  The possibility of the appearance of the states with a nonzero average
helicity in neutron matter is studied in the model with the Skyrme effective
interaction. By providing the analysis of the self-consistent equations at zero
temperature, it is shown that neutron matter with the Skyrme BSk18 effective
force undergoes at high densities a phase transition to the state in which the
degeneracy with respect to helicity of neutrons is spontaneously removed.
