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

Convergence properties of {\itshape ab initio} calculations of light nuclei in a harmonic oscillator basis