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

Details

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.