Radioactive fallout has been detected in New Zealand, providing new indications that a secret atomic explosion took place in the atmosphere of the southern hemisphere within the past three months.

The fresh radioactive debris in rainwater is the first corroborating evidence that a nuclear explosion was triggered near South Africa on the night of Sept. 22, when a U.S. surveilance satellite spotted what was presumed to be the fireball of an atomic explosion.

"Radioactive fallout was the key missing element in what we thought originally was a clandestine nuclear test," a White House source said yesterday. "The fallout in New Zealand could well be that missing element." y

The increase in radioactive fallout was reported yesterday by New Zealand's Institute of Nuclear Science at Gracefield, just north of the capital city of Wellington. The rise in fallout was described by Institute Director B. J. O'Brien was the kind one would expect from a small but recent atomic explosion in the atmosphere.

"What we see in our fallout here would be consistent with a nuclear explosion having a force equivalent of two to four kilotons," O'Brien said by telephone from Gracefield. "We've searched for other causes of this fallout but can find nothing else."

While South Africa has repeatedly denied being the source of whatever the satellite detected on Sept. 22, U.S. officials have suggested that South Africa triggered a test. So far, however, the State Department has said it has no confirming evidence that Pretoria was responsible for an atomic explosion.

O'Brien said yesterday that increases in radioactive fallout were measured in rainwater samples collected from Aug. 1 to Oct. 28, with short-lived radioisotopes such as barium-140, praseodynium-143 and ytrrium-91,, all of them fission products of nuclear explosions.

"We didn't see much of an increase," O'Brien said. "Just enough to suggest they came from a small nuclear test."

At the time that the State Department released the information that a U.S. satellite had seen what appeared to be a nuclear fireball, it estimated the size of the explosion as between two and four kilotons. This would be an extremely small atomic explosion, not more than one-fifth the size of the first atomic bomb dropped on Japan at the end of World War II.

The increase in New Zealand's fallout was measured for radioactive isotopes with half-lives no greater than 59 days, meaning that if they came from an atomic explosion, it was a recent one.A half life is the time it takes a radioactive isotope to lose half its radioactivity.

The half life is 12 days for barium 140, is 13 days for praseodynium-140, and 59 days for yttrium-91.

"What we've seen couldn't have come from an old test," O'Brien said.

"Whatever it is, it is a recent event."

Prevailing winds at the latitude of South Africa and New Zealand are west to east, meaning that radioactive debris near South Africa could be carried across the Indian Ocean toward Australia and New Zealand.

The U.S. surveillance satellite that spotted the suspected fireball Sept. 22 saw a double pulse of light in the atmosphere in a circle 3,000 miles wide over the South Atlantic and Indian Ocean south and cast of South Africa.

The twin light pulse is the characteristic "signature" of an atomic explosion. It is the fireball that briefly disappears from view when the explosion's shock wave makes it opaque from space, then reappears when the shock wave begins to dissipate.

The Vela satellites that look for nuclear explosions have seen 42 double spikes of light in the last 15 years, officials say. The first 41 were confirmed as atmospheric nuclear tests, exploded either by China or France. The 42nd event took place Sept. 22.

A curious piece of information about the suspected test also turned up yesterday in Washington. An aide of the Senate subcommittee on nuclear proliferation said the subcommittee asked the National Technical Information Service who had sought a computer search of the literature on nuclear explosions and the seismic detection of nuclear explosions.

"The answer we got back," the aide said, "was the defense and naval attache of the Republic of South Africa."