A band shape described by the Gaussian function: \[F\left(\nu - \nu _{0}\right) = \frac{a}{\sqrt{\pi }}\ \text{e}^{-a^{2}\ (\nu - \nu _{0})^{2}}\] In this equation, \(a^{-1}\) is proportional to the width of the band, and \(\nu _{0}\) is the frequency of the band maximum.