The dynamic form factor is related to the time-dependent density-density correlation
function by the means of the Fourier transformation:
The correlation function was calculated with non-logarithmic accuracy and is given
by formula (1.180). The evaluation of direct Fourier transformation
(1.181) would give us the expression for the dynamic form factor. It turns
out that it is easier to go other way around, i.e. guess the form of the -th
component of
(1.182) |
(1.183) |
As a reference we use formula 3.771(464/465) from Gradstein-Ryzhik book [GR80]:
The substitution , ,
gives an expression
in terms of
(1.184) |
(1.185) |
Comparing this result with (1.180) we fix so far unknown coefficient of the
proportionality to the value
and, finally, obtain