The Calculation and Research of Cross Section of Neutron and Pion in Neutron Renormalization Mix Loop Chain Diagrams and in SU (2) Model

Abstract: The process of elastic collision between proton, neutron and neutralπ0 is often solved by using potential model and adopting QCD theory in nucleus physics. It corresponds to experimental result in the high energy region, but it can’t accurately describe the collision process in the middle energy region sometimes. In this dissertation, the scattering of elastic collision between nucleus and neutral meson was researched in low energy region by using perturbation theory of quantum field theory.In this dissertation, we have calculated differential cross section of elastic collision between neutron n and neutralπ0 by SU(2) model and discussed the situation of renormalization chain propagator. We have separately finished the strictly analytic calculation to differential cross section in the propagator of the nucleon tree diagram, loop diagram and chain diagram and obtained the effective formula for the nucleus propagator under chain diagram approximate.It’s quite difficult to obtain the accurately calculation function of nucleon one loop diagram and chain diagram renormalization propagator in theory. Firstly, we separated availability physics finite quantity from the infinite by the method of momentum renormalization and matrix function expansion. Secondly, we obtained the one-dimension integral formula of the nucleon one loop renormalization finite quantity by adopting great momentum limitation integral. Thirdly, we finished the theoretical calculation of the nucleus propagator under complex chain diagram and discussed the convergence of the matrix function under loop diagram according to the results. Therefore, we obtained the accurate results of nucleus propagator under complex chain diagram.At last, we obtained accurate results of the differential scattering cross section of the nucleon loop and chain propagator after calculating the function of the differential scattering cross section us the results we have obtained.In this dissertation, we have discussed the radiation correction of one loop diagram and complex chain-loop diagram. We separated the function of fermions propagator, which includes matrix, into two parts, one part isγ? pmatrix with 4×4 and the other is unit matrix. We have found these two parts is quite small and the total correction is reasonable in the low energy region after discussing the corrections.At last, we analyzed the differential cross section of the tree diagram, loop diagram and chain diagram by figure and testified that it is right to calculate strong interaction by using perturbation theory of quantum field theory…
Key words: Differential scattering cross section; Renormalization finite quantity; Great momentum limitation integral; Radiation correction

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