  TmGa$_{3}$ (AuCu$_3$ structure) undergoes two phase transitions, an
antiferroquadrupolar transition at $\sim$ 4.29 K and long-range
antiferromagnetic ordering at $\sim$ 4.26 K. Due to the close vicinity of the
two phase transitions, TmGa$_3$ offers an interesting system to study the
interplay of charge and magnetic degrees of freedom. In order to understand
this interplay we have performed inelastic neutron scattering experiments on
TmGa$_{3}$ in the paramagnetic regime ($T >$ 5 K) to redetermine the crystal
electric field level scheme. By fitting our spectra at various temperatures we
obtain a new crystal field level scheme with Lea, Leask and Wolf parameters of
$x_{\rm LLW}$ = -0.44(2) and $W$ = -0.222(2) K. The total crystal field
splitting at 5K amounts to $\sim$ 2.3 meV, about an order of magnitude less
than found previously, but in good agreement with the splitting extrapolated
from the related ErGa$_3$ system.
  Our analysis yields a $\Gamma_{2}$ singlet as the crystal field ground state
followed closely by a (nonmagnetic) $\Gamma_{1}$ singlet at 0.009 meV. The next
excited states are a $\Gamma_{5}^{(2)}$ triplet at $\sim$0.5 meV, which is
almost degenerate to a $\Gamma_{4}$ doublet. This level scheme is adverse to
previous findings. Subsequent analysis of the magnetisation along several
crystallographic directions and the temperature dependant susceptibility as
well as of the magnetic contribution to the specific heat are consistent with
our new crystal field parameters. Implications for the antiferroquadrupolar and
the antiferromagnetic transition are discussed.
