to produce about 1 billionth of a gram (the amount used so far for particle/antiparticle collisions). In comparison, to produce the first atomic weapon, the cost of the Manhattan Project was estimated at $23 billion with inflation during 2007. Several studies funded by the NASA Institute for Advanced Concepts are exploring whether it might be possible to use magnetic scoops to collect the antimatter that occurs naturally in the Van Allen belt of the Earth, and ultimately, the belts of gas giants, like Jupiter, hopefully at a lower cost per gram. Uses Medical Matter–antimatter reactions have practical applications in medical imaging, such as positron emission tomography (PET). In positive beta decay, a nuclide loses surplus positive charge by emitting a positron (in the same event, a proton becomes a neutron, and a neutrino is also emitted). Nuclides with surplus positive charge are easily made in a cyclotron and are widely generated for medical use. Antiprotons have also been shown within laboratory experiments to have the potential to treat certain cancers, in a similar method currently used for ion (proton) therapy. Fuel Isolated and stored antimatter could be used as a fuel for interplanetary or interstellar travel as part of an antimatter-catalyzed nuclear pulse propulsion or another antimatter rocket. Since the energy density of antimatter is higher than that of conventional fuels, an antimatter-fueled spacecraft would have a higher thrust-to-weight ratio than a conventional spacecraft. If matter–antimatter collisions resulted only in photon emission, the entire rest mass of the particles would be converted to kinetic energy. The energy per unit mass () is about 10 orders of magnitude greater than chemical energies, and about 3 orders of magnitude greater than the nuclear potential energy that can be liberated, today, using nuclear fission (about per fission reaction or ), and about 2 orders of magnitude greater than the best possible results expected from fusion (about for the proton–proton chain). The reaction of of antimatter with of matter would produce (180 petajoules) of energy (by the mass–energy equivalence formula, ), or the rough equivalent of 43 megatons of TNT – slightly less than the yield of the 27,000 kg Tsar Bomba, the largest thermonuclear weapon ever detonated. Not all of that energy can be utilized by any realistic propulsion technology because of the nature of the annihilation products. While electron–positron reactions result in gamma ray photons, these are difficult to direct and use