Models for homogeneous line broadening in long-livednuclear states

Abstract

Nuclei embedded in a lattice are submitted to interactions with their surroundings. This produces a randomly fluctuating microfield at the nuclei, perturbing their energy levels. These perturbations can be considered as stochastic processes. Many of the fluctuating phenomena represent the result of a very large number of very small changes. The standard description of such fluctuations is a Gaussian process, defined as a process for which only the first and second moments are different from zero. If a radiating nucleus is constantly perturbed the radiated field can be regarded as undergoing phase fluctuations around the unperturbed nuclear Bohr frequency ω₀. The instant frequency can then be written as ω(t)=ω₀-x(t), where x(t) is the value of a stochastic variable X with zero mean. The first-order correlation function, whose Fourier transform gives the radiated frequency spectrum, depends on the probability function governing X. For a Gaussian, stationary, delta-correlated process, it is shown that the frequency spectrum is Lorentzian. For an arbitrary perturbation having a broad spectrum, it is shown that the frequency spectrum is again Lorentzian. For a narrow perturbation spectrum, the corresponding frequency spectrum is Gaussian.