The U.S. Government and the Veterans Administration do not agree. Six times since 1977, most recently on June 7, the V.A. has rejected Mr. Smitherman's claim to disability pay. That means that upon his death the wife he calls ''Momma'' will receive no pension.

In fact, of 2,883 radiation-related claims filed by veterans or their widows, the V.A. had granted only 16 by November 1982 - although from 1945 to 1977 the U.S. had detonated 600 atomic and nuclear weapons, 236 of them in the atmosphere and 5 underwater. By Pentagon estimates, between 250,000 and 500,000 service and civilian personnel were exposed to the atmospheric tests.

The V.A. steadfastly maintains that none of the rejected claimants, including John Smitherman, were sufficiently exposed to radiation to have suffered ill effects. As one result, more than 8,000 of those affected have formed the National Association of Atomic Veterans, of which Mr. Smitherman is president.

Theirs is an uphill battle. The Government never took precise measurements - either by amount or type - of the radiation doses that test personnel might have received. Nor did it maintain systematic records of who had been exposed; and many of the records that did exist were destroyed in a military warehouse fire at St. Louis. Until the Centers for Disease Control undertook a limited study of leukemia incidence in one test group in 1977, the Government had made no effort to find out what might have happened to the exposed persons. It still resists doing so, even though the C.D.C. study's preliminary results show that among the 3,224 men present at the ''Smoky'' test explosion in Nevada in l957, leukemia has been contracted at three times the expectable rate for their age group. Polycythemia vera, a rare pre-malignant disease of the bone marrow, has occurred among Smoky veterans at 1,000 percent above the expected rate. And the N.A.A.V. says that of 700 respondents to a questionnaire sent to its members, 39 percent reported some form of cancer, 67 percent some form of neuromuscular disease, and 51 percent various problems - such as skeletal and organ defects and retardation - in their offspring. Neither the questionnaire nor the limited C.D.C. leukemia study is conclusive. Neither, perhaps, is the fact that nearly half of the Marshall Island natives exposed to fallout from a 15- megaton thermonuclear explosion over Bikini on March 1, l954, have had thyroid tumors or other radiation-related problems. But surely the N.A.A.V. is justified in demanding what the Government has so far refused - ''a large-scale epidemiological study of atomic veterans'' by an independent agency, to determine the connection, if any, between radiation and disease - hence the responsibility of the Government. The study would be costly and difficult; but then so is death by cancer. For his part, John Smitherman does not intend to go gentle into whatever good night may be reserved for those who served their country without question. By Federal law, he cannot sue the V.A. to overturn its denial of disability pay; but last week he filed a $6.5 million malpractice suit, contending that the V.A. not only failed to diagnose his cancerous condition in l977 and thereafter, but that it neither wanted nor tried to make such a finding. If the suit prevails, he and his lawyers hope that the V.A. may be forced at last to take some responsibility for atomic veterans. That would be a legacy worth leaving, even if victory can do him little personal good. In a recent telephone interview he said he didn't know how much longer he had to live - ''God knows that and we don't'' - but that his doctors had told him, ''You'd better go home and spend as much time with Momma as you can.''