Spin Relaxation of Atomic Hydrogen in CaF2: Evidence for Local Modes

The spin-lattice relaxation time $T_1$ of atomic hydrogen in calcium fluoride has been measured at 3 kOe and at temperatures from 2.1 to 165°K. The values of $T_1$ can be expressed by $\frac{1}{T_1}=BT+C{\left(\frac{T}{\theta }\right)}^7{J}_6\left(\frac{\theta }{T}\right)+D_H\exp (-\frac{T_H}{T}),$ where $B=0.028\mathrm{}$ ${\sec }^{-1\mathrm{}}$°${\mathrm{K}}^{-1\mathrm{}}$, $C=2.7\mathrm{}\times {10}^4$ ${\sec }^{-1\mathrm{}}$, and $D=9\mathrm{}\times {10}^6$ ${\sec }^{-1\mathrm{}}$. The characteristic temperatures are: $\theta =474\mathrm{}$ °K and $T_H=850\mathrm{}\pm 60$°K. The temperature dependence of the first two terms is consistent with the usual direct and Raman processes, but their relative magnitudes are not well understood. Similar measurements have been made on atomic deuterium centers. The relaxation data for deuterium centers can be accurately fitted by an expression of the above form in which: there is an additional term due to cross relaxation; $B$, $C$, and $\theta$ have the same values; and $D_D=8\mathrm{}\times {10}^5$ ${\sec }^{-1\mathrm{}}$ and $T_D=640\mathrm{}\pm 80$°K. The characteristic temperatures of 850 and 640°K are interpreted in terms of local modes which involve the motion of the interstitial hydrogen and deuterium atoms with respect to neighboring fluorines. The basis for this identification is discussed in terms of Feynman diagrams.