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.
