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

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