beta decay, which would produce uranium-232, but this has not yet been observed experimentally. All isotopes from 232U to 236U inclusive have minor cluster decay branches (less than %), and all these bar 233U, in addition to 238U, have minor spontaneous fission branches; the greatest branching ratio for spontaneous fission is about % for 238U, or about one in every two million decays. The shorter-lived trace isotopes 237U and 239U exclusively undergo beta decay, with respective half-lives of 6.752 days and 23.45 minutes. In total, 27 isotopes of uranium have been identified, ranging in mass number from 214 to 242, with the exceptions of 220 and 241. Among the uranium isotopes not found in natural samples or nuclear fuel, the longest-lived is 230U, an alpha emitter with a half-life of 20.23 days. This isotope has been considered for use in targeted alpha-particle therapy (TAT). All other isotopes have half-lives shorter than one hour, except for 231U (half-life 4.2 days) and 240U (half-life 14.1 hours). The shortest-lived known isotope is 221U, with a half-life of 660 nanoseconds, and it is expected that the hitherto unknown 220U has an even shorter half-life. The proton-rich isotopes lighter than 232U primarily undergo alpha decay, except for 229U and 231U, which decay to protactinium isotopes via positron emission and electron capture, respectively; the neutron-rich 240U and 242U undergo beta decay to form neptunium isotopes. Enrichment In nature, uranium is found as uranium-238 (99.2742%) and uranium-235 (0.7204%). Isotope separation concentrates (enriches) the fissile uranium-235 for nuclear weapons and most nuclear power plants, except for gas cooled reactors and pressurised heavy water reactors. Most neutrons released by a fissioning atom of uranium-235 must impact other uranium-235 atoms to sustain the nuclear chain reaction. The concentration and amount of uranium-235 needed to achieve this is called a 'critical mass'. To be considered 'enriched', the uranium-235 fraction should be between 3% and 5%. This process produces huge quantities of uranium that is depleted of uranium-235 and with a correspondingly increased fraction of uranium-238, called depleted uranium or 'DU'. To be considered 'depleted', the uranium-235 isotope concentration should be no more than 0.3%. The price of uranium has risen since 2001, so enrichment tailings containing more than 0.35% uranium-235 are being considered for re-enrichment, driving the price of depleted uranium hexafluoride above $130 per kilogram in July 2007 from $5 in 2001. The gas centrifuge process, where gaseous uranium hexafluoride