One afternoon in April, six dozen wealthy Americans were entertained at a luncheon party in Midtown Manhattan, along with a special guest from Paris: Henri Loyrette, the director of the Louvre. The host of the exclusive gathering was the Swiss bank UBS, whose elite private bankers built a lucrative business in recent years by discreetly tending the fortunes of American millionaires and billionaires. But now, as the federal authorities intensify an investigation into offshore bank accounts, the secrets of this rarefied world are being dragged into the open - and UBS's privileged clients are running scared. Under pressure from the authorities, UBS is considering whether to divulge the names of up to 20,000 of its well-heeled American clients, according to people close to the inquiry, a step that would have once been unthinkable to Swiss bankers, whose traditions of secrecy date to the Middle Ages. Federal investigators believe some of the clients may have used offshore accounts at UBS to hide as much as $20 billion in assets from the Internal Revenue Service. Doing so may have enabled these people to dodge at least $300 million in federal taxes on income from those assets, according to a government official connected with the investigation. The case could turn into an embarrassment for Marcel Rohner, the chief executive of UBS and the former head of its private bank, as well as for Phil Gramm, the former Republican senator from Texas who is now the vice chairman of UBS Securities, the Swiss bank's investment banking arm. It also comes at a difficult time for UBS, which is reeling from $37 billion in bad investments, many of them linked to risky American mortgages.