Theory of the Influence of Environment on the Angular Distribution of Nuclear Radiation

The effect of electronic relaxation processes on the angular correlation and on the angular distribution of radiation from oriented nuclei is investigated. The influence of the environment on the radioactive nuclei is taken into account by reducing the density operator for the total system (nucleus and surroundings mutually interacting) to a density operator for the nucleus alone. Elimination of the unobserved bath variables is performed with the help of Zwanzig's projection-operator technique. The Liouville formalism is used throughout. The (initially unspecified) properties of the environment enter the theory via second-order correlation functions, which are defined in terms of equilibrium ensemble averages of certain bath operators, like, e.g., the hyperfine-field operator. The matrix elements of the nuclear-evolution operator (which is a superoperator in Liouville space) with respect to a complete orthonormal set of multipole operators are just the usual perturbation factors ${G_{k{k}^{\prime }}}^{q{q}^{\prime }}$ of perturbed-angular-correlations theory. The consequent use of the multipole representation yields immediately the final formulas needed in the expression for both the angular distribution of radiation from oriented nuclei and the angular correlation function. The general theory includes relaxation processes due to magnetic and quadrupole interactions. The important case of purely magnetic interactions is discussed in more detail. Specialization to relaxation caused by randomly fluctuating fields yields a formula which contains both the Abragam-Pound result for time-fluctuating quadrupole interaction and Micha's extension to randomly time-varying magnetic fields in multidomain ferromagnets. Exact high-temperature solutions are presented for single crystals in a static magnetic field and with magnetic-type relaxation processes (axially symmetric case). For nuclei with spin $I=1\mathrm{}$, the extension to arbitrary temperatures has been considered. The application of the present theory to the problem of multipole relaxation (which arises, e.g., in spin-lattice relaxation measurements with NMR/ON technique) is discussed.