Visiting Rome in the springtime has long been an American ritual. This year it seems to border on a daredevil act of courage. Apprehension and a sense of vulnerability hang heavy in the air for American travelers in this cool Mediterranean spring of Libyan terrorism and U.S. military reprisals.

The drama is heightened by taking TWA Flight 840 from New York to start this journey. TWA and other American carriers flying abroad have been avowed targets for Palestinian terrorists for more than a decade, and it was the continuation of this flight from Rome to Athens that was bombed on April 2, killing four Americans. The flight last night appeared to be about one-quarter full, and it is unclear whether a sudden fear of flying to the Mediterranean or a continuing strike by TWA's flight attendants contributed more to the light load.

What is clear is the shared concern aboard the aircraft. As a foreign correspondent for much of the past 20 years I have sought to cultivate a shell of indifference toward fellow travelers on most flights, in hopes of getting some work done or finishing off the latest Le Carre' thriller. On this TWA flight, however, small band that we are, we all look thoroughly at each other as we board and listen attentively to the languages fellow passengers are using.

What we are listening for is the sound of Arabic. What we are looking for is someone who looks Middle Eastern. For the space of this trip, whatever our nationalities or sympathies, we have become Israelis, prepared to suspect anyone from the Arab world as a foe, no matter his real identity or agenda. Muammar Qaddafi and Abu Nidal have conditioned us this way.

But the flight also demonstrates how far away Americans are from beginning to accept the siege conditions that 3 million Israelis have made routine in their lives. Security checks for this sensitive flight do not vary visibly from previous check-ins. The guards are relaxed and hurry passengers through if their luggage passes the X-ray scan and the metal detector.

Disembarking in Rome, where terrorists shot up the TWA counter last December, is different. The cleanup crew standing by to board is given a last check with a hand-held metal detector. Italian troops carrying automatic pistols and other weapons patrol the airport lounges, at times with dogs.

On arrival one is reminded of the tensions spawned by the acts of violence that Qaddafi and President Reagan have ordered against each other's citizens, in what newspapers here are calling "The Mediterranean Crisis." Trying to get to my hotel from the airport this morning, my taxi is halted by a police line in the center of Rome. A bomb squad is searching that citadel of Yankee wanderlust, American Express, up the street.

Fortunately the threat turns out to be empty, and I am allowed to continue to the hotel, where two Americans are paying their bills and checking out. "Americans are leaving," says the concierge, looking at me quizzically. "This is terrible."

If, as President Reagan said this week, we are being attacked because, like Mount Everest, we are there, more and more of us have decided not to be there this season, but to stay or return home. Tourism is plummeting here.

Embassies are on full alert, many American ambassadors now travel with full-time bodyguards, and even dependent school children are being told by security experts to vary the routes they take to school. But the American traveler, the target of several of the most recent outrages, remains largely naked and dependent on his own limited powers of observation. Or so it feels.

Americans are surprised that it is precisely the Mediterranean countries -- those countries nearest Libya and most directly challenged by Qaddafi -- that are the least supportive of the American military strikes.

What the Latin Europeans of Spain, France and Italy (which was once the colonial power for Libya) seem to fear is that the attacks will wind up setting the Mediterranean and the rest of the Arab world aflame and making Qaddafi an Arab nationalist hero, much as the British, French and Israeli strike against Egypt in 1956 did for Gamal Abdel Nasser.

What is happening now, it is explained here, is the Suez crisis in reverse, with Europe seeking to restrain the United States from making things even worse. Adding to the frustration is the knowledge that, unlike the Eisenhower administration, the Europeans are completely powerless in trying to restrain the Americans. It is not, European friends stress, that their governments disagree with Washington about the nature of Qaddafi and his actions. The disagreement is over methods.

"The problem of Qaddafi is the problem of Faust, one Europeans know well," a diplomat said. "You have to deal with evil, to try to contain it, and even sit down with it if that will help undermine the devil."