  The Bethe-Salpeter equation (BSE) can provide an accurate description of
low-energy optical spectra of insulating crystals - even when excitonic effects
are important. However, due to high computational costs it is only possible to
include a few bands in the BSE Hamiltonian. As a consequence, the dielectric
screening given by the real part of the dielectric function can be
significantly underestimated by the BSE. Here we show that universally accurate
optical response functions can be obtained by combining a four-point BSE-like
equation for the irreducible polarisability with a two-point Dyson equation
which includes the higher-lying transitions within the random phase
approximation (RPA). The new method is referred to as BSE+. It has a
computational cost comparable to the BSE but a much faster convergence with
respect to the size of the electron-hole basis. We use the method to calculate
refractive indices and electron energy loss spectra for a test set of
semiconductors and insulators. In all cases the BSE+ yields excellent agreement
with experimental data across a wide frequency range and outperforms both BSE
and RPA.
