  We present the results of spectroscopic measurements in the extreme
ultraviolet (EUV) regime (7-17 nm) of molten tin microdroplets illuminated by a
high-intensity 3-J, 60-ns Nd:YAG laser pulse. The strong 13.5 nm emission from
this laser-produced plasma is of relevance for next-generation nanolithography
machines. Here, we focus on the shorter wavelength features between 7 and 12 nm
which have so far remained poorly investigated despite their diagnostic
relevance. Using flexible atomic code calculations and local thermodynamic
equilibrium arguments, we show that the line features in this region of the
spectrum can be explained by transitions from high-lying configurations within
the Sn$^{8+}$-Sn$^{15+}$ ions. The dominant transitions for all ions but
Sn$^{8+}$ are found to be electric-dipole transitions towards the $n$=4 ground
state from the core-excited configuration in which a 4$p$ electron is promoted
to the 5$s$ sub-shell. Our results resolve some long-standing spectroscopic
issues and provide reliable charge state identification for Sn laser-produced
plasma, which could be employed as a useful tool for diagnostic purposes.
