  The ground-state electron density of a one-dimensional spin-orbit coupled
quantum dot with a Zeeman term and strong electron interaction is studied at
the fractional helical liquid points. We show that at fractional filling
factors $\nu=(2n+1)^{-1}$ (with $n$ a non-negative integer) the density
oscillates with $N_{0}/\nu$ peak. For $n\geq 1$ a number of peaks larger than
the number of electrons $N_{0}$ suggests that a crystal of fractional
quasi-particles with charge $\nu e$ (with $e$ the electron charge) occurs. The
reported effect is amenable of verification via transport measurements in
charged AFM-coupled dot.
