Acoustic modes in He I and He II in the presence of an alternating electric field

By solving the equations of ordinary and two-fluid hydrodynamics, we study the oscillatory modes in isotropic nonpolar dielectrics He I and He II in the presence of an alternating electric field $\mathbf{\text{E}}=E_0{\mathbf{\text{i}}}_z\sin (k_{0}z-{\omega }_{0}t)$. The electric field and oscillations of the density become ``coupled,‘’ since the density gradient causes a spontaneous polarization ${\mathbf{\text{P}}}_s$, and the electric force contains the term $({\mathbf{\text{P}}}_s\mathrm{\nabla })\mathbf{\text{E}}$. The analysis shows that the field $\mathbf{\text{E}}$ changes the velocities of first and second sounds, propagating along $\mathbf{\text{E}}$, by the formula $u_{j}\approx c_{j}+\chi_{j} E_{0}^{2}$(where$j=1, 2$;$c_{j}$isthevelocityofthe$j$-thsoundfor$E_{0}=0$,and$\chi_{j}$isaconstant)\mathrm{.}Wehavefoundthatthefield$$\mathbf{\text{E}}$$jointlywithawaveofthefirst(second)sound$(\omega,k)$shouldcreateinHeIIhybridacousto-electric(thermo-electric)densitywaves$(\omega + l \omega_{0},k + lk_{0})$,where$l=\pm 1, \pm 2, \ldots$. The amplitudes of acousto-electric waves and the quantity $\mathrm{\mid }{u}_1-c_1\mathrm{\mid }$ are negligibly small, but they should increase in the resonance way at definite $\omega$ and ${\omega }_0$. Apparently, the first resonance corresponds to the decay of a photon into two phonons with the transfer of a momentum to the whole liquid. Therefore, the spectrum of an electromagnetic signal should contain a narrow absorption line like that in the M"{o}ssbauer effect.