The Iwamoto-Yamada cluster expansion: Its structure and renormalization

Chun Wa Wong

MANFRED L. RISTIG, J. W. Clark, Francesco Calogero

Lothar Schäfer

E. Krotscheck, J. Nitsch, MANFRED L. RISTIG +1 more

Lothar Schäfer

We develop diagrammatic methods which give the explicit expression for the n th order term of the linked Iwamoto-Yamada cluster expansion in terms of the cluster integrals. The method applies independently of the number A of particles of the system. We carry through partial summations which for finite A result in a representation of the expansion by skeleton diagrams, whereas in the limit A → ∞ the expansion is reduced to two analytical equations. In addition, for finite A the renormalization establishes a connection between the expectation value of an arbitrary operator and the probability to find n hole states, 1 ≤ n ≤ A, occupied. Simple considerations raise some doubts concerning the convergence of the unrenormalized expansion.

Chun Wa Wong

The use of auxiliary single-particle potentials permits the inclusion of the dispersion effect in the energy of a many-Fermion system calculated in the independent-pair approximation of the Iwamoto-Yamada cluster expansion.