Research On The Low-energy Effective Field Theory Of Nuclear Matter

In the 1990s,Weinberg proposed that the nuclear interaction problem could be calculated by constructing the nuclear scattering potentials through chiral perturbation theory and then substituting these scattering potentials into the Lippmann-Schwinger equation?LSE?or Schr?dinger equation to calculate the scattering amplitude.Subsequently,this method has been widely used in the study of nucleon-nucleon scattering in vacuum and many successful results have been obtained.Since then,some scholars have tried to extend this effective field theory to nuclear matter,not achieving much success in nonperturbative context.For the divergences problem in LSE,many renormalization schemes have been developed,each with advantages and disadvantages,but the renormalization under the non-perturbation framework has always been controversial.About this problem,our team has developed a set of non-perturbed renormalization scheme over the years,which has achieved good results in a certain scope.Our thesis is devoted to the study of extending low-energy effective field theory to nuclear matter in nonperturbative context,that is,starting from the effective contact nucleon-nucleon potentials,the closed-form Brückner G-matrix is obtained by solving the Bethe-Goldstone equation?BGE?of ¹S₀ and uncoupled P channels.Then the idea of non-perturbation renormalization developed in the T-matrix in the vacuum case by our group is applied to the closed-form Brückner G-matrix.The physical parameters or renormalization group invariants are derived from the tight constraint of the closed-form Bruckner G matrix,with running coupling constants come up as natural corollaries,which is independent of Fermi momentum in contrast to those derived in KSW scheme.Then the closed-form Brückner G-matrix so determined are employed to explore some specific physical behaviors through numerical calculation,including:phase shift in vacuum,nucleon pairing phenomenon,and single particle energy of nuclear mater,finally obtained reasonable results.By studying these physical behaviors,we again sustained that some renormalization parameters that were previously considered to have no physical meaning are actually physical parameters with physical consequences.Our study provided new impetus to the effective field theory approach to nuclear matter in non-perturbative context and encouraging experiences for further investigations in higher order potentials and higher channels of Brückner G-matrix and in similar area of physics such as cold atom systems,etc.