A one-dimensional quantum mechanical model for nuclear-resonant scattering of gamma radiation from matter is developed assuming the source radiation is gamma decay. A closed-form, finite-sum solution for the radiated intensity is obtained by restricting the calculation to coherent forward scattering. The solution provides a unified microscopic picture of nuclearresonant scattering processes in which the radiation undergoes sequential scattering from one nucleus to another before reaching the detector. For recoil-free processes the various 'paths' to the detector contribute coherently. The solution for this case gives results identical to the classical optical model. The one-dimensional model shows that the 'speed-up' and 'dynamical beating' effects are primarily a consequence of the fact that the single-nuclear scattering processes are 180 • out of phase with the incident radiation while the double-nuclear-scattering processes are in phase with the incident radiation. All multiple-scattering paths are, and must be, included. The model can treat the incoherent processes, i.e. processes involving gamma emission with recoil or conversion-electron emission. The results show that a correction may be needed when analysing time-differential Mössbauer spectroscopic data due to incoherent processes that occur in the absorber.

Electron spin resonance study of γirradiated cadmium formate dihydrate and manganese(II) ions in cadmium formate dihydrate Several dihydrated formates inciuding:Ni (HCOO)2' 2Ht) and Fe(HCOOh·2H20 crystallize in a monoclinic structure whose unit cell contains two each of two inequivalent types of metal ions. The temperature variation of the powder susceptibility, Xp, of the Ni+ + salt suggests that those ions on one type of site become cooperatively ordered near 15.7°K while the rest remain essentially independent even at 1.3°K. XP for the Fe+ + salt exhibits a huge peak at 3.68°K associated apparently with the long-range ordering of moments on sites of both types. Mossbauer experiments at 300 0 K on the Fe+ + salt clearly distinguish ions on the two sites, the ratio of the effective electric}ield gradients being ",5 to 1. The smaller field gradient is assumed to characterize the site (type 1) . approximately octahedrally coordinated by oxygens from six formate groups. The Mossbauer spectrum near the transition point differs from those measured at 300°, 77°, 20 0 , and 4°K, The results show that the internal magnetic field is larger at the type 1 sites. Preliminary calculations uiing the observed nuclear hyperfine structure indicate that the ratio of magnetic fields at the two sites is about four to one.

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Relatively simple computational methods for interpreting Mössbauer spectra, in which there are simultaneously static quadrupole and hyperfine interactions, have been developed. Our explicit calculations are restricted to the case when either the source or absorber is a ``single line'' and the nuclear levels are the same as in the 57Fe 14.4-keV transition. Experimental spectra for powdered RbFeF3 and FeCr2S4 have been obtained and are analyzed using these methods. Our results show that although the quadrupole interaction ΔEQ is zero above the transition temperatures of both RbFeF3 and FeCr2S4 it is rather large below, i.e., in FeCr2S4, ΔEQ=0.78 mm/sec at 77° K and in RbFeF3, ΔEQ=3.00 mm/sec at 4°K. The isomer shift, the effective internal magnetic field, and its orientation with respect to the principal axes of the electric-field-gradient tensor in these substances at various temperatures are also obtained.

Previous theoretical descriptions of nuclear resonant scattering of synchrotron radiation have been based on the semiclassical optical model or on several quantum mechanical models. These models are fine but do not give a clear physical picture of all the processes. The theory presented here gives a clear physical picture of all the relevant aspects of nuclear resonant scattering. The model treats the nuclear resonant sample as a onedimensional chain of ''effective'' nuclei. However, the model is deceptive. It only appears to be one dimensional. It actually treats the sample as a series of ''effective'' planes. The analysis uses the time-dependent quantum mechanical techniques due to Heitler. A closed form solution, for the time-dependent forwardscattered intensity, is found. The only parameter in the theory is N the number of ''effective'' nuclei ͑planes͒ in the model. It is shown that the prominent experimental features, the ''speed-up'' and ''dynamical beat'' effects, are primarily due to a phase change of reemitted radiation, compared to the incident radiation, that occurs when radiation is absorbed and reemitted without recoil by a single ''effective'' nucleus ͑plane͒. The model also predicts results for the incoherent processes.