  We study the effects of non-local thermodynamic equilibrium (NLTE) on the
abundance analysis of barium, magnesium, and manganese from integrated light
spectroscopy, as typically applied to the analysis of extra-galactic star
clusters and galaxies. In this paper, our reference object is a synthetic
simple stellar population (SSP) representing a mono-metallic alpha-enhanced
globular cluster with the metallicity [Fe/H]=-2.0 and the age of 11 Gyr. We
used the MULTI2.3 program to compute LTE and NLTE equivalent widths of spectral
lines of Mg I, Mn I, and Ba II ions, which are commonly used in abundance
analyses of extra-galactic stellar populations. We used ATLAS12 model
atmospheres for stellar parameters sampled from a model isochrone to represent
individual stars in the model SSP. The NLTE and LTE equivalent widths
calculated for the individual stars were combined to calculate the SSP NLTE
corrections. We find that the NLTE abundance corrections for the integrated
light spectra of the the metal-poor globular cluster are significant in many
cases, and often exceed 0.1 dex. In particular, LTE abundances of Mn are
consistently under-estimated by 0.3 dex for all optical lines of Mn I studied
in this work. On the other hand, Ba II, and Mg I lines show a strong
differential effect: the NLTE abundance corrections for the individual stars
and integrated light spectra are close to zero for the low-excitation lines,
but they amount to -0.15 dex for the strong high-excitation lines. Our results
emphasise the need to take NLTE effects into account in the analysis of spectra
of individual stars and integrated light spectra of stellar populations.
