The house at 315 Kentucky Ave. in Alexandria stands empty and for sale, vacant for nearly a year since its owner, Dr. Robert S. Rixse, was shot to death at the front door while his three young daughters slept.

Homicide detectives say they believe that Rixse was in his bedroom, writing checks for the monthly bills, when his unknown assailant knocked shortly before midnight last July 1.

Rixse, clad in cut off blue jeans and a bathrobe, pulled open the door and was immediately shot at close range. The weapon was a small-caliber handgun without a silencer. There were "several shots and several wounds," said Alexandria homicide Detective Ron Graves.

The slayer drove away, slowly, in a compact car with its headlights off.

Those facts, plus other bits of physical evidence that police are unwilling to reveal, constitute much of what is known about the shooting, which shocked the suburban neighborhood of Beverley Hills.

What is unknown, police acknowledge, is who shot the 37-year-old Rixse, a pediatrician and popular civic activist, and why.

Graves and a fellow detective, Tony Harper, say they have concluded that the slaying was a case of murder-for-hire, a professional "hit." They have ruled out, they say, mistaken identity, burglary and other possible explanations for the death.

While police have amassed a thick investigative file, the case stands as one of the area's most intriguing unsolved slayings.

According to court records, Rixse won custody of his three daughters in a 1981 divorce case after an acrimonious legal battle with his wife, Diane (Mimi) Rixse, who later married Alexandria resident John Kennedy Robinson and settled nearby. The Robinsons gained custody of the Rixse daughters immediately after the shooting.

As part of a major investigation of the murder, Alexandria police interviewed many Beverley Hills residents about Rixse, his family, the Robinsons and Rixse's professional relationships. They combed Rixse's medical files looking for signs of possibly disgruntled patients.

In an interview last week from Georgia, where the Robinsons and their children now live, John Robinson said he and his wife had offered to cooperate "in any way we can" with Alexandria police, but that his family knew nothing about the slaying.

"We had absolutely nothing whatsoever to do with that man's death," Robinson said. "It's quite honestly something we just know nothing about. It was an absolute surprise to me. I was absolutely flabbergasted."

Alexandria police, saying they are unable to bring charges in the case, said recently that they are interested, nevertheless, in two drug dealers whom Robinson once knew.

According to interviews with law enforcement officials, detectives in Alexandria attempted soon after Rixse's death last July to interview a convicted drug smuggler, Gerald Lyle Hemp, 46, who they believed was serving a 40-year prison term in Tennessee and who was acquainted with Robinson.

Detective Harper declines to say how Alexandria police knew about Hemp.

Tennessee District Attorney General Al Schmutzer Jr., who prosecuted Hemp in 1983 for a smuggling scheme involving 614 pounds of cocaine, said he learned only after receiving the Alexandria inquiry that Hemp had been transferred early in 1984 to the Florida prison system.

Then, to the dismay of both Schmutzer and Alexandria police, Florida prison officials reported that Hemp had escaped July 10 by walking away from a minimum security work-release center in Lantana, Fla. Officials there said Hemp signed himself out to a dentist in town, kept the dental appointment, then disappeared.

(Schmutzer said he has received no satisfactory explanation for assigning Hemp, a convicted felon, to minimum security status.)

Alexandria detectives Graves and Harper said an interview with Hemp -- who was still jailed on the night Rixse was shot -- would have been "just one step" in the Rixse investigation. Florida officials say Hemp is believed to be in South America.

A further twist in the investigation, say Alexandria police, is the apparent murder in 1982 of an associate of Hemp's, Charles Leslie Kageler, 48, who also was an acquaintance of Robinson's. At the time of his death, Kageler was on the run from authorities after being indicted a year earlier for involvement in the same cocaine smuggling deal with Hemp.

Kageler's body, with a severe bruise on the head, was found floating on June 21, 1982, about 3 1/2 miles off Jupiter Beach, Fla. In an address book discovered in his clothing, Palm Beach County sheriff's investigators said, was Robinson's telephone number.

Palm Beach investigator Clint Etheridge said he contacted Robinson in an attempt to learn Kageler's identity. Etheridge said Robinson told him he planned to be in south Florida the next day and would drop by the sheriff's office.

The following day, according to Etheridge, Robinson visited him, viewed photographs of the body and identified it as Kageler's.

Etheridge said he believes Hemp may have been connected to the slaying of Kageler. The two men had had a falling-out over their drug smuggling activities, he said.

In the interview from Georgia, Robinson said he had known Hemp and Kageler. "But I didn't know them by those names," he said. "It was extremely casual. I didn't know what they were doing or where they were doing it."

According to Robinson, he met Kageler by chance in the Atlanta airport and the two men discussed joining in some financial investments. "I met Hemp as a result of Kageler," he said. "Kageler introduced me. I really don't remember, it was so long ago."

Robinson said he "absolutely didn't know anything about" Hemp's and Kageler's drug involvement. "It was a complete surprise to me."

Robinson also denied that he had visited Palm Beach County sheriff's officials. "The photos were sent to me and it was a person I knew as somebody else," he said.

Robinson said he was questioned last September by a federal grand jury in Tallahassee about Hemp and Kageler and about whether he knew how they had obtained drug smuggling accessories: air-to-ground radios, antisurveillance devices, night vision binoculars and false identification.

Robinson said he told the grand jury he had no knowledge about the matter. Assistant U.S. Attorney Alan Sprowes in Tallahassee said he was aware of Robinson but declined to elaborate, citing the secrecy of grand jury proceedings.

Alexandria detectives Graves and Harper said they have pursued the twisted Hemp-Kageler trail in a search for leads in Rixse's death partly because John and Mimi Robinson have been uncooperative with police.

Robinson disagrees. "Any time they want to pick up the phone and call our attorney to arrange an interview in Georgia , they can," Robinson said. "They've never called. The ball's in their court."