  The Similarity Renormalization Group (SRG) is a continuous series of unitary
transformations that can be implemented as a flow equation. When the relative
kinetic energy ($\Trel$) is used in the SRG generator, nuclear structure
calculations have shown greatly improved convergence with basis size because of
the decoupling of high-energy and low-energy physics. However this generator
can sometimes be problematic. A test case is provided by a study of initial
interactions from chiral effective field theories with large cutoffs, which can
lead to spurious deep bound states. We would like the SRG to decouple these
from the physical shallow bound states. However, with $\Trel$ the high- and
low-energy bound states are not decoupled in the usual sense. Replacing $\Trel$
by the momentum-space diagonal of the Hamiltonian ($H_d$) in the SRG generator
does produce decoupling, such that the shallow states are in the low-momentum
region and the deep bound states are at higher momentum. The flow toward
universal low-momentum interactions is also restored.
