To trace the signature of the (1405) resonance in the invariant mass, the direct neutron spectrum forreaction was investigated, using different types ofotential based on phenomenological approach and chiral SU(3) dynamics. It is shown that it is possible to observe the peak structure corresponding to (1405) resonance in the neutron energy spectrum. In this work, we solved the relativistic and non-relativistic momentum-space Faddeev equation for the kaon interacting with deuteron via different type of otentials. Using separableotentials in the Faddeev equations, we calculated the binding energies and widths of the ,,,andquasi-bound states on the basis of three- and four-body Alt-Graerger-Sandhas equations in the momentum representation. One- and two-pole version of interaction are considered in our calculations and the dependence of the resulting few-body energy on the two-body otential was investigated. The s-wave (3+1) and (2+2) sub-amplitudes are obtained by using the Hilbert-Schmidt expansion procedure for the integral kernels. As a result, we found a four-body resonance of the ,and quasi-bound states with a binding energy in the range energy55-70, 90-100 and 90-100 MeV. The obtained widths for these systems are 16-20, 7 - 20 and <v:imagedata src="file:///C:\\Users\\zamani\\AppData\\Local\emp\\msohtmlclip1\\01\\cli
