What is the title and who is the author of a 1960s science fiction story in which an artificial and miniature life form evolves quickly, is felt to be a threat to humanity, and is eventually bombed using an atomic bomb? By the time of the bombing the life forms are so advanced that they successfully shield themselves from the bomb.
I think this is Theodore Sturgeon's Microcosmic God, which was actually published in 1941. The lifeforms are called "neoterics" and live greatly accelerated lives, leading them to quickly outpace humanity technologically. In the story, the bombs weren't nuclear; there's a scene where Kidder, the scientist who created the neoterics, is running towards his house on one end of the island where he lived while the other end is being bombed. The other details match, though.
From the Wikipedia article:
A highly secretive and reclusive biochemist named Kidder produces inventions that transform human life, spanning every aspect of science and engineering. Unbeknownst to anyone, Kidder has developed a synthetic life form, which he calls "neoterics." These creatures live at a greatly accelerated rate, and therefore have a very short lifespan and produce many generations over a short period of time. This allows Kidder, by presenting them with a frequently changing environment, to "evolve" them quickly into highly intelligent lifeforms who fear Kidder and worship him like a god. Kidder can control his neoterics' environment, and thus force them into developing technology far beyond that of humans. While earlier inventions had been his own, Kidder created the neoterics with the intention that they would become the source of many newer and greater inventions which he could claim as his own.
Kidder's banker takes over the island on which he has built his laboratory, hoping to use a neoteric design for a new source of power to take over the world. When the banker strikes to kill Kidder and the workers who had assisted in building the power plant, Kidder asks the neoterics to throw up an impenetrable force field.
The story ends years later. It is unknown whether or not Kidder is still alive under the shield, and certain that the neoterics have continued to develop technology far in excess of anything controlled by humans. The reader is left to suppose that, if the neoterics were to decide to take the Earth, nothing would stop them.