Ab initio calculations of nuclear widths via an integral relation

In the last two decades it has been demonstrated that light nuclei are described accurately as collections of particles interacting through the bare nucleon-nucleon potential and a weaker three-body interaction. This description produces good quantitative agreement between calculations and experiment for properties of nuclei up to mass-12 and beyond, and it offers the prospect of a predictive ab initio theory of nuclei that can be applied to new problems with limited amounts of additional tuning. Widths of nuclear levels and the "virtual widths" or asymptotic normalization constants (ANCs) of bound states have been mostly neglected in ab initio studies. These quantities can provide additional tests of the models, in many cases not yet probed by experiment, and they can provide estimates of astrophysical cross sections. I will describe recent ab initio calculations of ANCs and widths using quantum Monte Carlo methods, present the results, and discuss the applicability of related techniques to future calculations of reaction and scattering cross sections.