No-Core Monte Carlo Shell Model Calculations with Unitary Correlation Operator Method and Similarity Renormalization Group

The unitary correlation operator method (UCOM) and the similarity renormalization group theory (SRG) are compared and discussed in the framework of no-core Monte Carlo shell model (MCSM) calculations for $^{3}$H and $^{4}$He. The treatment of spurious center-of-mass motion by Lawson's prescription is performed in the MCSM calculations. These results with both transformed interactions show good suppression of spurious center-of-mass motion with proper Lawson's prescription parameter $\beta_{\rm c.m.}$ values. The UCOM potentials obtains faster convergence of total energy for the ground state than that of SRG potentials in the MCSM calculations, which differs from the cases in the no-core shell model calculations (NCSM). This differences are discussed and analyzed in terms of the truncation scheme in the MCSM and NCSM, as well as the properties of potentials of SRG and UCOM.