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I abstract from a recent publication [1] the motivations for, analysis in andconclusions of a study of the ultraviolet and infrared momentum regulatorsinduced by the necessary truncation of the model spaces formed by a variationaltrial wave function. This trial function is built systematically from acomplete set of many-body basis states based upon three-dimensional harmonicoscillator (HO) functions. Each model space is defined by a truncation of theexpansion characterized by a counting number (N) and by the intrinsic scale($\hbar\omega$) of the HO basis. Extending both the uv cutoff to infinity andthe ir cutoff to zero is prescribed for a converged calculation. In [1] weestablished practical procedures which utilize these regulators to obtain theextrapolated result from sequences of calculations with model spaces. Finally,I update this subject by mentioning recent work on our extrapolationprescriptions which have appeared since the submission of [1]. The numericalexample chosen for this contribution consists of calculations of the groundstate energy of the triton with the "bare" and "soft" Idaho N3LOnucleon-nucleon (NN) interaction.

Infrared and ultraviolet cutoffs in variational calculations with a harmonic oscillator basis