When Israeli Prime Minister Menachem Begin left Jerusalem's Hadassah Hospital after being treated for a mild stroke last August, he shook hands with his fellow patients, wishing each a rapid recovery. Among them were two Jordanian Arabs, part of the 1,000 or so foreigners the hospital treats each year from nations at least legally at war with Israel.

One major reason they make the often risky trip is Dr. Oded Abramsky, 38, a former Israeli commando officer, who is now his nation's, and one of the world's, leading neurological immunologists. Last July Abramsky treated a relative of Iran's Ayatollah Khomeini for the debilitating neuromuscular disease of myasthenia gravis. A woman with epilepsy turned out to be close kin to Yasser Arafat, chief of the Palestine Liberation Organization. A victim of Parkinson's disease from Syria in 1976 had ties to Dr. George Habash, one of the most militant Palestinian leaders and a physician himself. "I am pretty certain," says Abramsky, "that Habash was instrumental in sending his relative to us. It was on the day when the Air France aircraft was hijacked and taken to Entebbe. Here was I, treating a close relation of a terrorist chief leading this inhuman act."

Yet medicine to Abramsky has no politics. "Look," he says, "the relation between a doctor and his patient is like between a lawyer and his client. He does not have to like him. He does not have to agree with him. But if he takes his case, he will give him his full know-how." Actually, Abramsky thinks personal involvement can be a deterrent to sound medical practice. "I will never treat members of my family or close friends," he declares. "When you are emotionally involved, you cannot trust your objective judgment."

Abramsky's clinical style of discourse masks his humanitarian instinct. In 1971, he appeared regularly on an Israeli radio show titled Doctor Behind the Microphone, which was beamed throughout the Mideast. Its function was to aid Arabs who could not find good local medical advice. Since their countries had no mail contact with Israel, Abramsky relates, "They used to send their letters via friends in Europe. I would reply, and [hostess Ilana] Bazry translated into Arabic. Of course we answered without mentioning names. Only their disease and city." (Abramsky left the program in 1977 but it is still on the air.)

The son of a professor of Jewish history and a housewife, Abramsky attended the Hebrew University of Jerusalem Medical School, where he now teaches. Along the way he did research at the Chaim Weizmann Institute, where he led a team which made important contributions in the study of myasthenia gravis.

By then, Abramsky had treated an enemy soldier for the first time while serving with a paratroop unit in 1968. "They brought a friend of mine in from Kibbutz Na'an," he recalls. "He was dead. With him they brought an Arab from the enemy camp. He was wounded. We gave every patient the needed treatment."

When Israel opened the bridges to Jordan's West Bank in 1967, the Hadassah Hospital began to treat Arabs in increasing numbers and from all social strata. The first lady of an African state that had severed diplomatic relations with Israel showed up last year, under extraordinary security, to be treated for infertility. An Arab prince from oil-rich Abu Dhabi had an appointment recently, as did the American mother of Jordan's Queen Noor, Mrs. Doris Halaby, to see Dr. Abramsky.

Abramsky and his wife, Henya, are the parents of three young sons and a daughter, 18, who is just beginning army service. That gives him ample reason to support the Arab treatment program. "Will it change their opinion of us?" he asks himself. "I don't think so. But it enables them to know us. We have gotten a reputation that we can be trusted." Yet tension rises when an Israeli is placed next to an Arab patient. "If," says Abramsky, "the Israeli's son was killed in war, thoughts may cross his mind whether this Arab took part in the battle. For such patients, it is difficult. For me, as a physician, it is not."