Line shapes of narrow optical bands: Infrared absorption by $U$ centers and heavier impurities in alkali halides

The shape of the bands for photon absorption and emission by the local constituents of a solid is governed mainly by processes involving many low-energy acoustic phonons. This applies not only to wide bands, such as those exhibited by $F$ centers, but also to narrow ones, as those observed for infrared absorption by local vibration modes of $U$ centers and heavier impurities. The line shapes are theoretically studied on a general basis to show they provide a nice example to illustrate the power of field theory and methods to reproduce experimental facts. To this aim, the phonon induced broadenings of infrared absorption lines by $U$ centers in KCl and KBr, and by substitutional ${\text{Ag}}^{+}$ in KI, were calculated to compare theoretical predictions with experiment. The agreement obtained between both is remarkable.

Figure 1

The function $J_{l^{\prime }l}^{\left(\text{ac}\right)}\left(t;T\right)$, as given by Eq. (61), for $T=100\text{K}$ and ${\Theta }_D=400\text{K}$. Segmented lines represent the parabolic approximation (wide bands), the linear approximation (narrow bands), and the asymptotic behavior giving rise to the zero phonon line.

Figure 2

Infrared absorption by localized modes of substitutional ${\text{H}}^{-}$ ($U$ center) in KCl at $T=57\text{K}$. The circles represent experimental data of Schaefer (Ref. 6) and the solid line depicts Eqs. (76, 77, 78) with the parameters of Table .

Figure 3

Same as Fig. 2 but for $T=90\text{K}$.

Figure 4

Infrared absorption by $U$ centers in KBr at $T=57\text{K}$. The circles represent experimental data of Schaefer (Ref. 6) and the solid line depicts Eqs. (76, 77, 78) with the parameters of Table .

Figure 5

Same as Fig. 4 but for $T=90\text{K}$.

Figure 6

Infrared absorption by ${\text{Ag}}^{+}$ in KI at $T=7.4\text{K}$. The circles represent experimental data of Takeno and Sievers (Ref. 15), and the solid line depicts Eqs. (76, 77, 78) with the parameters of Table .

Figure 7

Same as Fig. 6 but for $T=10.4\text{K}$.