Infinite order summation of particle-particle ring diagrams in a model-space approach for nuclear matter

Abstract

A ring diagram model-space nuclear matter theory is formulated and applied to the calculation of the binding energy per nucleon ( BE A ) , saturation Fermi momentum ( k F) and incompressibility coefficient ( K) of symmetric nuclear matter, using the Paris and Reid nucleon-nucleon potentials. A model space is introduced where all nucleons are restricted to have momentum k ⩽ k M, typical values of k M being ∼3.2 fm −. Using a model-space Hartree-Fock approach, self-consistent single particle spectra are derived for holes ( k ⩽ k F) and particles with momentum k F < k ⩽ k M. For particles with k > k M, we use a free particle spectrum. Within the model space we sum up the particle-particle ring diagrams (both forward- and backward-going) to all orders. A rather simple expression for the energy shift ΔE 0 pp is obtained, namely ΔE 0 pp is expressed as integrals involving the trace of Y( λ) Y +( λ) G M where G M is the model-space reaction matrix, the Y's are transition amplitudes obtained from solving RPA-type secular equations and λ is a strength parameter to be integrated from 0 to 1. We have used angle-average approximations in our calculations, and in this way different partial wave channels are decoupled. For the 3S 1- 3D 1 channel, the effect of the ring diagrams is found to be particularly important. The inclusion of the ring diagrams has largely increased the role of the tensor force in determining the nuclear matter saturation properties, and consequently we obtain saturation densities which are significantly lower than those given by most other calculations. For the Paris potential, our results for BE A , k F and K are respectively 17.38 MeV, 1.42 fm −1 and 96.3 MeV. For the Reid potential, the corresponding results are 15.15 MeV, 1.30 fm −1 and 110.7 MeV. Our calculated values for the binding energy per nucleon and saturation density are both in rather satisfactory agreement with the corresponding empirical values.