Renormalized Ring Diagram Energy in a Fermion System of Hard Spheres : The Off Energy Shell Effect

The off energy shell effect on the contribution to the energy from the renormalized three-particle ring diagram is studied for the ground state of a system of hard sphere fermions. The linked cluster formalism supplemented with infinite partial summation method, such as the K-matrix method, fails in giving a finite value to the energy of interest. In place of the K-matrix, we make use of the effective potential which improves the pseudopotential introduced by Fermi and exploited by Lee, Huang and Yang. Our potential prevents two spheres from penetrating each other. It gives a finite energy correction whose dominant part varies as a^4 loga with the small value of the core radius a. Correction term of order a^4 is also presented