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In the absence of shielding, "ordinary" nuclear weapons-those containing kilogram quantities of ordinary weapon-grade (6 percent plutonium-240) plutonium or uranium-238-can be detected by neutron or gamma counters at a distance of tens of meters. Objects such as missile canisters can be radiographed with high-energy x-rays to reveal the presence of the dense fissile core of any type of nuclear warhead, or the radiation shielding that might conceal a warhead. If subjected to neutron irradiation, the fissile core of any type of unshielded warhead can also be detected by the emission of promptor delayed-fission neutrons at a distance on the order of 10 meters.Devices capable of detecting the presence of nuclear weapons could be useful in verifying compliance with various arms control agreements. Examples include monitoring a ban of nuclear weapons on ships, verifying limits on the number of nuclear warheads on individual ballistic missiles, and verifying limits on the nuclear versions of dual-capable weapons such as sea-launched cruise missiles.To the best of our knowledge, all nuclear weapons contain at least several kilograms of fissile material-material that can sustain a chain reaction. Such material provides the energy for fission explosives such as those that destroyed Hiroshima and Nagasaki; it is also used in the fission triggers of

The rate of multiphonon relaxation of rare-earth ions in crystals has been calculated using the Kubo representation of the rate constant in terms of linear response time correlation functions. The nonadiabatic electron-phonon operator arising from the effect of the kinetic energy of the ions on the Born-Oppenheimer basis functions is employed in the first-order perturbation theory. The calculations yield the explicit dependence of the decay rate on the temperature, the transition energy gap, the phonon energy, and the displacements of the adiabatic potentials. Excellent agreement between theory and experiment has been obtained for the multiphonon relaxation phenomenon observed in LaF3:Er3+, LaCl3:Dy3+, LaCl3:Nd3+, and LaBr3:Dy3+. Although the comparison of theory and experiment is specialized to the nonradiative relaxation of rare earth ion excited states in crystals, the treatment given in the present paper is also generally valid for the relaxation of excited states by internal conversion in large molecules.

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164As a result of the last equation, the expansion of an arbitrary state vector |/) is invariant under the 3 R.