  This paper describes a new method for momentum reconstruction of charged
particles using multiple Coulomb scatterings in a nuclear emulsion detector
with a layered structure of nuclear emulsion films and target materials. The
method utilizes the scattering angles of particles precisely measured in the
emulsion films. The method is based on the maximum likelihood to newly include
information on the decrease of the energy as the particle travels through the
detector. According to the Monte Carlo simulations, this method can measure
momentum with a resolution of 10% for muons of 500 MeV/c passing through the
detector perpendicularly. The momentum resolution is evaluated to be 10-20%,
depending on the momentum and emission angle of the particle. By accounting for
the effect of the energy decrease, the momentum can be reconstructed correctly
with less bias, particularly in the low-momentum region. We apply this method
to measure the momentum of muon tracks detected in the NINJA experiment where
the momentum is also measured independently by using the track range. The two
measurements agree well within experimental uncertainties, verifying the method
experimentally. This method will extend the measurable phase space of muons and
hadrons in the NINJA experiment.
