Using effective bosons to capture nuclear deformation

Most nuclei are deformed, or at least have quadrupole correlations, and these are hard to capture ab initio. My group is exploring how to apply effective bosons to the In-Medium Similarity Renormalization Group (IMSRG) so that we may better capture the nuclear structure properties of deformed nuclei. As it stands, capturing nuclear deformation is done through of process of symmetry breaking steps and symmetry restoration steps. These symmetry restoration steps are expensive. Another difficulty is that some transition nuclei might not be deformed at the mean field level but might still have significant quadrupole correlations. Using effective bosons would be an alternative way to capture deformation without having to use the expensive steps of symmetry restoration. As an initial step, we perform a test using the equations of the similarity renormalization group to obtain the ground state of a one particle system in an anharmonic oscillator potential. This test is done with a one-dimensional and two-dimensional Hamiltonian. We test the accuracy of this method over various potential ranges and depths. We obtain encouraging results that give us an idea where we can expect the theory to hold in a many-body system.