We actually do use Nuclear Power in spacecraft through what is termed Radioisotope Thermoelectric Generator (RTG). This were used as far back the late 1950's mostly to generate electric power for deep space or long termed missions. read more
While we can use nuclear power for spacecraft, there are a lot of technical problems to solve. So far, solar power and advanced solar power generation systems are meeting the needs of most spacecraft being built or contemplated. read more
You would think that 34 years later we would have the technology to make this even more viable source of electricity then when the Voyagers were designed and built. The New Frontiers spacecraft seems like an excellent candidate for nuclear power. read more