  A hyperbolic singularity in the wave-function of $s$-wave interacting atoms
is the root problem for any accurate numerical simulation. Here we apply the
transcorrelated method, whereby the wave-function singularity is explicitly
described by a two-body Jastrow factor, and then folded into the Hamiltonian
via a similarity transformation. The resulting non-singular eigenfunctions are
approximated by stochastic Fock-space diagonalisation with energy errors
scaling with $1/M$ in the number $M$ of single-particle basis functions. The
performance of the transcorrelated method is demonstrated on the example of
strongly correlated fermions with unitary interactions. The current method
provides the most accurate ground state energies so far for three and four
fermions in a rectangular box with periodic boundary conditions.
