The three-body energy-dependent effective interaction given by the
Bloch-Horowitz (BH) equation is evaluated for various shell-model oscillator
spaces. The results are applied to the test case of the three-body problem
(triton and He3), where it is shown that the interaction reproduces the exact
binding energy, regardless of the parameterization (number of oscillator quanta
or value of the oscillator parameter b) of the low-energy included space. We
demonstrate a non-perturbative technique for summing the excluded-space
three-body ladder diagrams, but also show that accurate results can be obtained
perturbatively by iterating the two-body ladders. We examine the evolution of
the effective two-body and induced three-body terms as b and the size of the
included space Lambda are varied, including the case of a single included
shell, Lambda hw=0 hw. For typical ranges of b, the induced effective
three-body interaction, essential for giving the exact three-body binding, is
found to contribute ~10% to the binding energy.Comment: 19 pages, 9 figures, submitted to PR
