The general neutron induced reaction cross sections with the projectile neutron energy are being studied. As a result of this, the compound nucleus is formed through de-excitation of the selected nuclei by emitted particles γ and 2n with the reaction cross section at intermediate energy. The production of residual nuclide by neutron induced reaction on the selected nuclei has been investigated by using computer code projection angular-momentum coupled evaporation Monte Carlo code (PACE4). Dependence of Reaction Cross Section for Projectile Neutron with Different K Values on Target 55Mn in the Energy Range (0.5 - 3.42) Mev and Dependence of Reaction Cross Section for Projectile Neutron with Different K Values on 55Mn Target in the Energy Range (11.5 - 38.5) Mev. Then, the theoretical estimated value compared with the Experimental value the data which obtained from International Atomic and Energy Agency, Exchange format. Results show us the reaction cross section vs energy of projectile neutron with target nucleus Manganese and the emitted particles were γ and 2n respectively with new residual nuclei, i.e. 56Mn and 54Mn, in addition to this the best fit K values are 10 and 8 for each channels respectively. Finally the level density parameter is the dominant parameter that can influence the reaction cross section from the outcome of this software by varying with free constant parameter (K). i.e., 8, 10 and 12.