what is deffrence between nutron energy spectrum and nutron flux
Neutron energy spectrum is simply a description of the neutron population by energy, without any spatial reference. Neutron flux is a spatial description, the number of neutrons passing through a unit area per unit time.
However, neutron flux could be energy dependent, i.e. one can refer to a thermal flux, that is the flux of neutrons whose energies are below some particular energy (e.g. 0.025 eV). Or one can refer to a fast flux with E > 0.82 MeV or 1 MeV. The energy cut off is arbitrary.
If flux on has energy dependent flux, [itex]\phi(x,y,z,E)[/itex], then on can integrate over the entire energy spectrum or a portion of the energy spectrum to obtain the spatial flux for that range of energies, which would be [itex]\phi(x,y,z)[/itex].
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