We propose a first-principles methodology for calculating the behavior of isolated impurities immersed in quantum fluids. To obtain an accurate description of correlation effects between the impurity and the host, we work in the frame of reference in which the impurity is stationary, building on the work of C. H. Leung, M. J. Stott and C. O. Almbladh Phys. Lett. 57A 26 (1976). We apply our methodology to the case of a positron immersed in an electron gas. Our positron relaxation energies and annihilation rates are similar to those from the best existing many-body calculations. Our annihilating-pair momentum densities are significantly different from previous data and include a “tail” after the Fermi edge.