GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s52> GLYPH<s48>GLYPH<s46>GLYPH<s54> GLYPH<s48> GLYPH<s53>GLYPH<s48> GLYPH<s49>GLYPH<s48>GLYPH<s48> GLYPH<s73> GLYPH<s109> GLYPH<s40> GLYPH<s113> GLYPH<s44> GLYPH<s41> GLYPH<s32>GLYPH<s91> GLYPH<s97> GLYPH<s114> GLYPH<s98> GLYPH<s46>GLYPH<s32>GLYPH<s117> GLYPH<s110> GLYPH<s105> GLYPH<s116> GLYPH<s115> GLYPH<s93> GLYPH<s47>GLYPH<s40> GLYPH<s113> GLYPH<s118> GLYPH<s70> GLYPH<s41> FIG. 5: The imaginary part of the two-fluid density response function at unitarity. In contrast to the results shown in figure 4, where the relative weights of second and first sound are determined by W$_{2}$/W$_{1}$ , in Bragg scattering they are determined by the smaller ratio B$_{2}$/B$_{1}$ [see (23)]. As a result, second sound has a much smaller weight in Bragg scattering that first sound. At high temperatures, where x = c 2 $_{2}$/c 2 1 ≪ 1 (see figure 1), we have This result was first obtained almost 40 years ago [11, 14, 15, 31] in the context of Brillouin light scattering [13] in superfluid $^{4}$He near the critical region close to T$_{c}$ . For T ≲ 0 . 4 T$_{c}$ , one can see from figure 1 that we can no longer assume x ≪ 1 and hence expand (29). As noted above, the result in (30) was obtained in the classic literature on superfluid $^{4}$He. The Landau-Placzek ratio ϵ$_{LP}$ is extremely small (10 − 2 − 10 − $^{3}$) in superfluid $^{4}$He and thus second sound has generally a very small amplitude in the dynamic structure factor. However, under pressure and close to T$_{c}$ , the magnitude of ϵ$_{LP}$ in liquid $^{4}$He can be signif- icantly increased (to about ϵ$_{LP}$ ∼ 0 . 2) such that a second sound doublet in S ( q, ω ) can be measured using Brillouin light scattering techniques [13]. Such studies [16, 17] have verified the correctness of W$_{2}$/W$_{1}$ = ϵ$_{LP}$ in liquid $^{4}$He at a pressure of P = 25 atmospheres in the 16 W$_{2}$ W$_{1}$ = ϵ$_{LP}$ [1 + 2(1 + ϵ$_{LP}$ ) x + · · · ] ≃ ϵ$_{LP}$ = γ − 1 . (30)