  We qualify the main features of the spectrum of the Hamiltonian of point
interaction for a three-dimensional quantum system consisting of three
point-like particles, two identical fermions, plus a third particle of
different species, with two-body interaction of zero range. For arbitrary
magnitude of the interaction, and arbitrary value of the mass parameter (the
ratio between the mass of the third particle and that of each fermion) above
the stability threshold, we identify the essential spectrum, localise the
discrete spectrum and prove its finiteness, qualify the angular symmetry of the
eigenfunctions, and prove the increasing monotonicity of the eigenvalues with
respect to the mass parameter. We also demonstrate the existence or absence of
bound states in the physically relevant regimes of masses.
