own families, what do we do?

The first, and mostly useless, response is to call for more government regulation. That can lead to police "clearances" and higher professional standards for day- care workers, neither of which addresses the problem. Police investigations will weed out those people who already have been convicted of child abuse or similar offenses, but most of those charged in the recent cases had no prior records. Nor is there any basis for supposing there is a link between professional training and pederasty, or that college training is a cure for whatever ails child abusers.

Parents can take more care than they usually do to question their children about their day-care activities, listening for even the smallest clue that something may be wrong. But in fact the options seem limited. We don't know what to do.

The students at Brown didn't know what to do either, except to register the point that they are less frightened of the attitudes our leaders see as weakness than they are of their macho responses to international problems that might be better addressed through diplomacy. At least the Brown students have the assurance of knowing that the leaders don't want nuclear war either. The other thing is different. The parents of small children and the people who abuse them don't want the same thing. And unlike the international situation, we don't even know who the enemy is.

The most crucial difference, though, is the immediacy of the threat. I'm not fond of nuclear annihilation, and I frequently worry that our national leaders will blunder into some world-threatening exchange. But compared with the anxiety of a parent who fears his child may be victimized by the very people who claim to love it, the prospect of nuclear disaster seems almost trivial.