An analytic model is developed to describe the inelastic processes occurring when keV Ne+ ions are scattered at grazing incidence by the (100) surface of LiF. The large energy losses (up to 30 eV) of the reflected Ne+ particles reported by Borisov et al (1999 Phys. Rev. Lett. 83 5378) are shown to arise specifically from the long-range coupling between the projectiles and the so-called Fuchs-Kliewer (FK) optical phonons of LiF whose fields extend far outside the surface. The strength of the coupling is estimated, allowing one to compute the average number of excited FK phonon quanta (HωS = 0.071 eV) and hence the mean energy losses. For emerging, neutralized Ne0, a distinct energy loss mechanism is shown to occur, namely the excitation of FK phonons and other types of surface collective modes associated with the screening of the F0 'hole' left behind by the neutralization process. This mechanism contributes a large fraction of the loss, additional to that suffered by the incident Ne+ ion. The model explains the experimental observations quantitatively (1999 Phys. Rev. Lett. 83 5378). The paper ends with a discussion of the large energy broadening of the observed loss peaks.