# EPJ A - The Similarity Renormalization Group for Three-Body Interactions in One Dimension

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- Published on 10 August 2012

One important message that has emerged from developments of effective field theories and effective Hamiltonians for nuclear physics is that many-body forces are inevitable whenever degrees of freedom are eliminated. At the same time, first-principles calculations have shown that two-body forces alone are not able to give an accurate account of the energies of light nuclei and the saturation of nuclear matter. Three- (and possibly more-) body forces are thus essential in low-energy nuclear physics. The construction of effective interactions through elimination of degrees of freedom can be done either by imposing a cut-off on the Hilbert space or by applying a transformation to put the Hamiltonian into a simpler form, such as a diagonal matrix. The Similarity Renormalization Group follows the latter route by means of a continuous set of transformations. It has proved to be a powerful tool in low-energy nuclear physics, where it has been applied mainly in the context of expansions using harmonic-oscillator basis states.

The present paper provides the first application of this method to three-body interactions in a momentum-space basis. Although the models studied are simple ones, consisting of bosons in one dimension, the structure of the evolution equations has the full complexity of any set of three-body equations. The results show the expected decoupling of high- from low-momentum states for both two- and three-body interactions, which means that only low-momentum matrix elements of the evolved potentials are needed to describe low-energy states. This work paves the way for applications to few-nucleon scattering processes and nuclear matter, starting from realistic nuclear forces in three dimensions.

**The similarity renormalization group for three-body interactions in one dimension. **

O. Åkerlund et al., Eur. Phys. J. A (2011) **47**: 122, DOI 10.1140/epja/i2011-11122-4