  Laser-produced Sn plasma sources are used to generate extreme ultraviolet
(EUV) light in state-of-the-art nanolithography. An ultraviolet and optical
spectrum is measured from a droplet-based laser-produced Sn plasma, with a
spectrograph covering the range 200 - 800 nm. This spectrum contains hundreds
of spectral lines from lowly charged tin ions Sn$^{1+}$ - Sn$^{4+}$ of which a
major fraction was hitherto unidentified. We present and identify a selected
class of lines belonging to the quasi-one-electron, Ag-like ([Kr]$4d^{10} nl$
electronic configuration), Sn$^{3+}$ ion, linking the optical lines to a
specific charge state by means of a masking technique. These line
identifications are made with iterative guidance from COWAN code calculations.
Of the 53 lines attributed to Sn$^{3+}$, some 20 were identified from
previously known energy levels, and 33 lines are used to determine previously
unknown level energies of 13 electronic configurations, i.e., $ 7p $, $ (7,8)d
$, $ (5,6)f $, $ (6-8)g $, $ (6-8)h $, $ (7,8)i $. The consistency of the level
energy determination is verified by the quantum-defect scaling procedure. The
ionization limit of Sn$^{3+}$ is confirmed and refined to 328908.4 cm$^{-1}$
with an uncertainty of 2.1 cm$^{-1}$. The relativistic Fock space coupled
cluster (FSCC) calculation of the measured level energies are generally in good
agreement with experiment, but fail to reproduce the anomalous behavior of the
$5d$ $^2$D and $nf$ $^2$F terms. By combining the strengths of FSCC, COWAN code
calculations, and configuration interaction many-body perturbation theory
(CI+MBPT), this behavior is shown to arise from interactions with
doubly-excited configurations.
