A Beliaev theory incorporating a semi-phenomenological roton backflow effect

We have developed a Beliaev theory incorporating a semi-phenomenological ro ton backflow effect in order to examine the effect of the backflow on the Q uantum Evaporation of atoms from the free surface of superfluid He-4. A the ory of Quantum Evaporation based on a real-space Beliaev theory neglecting roton backflow was recently developed by Sobnack et al. [Phys. Rev. B 60, 3 465 (1999)] and in this paper we discuss the extension of the theory to inc lude the backflow physics from the Aldrich-Pines polarization potential the ory of the 1970's. The calculation of the effect of the backflow on Quantum Evaporation is presented elsewhere.