|MadSci Network: Physics|
This is a very difficult question to answer because the answer is both yes and no. If you mean from "first principles" by combining enough protons, neutrons and electrons to make an atom, the answer is no except for slow neutron capture by Hydrogen to form Deuterium (hydrogen of atomic weight about 2 with one proton, one neutron, and one electron). For all other atoms, the difficulty of making a simultaneous multi-particle collision that will "stick together" is so great that the probability of, say 2 hydrogen nuclei (2 protons) and two neutrons (where to get these is a problem except in a reactor) coming together to from a helium (He-4) atom is essentially zero. Now, on the other hand, if you mean can an atom that doesn't exist in nature be created, the answer is yes. There is a series of transuranic elements (elements heavier than uranium) that have been created by bombarding one atom with another. Recently scientists created isotopes of atomic number 116 and 117. These are superheavy elements made in huge accelerators. This method will work to form many radioactive nuclides, such as Iodine-123 used in nuclear medicine and research. A suitable target is bombarded with a particle (proton, deuteron, triton, He-3, He-4, and on up to even Ca-48). The resulting product may be very unstable and decay with a very short half life, or it may have a half life long enough to make a useful quantity for research or medical diagnosis (nuclear medical imaging). These are very energy intensive processes, and require very large physical facilities, such as high energy "atom smashers" many kilometers in diameter. As a note, it is possible to turn lead into gold through this process, but the cost is so great that it costs more than buying gold on the market. Either way, I hope this helps to answer your question.
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