content_image/334709.jpg content_image/334715.jpg
<img src='content_image/334709.jpg'>

momentum transferred to the gas is related to the imaginary part of the density response function [see (4)], through a convolution of the atomic density: 

<img src='content_image/334715.jpg'>

In this expression, Im χ$_{nn}$ ( q, ω ; r ) is the imaginary part of the density response function, evaluated within a local density approximation (LDA). The imaginary part of the two-fluid density response function is given by (17) and should be evaluated at the local value of the density. The LDA is justified for wave vectors much larger than the inverse of the size of the trapped gas, so that the system can be considered, locally, as a uniform body. 

Results for the momentum transferred given by (34), as a function of ω/qv$_{F}$ , are shown in figure 9 for T = 0 . 75 T$_{c}$ and choosing σ = 0 . 5 R$_{TF}$ , where R$_{TF}$ ≡ √ ℏ /mω (24 N ) 1 / 6 is the Thomas–Fermi radius of a noninteracting two-component Fermi gas. Although small, the second sound peak is well separated from the first sound peak, revealing that two- photon Bragg spectroscopy might become a practical way to measure second sound. Above and below this temperature, the contribution of second sound to the momentum transfer 

