Optical Properties of K between 4 and 10.7 eV and Comparison with Na, Rb, and Cs

The optical and dielectric constants of K have been determined from reflectance and transmission measurements for photons of energy between 4.0 and 10.7 eV. Reflectance measurements were made as a function of incident angle at a K-Mg${\mathrm{F}}_2$ interface in an ultrahigh-vacuum system. The refractive index ($n$) was determined from the critical angle for total internal reflection and the absorption coefficient ($k$) from the slope of the reflectance curve at the critical angle and from transmission measurements. The real part of the dielectric function (${\epsilon }_1$) and the optical conductivity $\sigma =\frac{\omega {\epsilon }_2}{4\pi }$ were derived from $n$ and $k$. In $\sigma$ we find a broad peak centered at 8 eV. This absorption peak is discussed along with comparable peaks in Na, Rb, and Cs. One-electron and many-body processes that might give absorption in this energy region are discussed. ${\epsilon }_1$ is analyzed in terms of a nearly-free-electron model to obtain a value of the effective mass ($m_{\mathrm{eff}}$) and of the contribution of core polarization ($4\pi n_0\alpha$) to ${\epsilon }_1$. We find $4\pi n_0\alpha =0.15\mathrm{}\pm 0.01$ and $\frac{m_{\mathrm{eff}}}{m_0}=1.01\mathrm{}\pm 0.01$.