Abstract
A statistical analysis is made of spin transitions induced by dipole interactions which change the total magnetization while exactly conserving energy. The first-order effect of the dipole operator can be described by a function $\ensuremath{\Phi}(\ensuremath{\omega})$, which is related to the level broadening observed in resonance lines. The second-order effect leads to a function $\ensuremath{\chi}(\ensuremath{\omega})$ which represents the power spectrum of the dipole operator. The cross-relaxation probability ${W}_{\mathrm{CR}}(\ensuremath{\omega})$ is given by the convolution of these two functions. ${W}_{\mathrm{CR}}$ is calculated explicitly in various approximations, without appeal to moments. For single-spin flips in magnetically dilute systems, the magnitude of ${W}_{\mathrm{CR}}$ depends linearly on the concentration $n$. There is a very sharp peak at $\ensuremath{\omega}=0$ with a width proportional to the geometric mean of the resonance width and of the nearest-neighbor dipole energy.
Published Version
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