  We investigate two distinct sources of uncertainty in low-energy nuclear
physics calculations and develop ways to account for them.
  Harmonic oscillator basis expansions are widely used in ab-initio nuclear
structure calculations. Finite computational resources usually require that the
basis be truncated before observables are fully converged, necessitating
reliable extrapolation schemes. We show that a finite oscillator basis
effectively imposes a hard-wall boundary condition. We accurately determine the
position of the hard-wall as a function of oscillator space parameters, derive
extrapolation formulas for the energy and other observables, and discuss the
extension of this approach to higher angular momentum.
  Nucleon knockout reactions have been widely used to study and understand
nuclear properties. Such an analysis implicitly assumes that the effects of the
probe can be separated from the physics of the target nucleus. This
factorization between nuclear structure and reaction components depends on the
renormalization scale and scheme, and has not been well understood. But it is
potentially critical for interpreting experiments and for extracting
process-independent nuclear properties. We use similarity renormalization group
(SRG) transformations to systematically study the scale dependence of
factorization for the simplest knockout process of deuteron
electrodisintegration. We find that the extent of scale dependence depends
strongly on kinematics, but in a systematic way. Based on examination of the
relevant overlap matrix elements, we are able to qualitatively explain and even
predict the nature of scale dependence based on the kinematics under
consideration.
