Summation of ring diagrams of nuclear thermodynamic potential

Elise Bergli, Morten Hjorth-Jensen

V. Somà, Piotr Bożek

In medium $T$-matrix calculations for symmetric nuclear matter at zero and finite temperatures are presented. The internal energy is calculated from the Galitskii-Koltun's sum rule and from the summation of the diagrams for the interaction energy. The pressure at finite temperature is obtained from the generating functional form of the thermodynamic potential. The entropy at high temperature is estimated and compared to expressions corresponding to a quasiparticle gas.

Nouredine Zettili

Aleksandar Belić, David J. Dean, Morten Hjorth-Jensen

Shen Yang, Meng Jiang, T.T.S. Kuo +1 more

Certain types of ring diagrams of the thermodynamic potential \ensuremath{\Omega} can be summed up to all orders using two apparently very different methods---the eigenvalue method and the transition-amplitude method. A relatively simple derivation of these methods is given, and we show that these two methods are exactly equivalent to each other. To study their numerical applications we have calculated the particle-particle, hole-hole ring diagrams of \ensuremath{\Omega} for nuclear matter with both methods, using a modified Gogny interaction. Our results suggest that the strength-parameter integration involved in the transition-amplitude method can be accurately performed using a small number of mesh points and both methods seem to be suitable for numerical calculations.

E. Bauer

The response function to an external prove is evaluated using the ring approximation in nuclear matter. Contrary to what it is usually assumed, it is shown that the summation of the ring series and the solution of the Dyson's equation are two different approaches. The numerical results exhibit a perceptible difference between both approximations.