Theory of Nuclear Resonance Intensity in Dilute Alloys

Abstract

Experiments of Bloembergen and Rowland have shown that the intensity of the nuclear resonance signal in metallic Cu decreases rapidly when small quantities of other elements are alloyed with it. These results require that each solute atom produces significant electric field gradients in its vicinity, sometimes affecting as many as 85 neighboring Cu nuclei. In this paper we show that field gradients of approximately the required magnitude arise from the redistribution of the conduction electron charge density near the solute atoms. A crucial feature of our theory is that at large distances $r$ from a solute atom the electron density behaves as $\frac{cos(2{k}^{0}r+\ensuremath{\phi})}{{r}^{3}}$ where ${k}^{0}$ is the Fermi wave number and $\ensuremath{\phi}$ is a phase. Our agreement with experiment is a confirmation of this behavior. Such an oscillatory behavior is a consequence of a discontinuous drop at the Fermi surface of $n(\mathrm{k})$, the occupation probability of the conduction band function with wave vector k.