  The possible superfluid transition of supercooled liquid parahydrogen is
investigated by quantum Monte Carlo simulations. The cooling protocol adopted
here allows for the investigation of a fluid phase down to a temperature T=0.25
K. No evidence of superfluidity is found, as exchanges of identical particles
are strongly suppressed even at the lowest temperature. Is shown that, contrary
to a commonly held belief, it is not the well depth of the pair-wise
interaction but rather its relatively large hard core diameter that physically
hinders superfluidity in parahydrogen.
