Computation Of The Normal And Anomalous Terms In The Lowest Order Anharmonic Contributions To The Debye-Waller Factor For Sodium Metal

It has been shown by Maradudin and Flinn1(1963) that, in weak anharmonic crystals, the lowest order anharmonic contributions to the Debye-Waller factor are of0(λ2), where λ is the Van Hove2(1961) ordering parameter. There are four such terms, two of them are of$0(\mathop{\lower-0.03pt\hbox{$q$}}\limits_{\raise5pt\hbox{\tiny$\sim$}}{}\!^2_o)$}(where$\mathop{\lower-0.03pt\hbox{$q$}}\limits_{\raise5pt\hbox{\tiny$\sim$}}_o$}is the scattering wave-vector) and are known as the normal terms. Other two terms are of$0(\mathop{\lower-0.03pt\hbox{$q$}}\limits_{\raise5pt\hbox{\tiny$\sim$}}{}\!^4_o)$}and are known as the anomalous terms. These four terms are of significant complexity. In this present work, a computation of these four terms will be reported for sodium metal and the results will be compared with experimentally determined values.