Hargreaves, American correspondent for British commercial television, seems to have modeled his State of the Nation report on Anthony Sampson's Anatomy of Britain. Superpower is in fact an anatomy of the U.S.A., a cool, modulated dissection of America on the brink of a new era. A superpower it still is; the richest, most variegated country in the world. But a superpower beset with unprecedented ills -- economic, social, political, spiritual. A giant facing onsetting middle age and the prospect of at least a relative slackening in its industrial sinews, its cities, its political and military leverage abroad. The twice-devalued dollar tells the story; so does the lopsided trade in balance of the trillion-dollar economy -- this year a colossal $30.5 billion or ""three times the official value of all the gold in Fort Knox."" On the level of national politics the sores are even more apparent: in the foundering fortunes of Richard Nixon, the righteous Puritan who spawned Watergate and brought the presidency to ""its lowest point of regard since the United States first became a major figure in the world arena."" In Congress, which in the words of one senator, ""has become a third or fourth-class power, a separate and thoroughly unequal branch of our national government."" Or, for the most glaring signs of decay, look as Hargreaves does at the cities. There is a neighborhood in Boston where the infant-mortality rate ""compares unfavorably with the Congo."" New York's South Bronx is ""a necropolis -- a city of death."" And it's the same or worse in large sectors of St. Louis, Detroit, Cleveland, Chicago -- ""utter desolation"" in the words of the Commission on the Cities in the Seventies. You've heard all this before? Yes, to be sure. But Hargreaves' methodical scanning of American society is so judicious, so unhysterical, so unlike the tirades and laments of most media Cassandras, that the book is sure to gain the attention and prestige it deserves.