Scattering problem for four-nucleon system

The Faddeev-Osborn equation for the nucleon-trinucleon elastic scattering is studied by generalizing the exact approach of the boson-triboson case. The Schmidt expansion theorem is used to express the 3+1 and 2+2-subamplitudes at energies in the continuous spectrum region as an infinite series of separable terms. Employing the pole term decomposition for these subamplitudes expressed in terms of the Schmidt expansion we can define, in conformity with the Faddeev residue prescription, respective four-nucleon amplitudes that describe elastic/rearrangement, partial breakup and full breakup scattering processes. Acquired simultaneous equations of these amplitudes take the form of multichannel two-particle Lippmann-Schwinger type, which we call Faddeev-Osborn equation. Assuming as an s-wave spin-dependent, rank two separable potential of the Tabakin type for the two-particle interaction, are derived the Faddeev-Osborn equation for the nucleon-trinucleon elastic scattering which includes spin and iso-spin analysis and angular momentum decomposition. To treat singularities appeared in our equation, the numerical calculation is performed in the frame-work of the complex-valued analysis by introducing contour rotation method. The N-T elastic scattering amplitude for a S=T=0, L=0 state of a four-nucleon system is obtained numerically in the incident laboratory energy region of 0.01 - 6.0 Mev, including only 1=0 state for the 3+1-subamplitude. (author)