On April 11, 1979, First Lady Rosalynn Carter had her picture taken at a luncheon at the Capital Hilton Hotel here with James V. (Jimmy) Eppolito, son of a powerful New York City narcotics and loansharking figure, James B. Eppolito.

A White House photographer recorded the scene, promising an 8-by-10 glossy color print to the younger Eppolito. The promise was never kept, although Eppolito and his family did manage to obtain other black-and-white from a free-lance photographer who was also on hand.

Both Eppolitos, father and son, were gunned down in a mob killing in New York on Oct. 1. It is widely believed in local and federal law enforcement circles here and in New York that they might be alive today if Jimmy Eppolito had been a little more camera shy and kept a lower profile.

That luncheon, with the first lady attending with Jimmy Eppolito and his friends also present, was a curious affair. And the way Mrs. Carter's presence was arranged is even more curious.

The luncheon was billed as a benefit for "Cities In Schools," reported to be one of Mrs. Carter's favorite charities. The man behind the luncheon was John Ellsworth, later exposed on television as a con man and convicted felon.

Ellsworth's contact in the White House for the luncheon was Maurice Weir, who at that time was driving in Thunderbird leased at $300 per month by International Children's Appeal, one of Ellsworth's phony charities.

One source close to the Eppolito homicide investigation in New York said last week that Jimmy Eppolito's desire to fraternize publicly with Mrs. Carter and others at the White House had annoyed his family's underworld associates by focusing "too much heat" on illegal activities that included gun-running and drug trafficking.

Eppolito brought his wife with him to the luncheon. The other guest included two other suspected drug dealers who were at that moment under investigation in Manhattan, one of them for a bust that netted $50 million worth of hashish.

The Secret Service claimed after several days on inquiries last week that they have no way of knowing whether or not the Eppolitos were ever given even routine security checks. "It's their (the Carters') house," one agent said last week. "If they ask us to check on somebody, we do, and send what we find out back to them. What they do with it after that is their business."

Press spokesmen for both Mrs. Carter and the president refused last week to check routine social and visitors' records to determine if Mrs. Carter and other members of here family had visited with Eppolito and his associates either at the White House or elsewhere.

No White House photos could be located. Not even after other photos of the April 11 luncheon had been found and copied elsewhere would the White House return telephone inquiries about the vents of that day.

The entire schedule surrounding that luncheon is potentially embarrassing for the Carter administration. The day's events were arranged for Mrs. Carter by John Ellsworth, a 33-year-old, 300-pound con man and convicted felonwho was exposed by ABC's "20/20" last July as the founder of the International Children's Appeal.

ICA, conceived to capitalize on the International Year of the Child, has now folded, and Ellsworth has disappeared.

Ellsworth staged the annual White House Christmas party for the children of the Washington Diplomatic Corps and ingratiated himself with Chip Carter. Associates of Ellsworth claim that he was frequently invited to the executive mansion to watch private movie showings with the president's son.

Ellsworth's contacts in the Carter camp included Maurice Weir, who works out of the White House, running the Cities In Schools program in the District. According to leasing records for Ellsworth's ICA, made available to The Washington Post by a former ICA employe, Weir drove a Thunderbird rented by ICA from the Bensonhurst Leasing Cop. in Brooklyn.

Weir confirmed last week that he had used the car in 1979 and that he was given the FBI a statement to that effect. Weir claims that he had the car "only two weeks."

But Andrew Amplo, general manager of Bensonhurst, says that his company's records show that Weir had "two Thunderbirds" leased by ICA.

"We didn't even know he had the first one, in 1978," Amplo said, "until an insurance company informed us that he had had an accident involving more than $1,000 in Arlington, Va."

He added:

"I told Ellsworth that if Weir was going to drive their leased cars, his name would have to be listed as an 'alternate driver' with the insurance companies. ICA put Weir down on five different vehicles in June 1979.

The White House switchboard put five calls to Maurice Weir through to an office on Friday where a secretary reported twice that he was "out for a few minutes" and would call back. Press spokesman Rex L. Granum said he would not be able to discuss Weir's job or how long he has worked in the White House.

All such information would have to come from Mrs. Carter's staff and those who could help you are out of the country, he said.

Weir himself said he could not discuss his relationship with Ellsworth of the events of April 11, on "advice of my lawyer."

On April 11, Mrs. Carter first visited Terrell Junior High School for a picture-taking session arranged by Weir to promte "Cities In Schools." Then she went on to that luncheon at the Capitol Hilton.

As far as can be determined, there was minimal, if any, press coverage of the luncheon. Several of those present claim most of the program consisted of people getting up and paying tribute to John Ellsworth. The bill, according to the Capital Hilton business office wass sent to a young woman in New York City who has been identified by police as John Ellsworth's girlfriend.