  A quantum mechanical three-body problem for two identical fermions of mass
$m$ and a distinct particle of mass $m_1$ in the universal limit of zero-range
two-body interaction is studied. For the unambiguous formulation of the problem
in the interval $\mu_r < m/m_1 \le \mu_c$ ($\mu_r \approx 8.619$ and $\mu_c
\approx 13.607$) an additional parameter $b$ determining the wave function near
the triple-collision point is introduced; thus, a one-parameter family of
self-adjoint Hamiltonians is defined. The dependence of the bound-state
energies on $m/m_1$ and $b$ in the sector of angular momentum and parity $L^P =
1^-$ is calculated and analysed with the aid of a simple model.
