Second Lt. Christopher M. Cooke, deputy commander an Air Force Titan missile crew, admitted May 9 that for about the previous year he had been "photographing, copying and giving to the Soviets" secret information about the nation's strategic nuclear arsenal, the Air Force charged in court yesterday.

In making a first sworn statement two days earlier, Cooke, 25, of Richmond, had claimed he visited the Soviet Embassy here only to collect informaton for a research paper on U.S.-Soviet relations, the court papers said.

Cooke hoped that he eventually might join the CIA as a political analyst, according to the court papers.

In that 17-page statement, attached to the court papers, Cooke described how he used the name "Mark Johnson" in visits to the embassy and even called his father from there to tell him he was having car trouble.

Cooke was picked up by Air Force investigators after they followed hom to the embassy May 2. At the time, he was not carrying his military identification but had a passport and British currency with him, the papers said.

Although Cook is being court-martialed by the Air Force for his contacts with the embassy, the Justice Department has been hesitant to press espionage charges because of a controversy about the whether he was granted full immunity in return for his confession.

The Air Force announced May 28 that Cooke was being investigated, and unidentified officials told reporters that codes on U.S. strategic missiles had to be changed because of the contacts. But yesterday's court filing apparently is the first official government account of Cooke's alleged espionage activities.

The Air Force filed the papers yesterday in the U.s. Court of Military Appeals in response to a petition from Cooke's military attorney to block the court-martial and release Cooke from custody because of misconduct by Gen. Richard H. Ellis, since retired as head of the Strategic Air Command.

Controversy in the case centers on Cooke's claim that the Air Force reneged on an agreement granting him immunity.

The Air Force admits that Cooke was questioned and gave his original statement without being informed of his rights. Cooke was not allowed access to an attorney until May 9, after he had refused to take a lie-detector test without a promise of an honorable discharge, the papers said.

The dispute arose when Cooke confessed that he turned over classified nuclear secrets to the Soviets. Cooke's attorney and some Air Force investigators have testified that the immunity agreement was to apply to all this statements, but SAC leaders insist that the deal was negated because Cooke lied in his first statement.

The Air Force acknowledged in a footnote in the filing that ill immunity agreements are supposed to be coordinated first with the Justice Department. That not done because SAC never intended to give Cooke immunity, the papers said.

Ellis had not authorized it personally, so a promise by a subordinate general had no more effect than if he said "the moon was made of green cheese," Air Force lawyers argued.

In a telephone interview from Richmond last night, the lieutenant's mother, Betty Cooke, said, "They [air Force office] have broken their bond and their word." She said her son is being held at McConnell Air Force Base in Kansas, where has missile crew was based.

In his first sworn statement to Air Force investigators, Cooke said he first went to the embassy last Dec. 17. But the Air Force has said he made his first contacts several months earlier in midsummer.

In their filing, Air Force attorneys said Cooke once "compromised information" to Alan J. Ward a professor at Cooke's college, William & Mary in Williamsburg, Va. Ward could not be reached for comment. He has said the information was "nothing that couldn't be read in a military magazine," according to Mrs. Cooke

Arguing against releasing Cooke from custody, the Air said he might flee because he has friends overseas, has traveled abroad "on the spur of the moment" and has a former identity he could easily assume. That identity was not further explained.

The papers addded that Cooke was "intrigued with spy and clandestine scenarious" and had spoken to one individual about selling classified information.

In his statement May 7, Cooke gave this description of his contacts with the Soviets:

On the Dec. 17 visit, he told embassy officials has name was Mark Johnson and, while he insisted he left no classified documents, he did give the Soviets some photo negatives of charts from his master's degree thesis on U.S.-Soviet "tactical nuclear doctrine."

Cooke said he left negative for "pyschological impact," to enhance the "aura" of his role as a possible source of information. In an accompany note, he asked that a Soviet official go to a Richmond motel two days later to meet him. When no one did, he returned to the embassy Dec. 23 and, in a discussion with an official, said, "I'm on a missile crew."

When he left, Cooke said, he was "quite optimistic. I felt that they were interested in using me as a medium for the promulgation of a policy shift or some sort of initiative which would provide me with a first-rate piece of publishers material."