Article

# Exact calculation of three-body contact interaction to second order

European Physical Journal A (Impact Factor: 2.04). 03/2012; 48(5). DOI:10.1140/epja/i2012-12058-9
Source: arXiv

ABSTRACT For a system of fermions with a three-body contact interaction the
second-order contributions to the energy per particle $\bar E(k_f)$ are
calculated exactly. The three-particle scattering amplitude in the medium is
derived in closed analytical form from the corresponding two-loop rescattering
diagram. We compare the (genuine) second-order three-body contribution to $\bar E(k_f)\sim k_f^{10}$ with the second-order term due to the density-dependent
effective two-body interaction, and find that the latter term dominates. The
results of the present study are of interest for nuclear many-body calculations
where chiral three-nucleon forces are treated beyond leading order via a
density-dependent effective two-body interaction.

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