Our research suggests that the death of Osama bin Laden could well become a major turning point in the war on terror, making Americans substantially safer -- but only if we follow up in the right way over the next year. If we do, and if we are very lucky, the war on terror could one day truly become a thing of the past.

Leadership decapitation on its own rarely lowers either the life expectancy of terrorist groups or their ability to carry out violent attacks, and our work shows it may sometimes have the opposite effect. Israeli forces assassinated numerous leaders of Hezbollah and Hamas with little success in reducing violence. In 2006, the U.S. killed Abu Musab Al-Zarqawi, the infamous terrorist leader in Iraq, only to see violence rise more than 50 percent the following year.

Particularly ominous are the findings on leadership decapitation for religious terrorist groups like al-Qaeda. The odds that a religious terrorist group will collapse in the wake of a decapitation are 17 percent. That is especially discouraging considering that the odds of such a group dissolving when there is no decapitation are 33 percent. Put differently, killing leaders of a religious terrorist group appears to increase the group's chances of survival from 67 to 83 percent.

What appears to matter most for the long-run trajectory of decapitated terrorist groups is popular support. The most successful groups are those with support that transcends the leader's charisma; their strength comes from promoting a popular agenda. The more popular the group's cause, the more resources and prestige it has to draw new leaders to replace those who are removed. Ten years of operation appears to be the crucial threshold -- the point after which groups with popular support can replace the loss of the top leader, often with younger individuals seeking to make a name for themselves through more aggressive attacks, and safely survive.

Terrorist groups like al-Qaeda that carry out campaigns of suicide attacks depend on significant popular support. Otherwise they would not be able to generate wave after wave of suicide missions that can cost the lives of their most ardent followers. Studies at the University of Chicago show that suicide bombing campaigns virtually always arise from popular resentment toward military occupation or territorial domination.

Al-Qaeda fits this pattern. For nearly two decades, the presence of large-scale U.S. ground forces in Muslim countries has been far and away al-Qaeda's principle recruiting asset. What made bin Laden famous in the first place was not his religious commitment to Islamic fundamentalism, which would hardly separate him from many other would-be Muslim leaders. Rather, bin Laden's popular support originally stemmed from his stance against U.S. ground forces in the Arabian Peninsula in the early 1990s.