  Fuzzy dark matter (FDM) is an intriguing candidate alternative to the
standard cold dark matter (CDM). The FDM model predicts that dark halos have
characteristic core structures generated by the effect of quantum pressure,
which is different from the structure of CDM halos. We devise a semi-analytic
model of a FDM halo density profile by assuming that the density distribution
results from the redistribution of mass in a halo with the Navarro-Frenk-White
profile. We calculate the mass redistribution radius by considering dynamical
relaxation within the FDM halo. We adopt a concentration-halo mass relation
with lower concentration compared to that in the CDM model below the half mode
mass, which originates from the suppressed matter density fluctuations at small
length scales. Our model reproduces the core-halo mass relation (CHMR) found in
the numerical simulation of \citet{2014NatPh..10..496S} at $z<1$. We show that
the CHMR is well described by a double power law, unlike previous studies that
approximate it by a single power law. Our model predictions are in reasonable
agreement with the results of the largest FDM simulation of
\citet{2021MNRAS.506.2603M} at $z=3$. We find that the core mass for a given
halo mass follows the log-normal distribution, both in our model and in the
simulation results for the first time, and quantitatively compare the variance
of the distribution among them. Although our model does not fully explain the
scatter of the CHMR, we show the scatter of the concentration-halo mass
relation sizably contributes to them.
