Many-body Green functions in nuclear physics

George A. Clovis

Hisashi Horiuchi, Kiyomi Ikeda, Kiyoshi Katō +1 more

Josef Speth, N. Lyutorovich

Many-body Green functions are a very efficient formulation of the many-body problem. We review the application of this method to nuclear physics problems. The formulas which can be derived are of general applicability, e.g., in self-consistent as well as in nonself-consistent calculations. With the help of the Landau renormalization, one obtains relations without any approximations. This allows to apply conservation laws which lead to important general relations. We investigate the one-body and two-body Green functions as well as the three-body Green function and discuss their connection to nuclear observables. The generalization to systems with pair correlations are also presented. Numerical examples are compared with experimental data.

Ville J. Härkönen

We combine the recently developed many-body Green's function theory for electrons and nuclei with the exact factorization of the wave function. The existing Born-Oppenheimer Green's functions are shown to be special cases of our exact approach. We consider the limitations of the laboratory frame formulation of the Green's function theory and discuss why the body-fixed frame formulation is needed in order to go beyond the Born-Oppenheimer theory. We give exact forms of the electronic and nuclear Green's functions written in terms of the exact factorized states, providing a systematic approach beyond the Born-Oppenheimer approximation. The lowest order approximation to the exact electronic Green's function is found to be an expected value of the Born-Oppenheimer electronic Green's function with respect to the nuclear density.

J.P. Jeukenne, A Lejeune, Claude Mahaux

Arnau Rios, Pawel Danielewicz, Pawel Danielewicz +2 more

Nonequilibrium Green's functions represent underutilized means of studying evolution of quantum many‐body systems. In view of a rising computer power, an effort is underway to apply the Green's functions to the dynamics of central nuclear reactions. As the first step, mean‐field evolution for the density matrix for colliding slabs is studied in one dimension. Strategy to extend the dynamics to correlations is described.