Breadth of theFBand in NaCl

The breadth of the $F$ band in NaCl is calculated for various temperatures, primarily in order to investigate the status of the semiempirical configuration coordinate treatment of such problems. The main new feature of the calculation, which involves no adjustable parameters, is the use of the realistic normal modes employed in the Born-Blackman theory of specific heats. The eigenvectors as well as the eigenfrequencies of these modes are used. Modifications of the modes due to the missing ion at the $F$ center are ignored. The coupling to the $F$ center is determined from electrostatic forces on individual ions. Simpson's $F$ center wave functions are used and the calculated breadths are all about 85% of the experimental values. It is found that the main contributions to the breadth come from modes in a fairly small range of frequencies (much lower than the frequencies of the longitudinal optical modes considered in previous calculations) which includes the empirical configuration coordinate frequency. This last result helps to clarify the relation of the hypothetical configuration coordinate mode to the actual modes of lattice vibration.