Summation of ring diagrams of nuclear thermodynamic potential

Abstract

Using an imaginary-time linked diagram expansion of the thermodynamic potential Ω, we derive methods by which the particle-particle (hole-hole) and the particle-hole ring diagrams of Ω can each be summed up to all orders in a rather convenient way. A model space P and a corresponding finite temperature reaction matrix K are introduced in order to take care of the strong short-range correlations between nucleons. Methods of the finite temperature Green functions are employed. The contribution from the particle-particle (hole-hole) ring diagrams to Ω is given in terms of simple integrals of the form ∝ 0 1d λ tr p { M( λ) K} where λ is a strength parameter, and M a thermal transition matrix which is calculated from a finite-temperature RPA-type secular equation. Solutions of this equation are derived, and their possible connections with phase transitions are discussed. The particle-hole ring diagrams are treated in a similar way. Applications of the present approach and prospects for formulating a Brueckner-type theory of nuclear matter at finite temperature are discussed.