MOSCOW -- Pyatras Pakenas, a Soviet lawyer separated from his American wife for seven years, is pinning his "last hope" for emigration on Mikhail Gorbachev.

Pakenas already feels indebted to the Kremlin leader for the week the couple spent together last month, when his wife, Galina Vileshina, who emigrated to the United States in 1980, was allowed to fly here from Florida.

He stayed in the Moscow airport for three days when fog stalled Vileshina's plane in London. When she finally arrived, the tears and emotions of seven years apart came tumbling out. "I fell in love all over again," she said in an interview before returning to Florida.

On the eve of Gorbachev's departure for the United States, Pakenas has made a plea to the Kremlin leader personally to overrule officials who have rejected his 17 appeals to join Vileshina. "I have no state secrets, no hostilities. I am not a dissident," the 54-year-old Lithuanian from Vilnius said in an interview here as he stayed close to his wife during her brief, emotion-packed visit, "I just want to be together with my family."

As Gorbachev's third meeting with President Reagan nears, Pakenas and other "refuseniks" are banking on that summit to bring them a personal breakthrough.

Irina Ushakova, a computer programmer who lives in Odessa, on the Black Sea, dramatized her appeals to Gorbachev to allow a reunion with her husband, Alexander Ushakov of Arlington, Va., by starting a hunger strike this week. "It's the only way," she said.

Ushakova, who has breast cancer, has been separated from her Soviet-born husband since 1984, when he defected to the West.

As American and Soviet officials met to prepare the human rights part of the summit agenda, Soviet dissident Naum Meiman pushed his 12-year campaign to emigrate into an emergency phase, regularly calling journalists and western diplomats for news of a possible turn in his case. Recently diagnosed by a group of American doctors as in need of a prostate operation, Meiman said, "I am on the last leg."

And yet, pleas to Gorbachev to allow Meiman to emigrate, including a letter to the Soviet leader signed by every member of the U.S. Senate, have gone unanswered. "Maybe when he is in the States," Meiman said of Gorbachev, "he will not forget that I am still here."

Indeed, as the summit approaches the Soviet leadership has sought to improve the U.S.-Soviet atmosphere by freeing several Soviets who had long been refused permission to emigrate, including activists Ida Nudel and Vladimir Slepak, who have left for Israel and the United States respectively.

In keeping with the letter and spirit of the 1975 Helsinki accords, the Soviet Union is "simplifying human contacts and the solution of questions of family reunion," Rudolf Kuznetsov, who heads the Moscow visa office, said in a recent interview with the official Soviet news agency Tass.

And yet, for every Soviet human rights case that is resolved, a half dozen others come up.

Russian translator Vladimir Boronin, who fought for five years to be relieved of his Soviet citizenship on the grounds that Soviet socialism was not fulfilling its promises, was granted his request in an unprecedented decision of a special Supreme Soviet commission in October.

No sooner was Boronin preparing to leave for the United States, however, than a religious group of 178 Estonians wrote to Gorbachev and Reagan to ask that they, too, be stripped of their Soviet citizenship.

Charging the Soviet state with religious persecution, the so-called "Charter 87" Christian activists, based in the Estonian capital, Tallinn, addressed an angry letter to Gorbachev and hand-delivered it to the Central Committee on Oct. 19.

"We the undersigned renounce the citizenship of the Soviet Union and the spirituality that is dominating here," it said, "and wish until these conditions are settled, to emigrate to such a state where human rights are not trampled underfoot."

Despite new attempts by the Soviet leadership to address human rights issues head-on, such cases of open dissent draw harsh responses. Rein Mets, a religious leader of Charter 87, said that members of the group were followed and harassed by authorities in Tallinn after the letter was dispatched. Last week, a newspaper launched a series of attacks against the group, charging its members with religious fanaticism, Mets said in a telephone interview.

In Moscow, too, demonstrations by dissidents on the eve of the summit have been promptly thwarted by heavy-handed Soviet security forces.

On Nov. 24, Soviet plainclothesmen moved in quickly to cut the cables and destroy some of the equipment used by American television crews who were trying to film a demonstration by Jewish dissidents.

Such moves have prompted a debate among some Soviet intellectuals and Moscow-based westerners about whether the human rights improvements that have occurred in the Soviet Union are substantive or cosmetic.

Some improvements are indisputable. By the end of this year, U.S. officials estimate that about 8,000 Jews will be allowed to leave the Soviet Union -- eight times more than last year.

The rate of emigration for ethnic Germans has risen even more sharply. By the end of this year, it is estimated that 12,000 will leave for West Germany -- more than 12 times the number in 1986.

The number of Soviet citizens who were allowed to travel abroad on private business doubled in the first six months of this year over last year, Kuznetsov told Tass.

Still, the total figure of Soviet emigration to the West this year remains well below that of 1979. That year, 51,000 Jews alone were allowed to leave.

Some individual cases also demonstrate that Soviet emigration procedures, although improved, are still flawed.

Gorbachev has said that Soviets who have done secret work will be allowed to leave after 10 years. But dozens of Soviets are still being prevented from leaving on the grounds that they would give away secrets.

Meiman has been told that the nuclear work he did in the mid-1950s disqualifies him from emigrating to the West.

As Meiman nears 80, however, and his brief spell of nuclear work fades into the distant past, he searches his soul for other reasons that might have stalled his emigratration application for years.

"If Gorbachev knew about my case," he said, "maybe he could bring some reason to it."