While talk show hosts and politicians have been fixated on illegal immigrants pouring into the United States, a more chilling potential danger comes from terrorists traveling to the United States on a perfectly legal basis.

[IMGCAP(1)]The menace detailed in the summer issue of Foreign Affairs by the scholar Robert Leiken of the Nixon Center is that of “passport-carrying, visa-exempt mujahedeen coming from the United States’ Western European allies.”

Leiken wrote his article before last week’s London transit bombing, but in the wake of that attack, his description of the rise of European terrorist cells and their potential danger to the United States is all the more trenchant.

Western Europe is now host to 15 million to 20 million Muslims, or 4 to 5 percent of the population (versus 3 million and less than 2 percent in the United States). A small but growing number are subject to the influence of radical clerics and al Qaeda recruiters.

“Unlike American Muslims, who are geographically diffuse, ethnically fragmented and generally well-off,” Leiken writes, “Europe’s Muslims gather in bleak enclaves with their compatriots,” isolated from their host population and “bitter” in outlook.

Leiken describes two types of jihadist who make their homes in Europe. One group consists of “aliens, typically asylum seekers or students who gained refuge in liberal Europe from crackdowns against Islamists in the Middle East.” They include radical clerics, often funded by Saudi Arabia, who open mosques and recruit for terrorist networks.

Their targets are “a group of alienated citizens, second- or third-generation children of immigrants, who were born and bred under European liberalism.” Some are unemployed youth. Others are well-educated, but resentful of their host cultures.

According to The New York Times, counterterrorism officials estimate that 10,000 to 15,000 Muslims living in Britain are supporters of al Qaeda and that about 600 have received military training in Afghanistan and elsewhere.

The danger to the United States is that jihadist recruits carry European Union passports and are therefore entitled to visa-free travel into the United States without an interview.

Convicted terrorist conspirator Zacarias Moussaoui and shoe-bomber Richard Reid both traveled to the United States under the Visa Waiver Program. Those who carried out the Sept. 11, 2001, attacks originally arrived with valid visas.

What to do? Some restrictionist foes of immigration call for elimination of the waiver program, but it would be economically and politically devastating to make some 14 million annual visitors go to a U.S. embassy for an interview before coming to the United States. They probably would go elsewhere, depriving the United States of the opportunity to turn a foreigner into a friend.

What’s more, a 45-second encounter with a consular officer wouldn’t necessarily detect a potential terrorist.

The United States already is losing its reputation around the world as a magnet for upwardly mobile students and workers because of post-Sept. 11 visa restrictions.

Former U.S. officials say that a Thai princess was placed in handcuffs by immigration authorities because she tried to enter the United States prior to the effective date of her student visa and was freed only through the intervention of then-Secretary of State Colin Powell.

So, what to do? Three years ago, according to a CNN report last week, Congress tried to tighten the visa waiver program by requiring that the United States and its visa-waiver partners issue machine-readable passports with biometric identification.

But Congress has extended its original deadline three times from October 2003 until August 2006. The Department of Homeland Security announced that new U.S. passports issued this October will meet the biometric requirement — but the machines needed to read them are not yet available. And, even if they were, that does not solve the problem of reading E.U. passports.

Leiken suggests that U.S. and European authorities should insist that airlines require U.S.-bound travelers to submit passport information when they purchase their tickets, giving the new U.S. National Targeting Center time to check potential entrants without delaying flight departures.

And he suggests that officers should be stationed at check-in counters to weed out suspects.

Another solution, authorized by Congress, is to station U.S. immigration officers at more foreign airports — currently, they’re at Canadian and some Caribbean airports, but not at major European cities — to check passports against terrorist watch lists. Money for the program hasn’t been appropriated.

Most important, though, is intelligence. Checklists are only as good as the information that backs them up. British officials confess they were caught blind by the July 7 attacks, much as the United States was on Sept. 11.

The Brits acknowledge now that numerous officials warned in advance that a terrorist attack was likely. We’ve been warned, too.