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Within 48 hours of Alon’s murder, his body and family were sent home on Air Force Two, reportedly at the behest of President Nixon and Secretary of State Henry Kissinger.

At a memorial service, Israeli Defense Minister Moshe Dayan blamed Arab terrorists for Alon’s death. After determining that the killing was neither a botched robbery nor a crime of passion, the Federal Bureau of Investigation focused on Black September, a Palestinian terrorist group responsible for the murder of 11 Israeli athletes at the 1972 Olympic Games in Munich.

In March 1973, Black September attempted to set off three car bombs in New York during a visit by Israeli Prime Minister Golda Meir, part of a clandestine war of targeted killings between the Jewish state and its Arab enemies.

Despite an extensive investigation that reportedly involved running down a 90-person list of people classified as terrorists, checking out leads supplied by Israeli intelligence, and looking into Arab faculty and students at Washington-area universities, the FBI was unable to locate a murder weapon, develop a suspect or make a single arrest.

In 1976, the agency officially closed the case.

“Back then, there was no DNA, no computers, no cellphones,” Mr. Burton said. “The original FBI case agent had never investigated a murder before. The local agents were busy running Watergate leads and leads on ‘Hoover subversives.’ The police and the FBI were not equipped to investigate this kind of attack.”

A mystery deepens

Every night was the same: Mr. Burton would finish his shift as a Montgomery County police detective, then drive past the former Alon residence on his way home, sleepless and troubled.

“I must have drove by the house a hundred times, just thinking about what happened, tracing how I thought the bad guys got away,” he said. “I grew up on those streets. It stuck with me.”

At the time of Alon’s death, Mr. Burton was 16. He didn’t know the Alon family, even though he lived around the corner from their house and went to the same high school as their daughter Dalia.

Still, the killing haunted him. He signed on with the Bethesda-Chevy Chase Rescue Squad — the same unit that had transported Alon to nearby Suburban Hospital — and then became a police officer, regularly discussing the case with his colleagues.

In the mid-1980s, Mr. Burton joined the counterterrorism division of the U.S. Diplomatic Security Service. Busy investigating embassy bombings and airline hijackings, he nevertheless began looking into Alon’s death — and amid a series of dead ends and deceased possible sources, he was stunned to discover that in 1977 the FBI destroyed all evidence in the case, including the fatal copper-jacketed bullet.

“When I told the original FBI case agent about that, he was shocked,” Mr. Burton said. “To be blunt, I think our government did a very poor job looking at this.”

Like Mr. Burton, Alon’s widow also had been searching for answers. Atop a piano inside her family’s living room in Israel, Mrs. Alon kept a shrine to her departed spouse. Photos. Military medals. A single fresh rose, perpetually replaced and in bloom.

“You felt my father’s presence when you came home,” Ms. Alon-Rosenschein said. “Always. You couldn’t miss it.”

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