  We study recently proposed ultraviolet and infrared momentum regulators of
the model spaces formed by construction of a variational trial wavefunction
which uses a complete set of many-body basis states based upon
three-dimensional harmonic oscillator (HO) functions. These model spaces are
defined by a truncation of the expansion characterized by a counting number
($\mathcal{N}$) and by the intrinsic scale ($\hbar\omega$) of the HO basis; in
short by the ordered pair ($\mathcal{N},\hbar\omega$). In this study we choose
for $\mathcal{N}$ the truncation parameter $N_{max}$ related to the maximum
number of oscillator quanta, above the minimum configuration, kept in the model
space. The ultraviolet (uv) momentum cutoff of the continuum is readily mapped
onto a defined uv cutoff in this finite model space, but there are two proposed
definitions of the infrared (ir) momentum cutoff inherent in a
finite-dimensional HO basis. One definition is based upon the lowest momentum
difference given by $\hbar\omega$ itself and the other upon the infrared
momentum which corresponds to the maximal radial extent used to encompass the
many-body system in coordinate space. Extending both the uv cutoff to infinity
and the ir cutoff to zero is prescribed for a converged calculation. We
calculate the ground state energy of light nuclei with "bare" and "soft" $NN$
interactions. By doing so, we investigate the behaviors of the uv and ir
regulators of model spaces used to describe $^2$H, $^3$H, $^4$He and $^6$He
with $NN$ potentials Idaho N$^3$LO and JISP16. We establish practical
procedures which utilize these regulators to obtain the extrapolated result
from sequences of calculations with model spaces characterized by
($\mathcal{N},\hbar\omega$).
