Study Of The Pion-nucleon Interaction In A Relativistic Hartree-Fock Theory

In the past fifty years,relativistic quantum field theories ha ve been developed to study the properties of high-density matte r and finite nuclei.In these theories,baryons interact through th e exchange of virtual mesons,static nucleon-nucleon potentials need not be introduced.Furthermore,the model can be solved in the mean field approximation and the "mean-field theory" (MFT)also appears to be correct at high density and gives an accurate description of finite nuclei.The renormalizability of the model ensures that finite corrections to the MFT can be calcul ated in a well-defined fashionIn this text,we consider a system composed of nucleons c oupling only with pion at the finite density.Relativistic HartreeFock (HF)equations for nuclear matter are solved for both pse udoscalar and pseudovector pion-nucleon couplings.And we res earch theπ-N interaction in two situations:First,we do not include the propagation of virtual nucleons and antinucleon s.In this section,there is range of integration in G_D,so the cal culation needn't to be renormalized,we can figure out M_k~*,k~* and E_k~*,by solving Dyson equation.Then we add the contributi ons from virtual nucleons and antiucleons which are smaller tha n those from real nucleons.Theoretically the integral equations of ps coupling are renormalizable,we do it by dimension norm alization.But for pv coupling,the integral equations are nonren ormalizable,there we first do dimension normalization,and then cut off the infinite term directly.Because the contributions fro m pions are much smaller than those from nucleons,we mainly consider the contributions from nucleons.And for the contribut ion of pions,we only give out theoretical derivation.We can fi nd out that compared with real nucleons,the contributions from virtual nucleons and antinucleons are small,they can be treate d as the modification of real nucleons.In this text,we mainly use the method of dimension norm alization.First,one approximation is introduced to avoid renorm alization,and the results are very sensitive to the form of the i nteraction.Then the part which has been omitted will be renor malized.In this process,we apply an approximate renormalizati on method which deducts the infinity item in lagrangian density directly.Research ofπ-N model is a popular problem in the past 50 years. There are many discussions ofπ-N model,such as Longitudinal electromagnetic response function and one loop Dyson equation.In this text,we mainly discuss how to calculate the HF energy density ofπ-N interaction and add on the contributions from virtual nucleons and antinucleons.By this way,we can gain some reasonable results.