Unitary Transformations for Nuclear Structure Calculations

The explicit treatment of short-range correlations generated by realistic and chiral potentials is the main goal of the Unitary Correlation Operator Method (UCOM) and the Similarity Renormalization Group (SRG) approach. Both methods use unitary transformations to derive phase-shift equivalent nucleon-nucleon interactions. Even if both methods are conceptually completely different, the underlying unitary transformation can be traced back to generators with the same structure. The first part of the thesis discusses the basic concepts of the UCOM and the SRG. Exploiting the connection of the generators of these two methods, correlation functions that define the unitary transformation in the UCOM are extracted from SRG calculations, leading to improved convergence in No-Core Shell Model (NCSM) calculations and improved Hartree-Fock results. Alternatively, UCOM correlation functions are obtained by parameterizations whose parameters are determined by energy minimisation. Correlation functions with structures adapted to the SRG-generated UCOM correlation functions produce good results in many-body calculations for realistic and chiral interactions. Alternative choices of the SRG generator are explored in the second part, with the aim to optimize the balance between induced many-body forces and good convergence behaviour. One choice adds an explicit scale parameter to the square of the momentum, while other choices change the power of momentum. The first choice increase the effect of three- and higher-body contributions and the convergence behaviour becomes worse. In case of the different powers of momentum in the generator, the results are very similar for all flow parameters. Therefore, the choice of the generator used so far provides a good balance between convergence behaviour and induced many-body forces. The unitary SRG and UCOM transformation of other observables is the topic of the third part. It is performed in a consistent way for radii and multipole operators, which are long-ranged operators. Hartree-Fock calculations for SRG-transformed charge radii deviate only little from the calculations using the bare operators, leading to changes less than 1%. The same holds for UCOM transformed radii. Consistent transition strengths obtained from Random Phase Approximation calculations show more significant deviations from the untransformed strengths for the monopole case with SRG transformation. The UCOM transformation leads to much smaller effects here. In the case of quadrupole transitions smaller effects due to the unitary transformation are observed for both, the UCOM and the SRG transformation. These results are con- firmed in case of the SRG-transformed quadrupole transition in NCSM calculations