This paper is mainly concerned with the prediction of absorption-line spectral features in cool stars, to be used as input in stellar population synthesis projects. From a detailed comparison with the solar intensity spectrum, we have refined the main parameters of atomic and molecular absorption lines that are prominent in the 4850-5400 Angstrom wavelength interval. This line list was used to compute an extensive library of synthetic stellar spectra at high resolution in the temperature range T-eff = 4000-8000 K, surface gravity interval log g = 1.0-5.0 dex, metallicities ([M/H]) from -1.0 to +0.5 dex, and microturbulent velocity xi = 2 km s(-1). The computations were performed by using the latest release of Kurucz's model atmospheres and numerical codes. The library contains a total of 693 synthetic spectra, from which iron and magnesium indices were obtained, together with the corresponding ''pseudocontinuum'' fluxes. We illustrate the behavior of five ''Lick-like'' spectral indices, namely, Mg-1, Mg-2, Mg b, Fe5270, and Fe5335, in terms of the main atmospheric parameters, namely, effective temperature, surface gravity, and metallicity. The trend of the indices with microturbulent velocity is also illustrated by means of an additional set of spectra computed at different microturbulent velocities. Transformation equations of the theoretical grid into the Lick/IDS observational database are presented, showing the full consistency of our grid with the empirical database.