The Similarity Renormalization Group for three bosons in a momentum-space partial-wave basis

Abstract

The Similarity Renormalization Group (SRG) flow equation is explored for systems of two and three spinless bosons in a momentum-space partial-wave basis. The two- and three-body binding energies as well as the phaseshifts are used to gauge that the transformation is unitary and to study how well the SRG decouples high- and low-energy physics. I consider four different potentials with different characteristics: Two simplied nucleon potentials and two inter-atomic helium potentials (a soft-core potential and the state-of-the-art LM2M2 potential that is fitted to a wealth of experimental data). An initial three-body force is included for two of these potentials. Even with only two-body terms in the initial hamiltonian, SRG induced many-body forces are shown to arise during the transformation. These induced forces are computed for the three-body system and their evolution is studied as a function of the flow parameter. In all cases the SRG transformed potentials display greatly improved decoupling. This is achieved with a three-body binding-energy deviation of less than 0.1% in all cases except for the soft-core helium potential.