2004/04/09 by Thomas Luu, T. C. Luu, S. Bogner +4 · 11 citations
Physics and Astronomy · Psychology · #Atomic and Molecular Physics #Computer science #Nuclear physics research studies #Psychology #Quantum Chromodynamics and Particle Interactions #nucl-th
paper · pdf · doi:10.1103/physrevc.70.014316
published in Physical Review C 70(1) (American Institute of Physics) · 19 pages, 9 figures, submitted to PRC
arxiv created 2004/04/09 · openalex publication_date 2004/07/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The three-body energy-dependent effective interaction given by the Bloch-Horowitz equation is evaluated for various shell-model oscillator spaces. The results are applied to the test cases of the three-body problem (3H and 3He), where it is shown that the interaction reproduces the exact binding energy, regardless of the parametrization (number of oscillator quanta or value of the oscillator parameter b) of the low-energy included space. We demonstrate a nonperturbative 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 \ensuremathΛ are varied, including the case of a single included shell: \ensuremathΛ\ensuremathℏ\ensuremathω=0\ensuremathℏ\ensuremathω. For typical ranges of b, the induced effective three-body interaction, essential for giving the exact three-body binding, is found to contribute \ensuremath∼10% to the binding energy.