Israel yesterday became the third U.S. ally to formally seek participation in President Reagan's Strategic Defense Initiative, joining West Germany and Britain in an effort to obtain "Star Wars" research contracts.

The SDI program, which is controversial in this country and among many U.S. allies, is intended to develop weapons to shoot down Soviet nuclear missiles. Israel is more interested in adapting SDI technology to its conventional defense needs, chiefly shooting down shorter-range ballistic missiles based in Syria, officials said.

"We expect to do the things within this research and development program in the way that it will help our own problems along," Israeli Defense Minister Yitzhak Rabin said yesterday. "Every research and development, for example in the field of lasers, helps everything."

Rabin's comments came after a Pentagon ceremony at which he and Defense Secretary Caspar W. Weinberger signed a memorandum of understanding laying out ground rules for Israeli participation in Star Wars research. The contents of the agreement are classified, and officials revealed few details worked out during six weeks of negotiation.

Weinberger said that Israeli participation will "advance the research program in significant ways, and that in turn will, I think, advance the cause of peace and freedom." Rabin said that SDI is "a project of great interest to the future of the world."

The Reagan administration has sought similar agreements with as many allies as possible to demonstrate broad political support for the program. In return for offering such support, Israel will have a better chance of winning subcontracts from U.S. corporations in SDI research, according to Joyce R. Starr, director of the Near East Program at Georgetown University's Center for Strategic and International Studies.

Starr recently led a delegation of U.S. arms makers to Israel to explore the possibility of cooperating on SDI work. She said the executives were impressed with some of the technology being explored in Israel, particularly in lasers, computers, and "command and control" of complex weapon systems, but made clear to the Israelis that a government-to-government agreement would have to be signed before subcontracts could flow.

A number of countries, while expressing interest in obtaining contracts from the multibillion-dollar SDI program, have been reluctant to endorse the program's goal, which is to develop a space-based system of weaponry that might ultimately cost hundreds of billions of dollars. The West Germans, for example, sent their economics minister to Washington in March to sign the agreement rather than their defense minister, as Weinberger wanted, to show that they viewed the pact as a commercial arrangement more than an endorsement of SDI's goals.

In Britain, the Defense Ministry took the lead in signing the pact late last year. Japan and Italy also reportedly are interested in pursuing SDI contracts, but no other agreements are being negotiated now, according to Frank J. Gaffney, deputy assistant defense secretary.

Gaffney said the pacts with Israel, West Germany and Britain do not guarantee those countries any contracts, but will allow them to sidestep some Pentagon bureaucracy -- which, "as anyone familiar with the procurement process knows, does have its disadvantages," he said.

"There's no floor, there's no ceiling," to the dollar value of contracts Israel can compete for, Gaffney added.