Using integral relations to improve ab initio structure and reaction calculations for light nuclei

The variational Monte Carlo and Green's function Monte Carlo methods, which use random sampling in position space instead of basis expansions, have been used in many accurate ab initio calculations of energy levels and transition probabilities in light nuclei. However, they have had more difficulty with "long-range" properties like scattering amplitudes and the large-radius tails of bound states. It can be hard to produce reasonable variational trial functions that capture both pairwise interactions of nucleons at short range and the clustering properties that dominate at long range. It can also be difficult to find Monte Carlo sampling schemes that probe the low-probability tails and "off-diagonal" quantities effectcively. We will describe calculations that mitigate these difficulties by avoiding direct calculation of long-range amplitudes in the wave function and instead finding them from integrals over better-computed short-range parts of the wave function: single-particle spectroscopic overlaps at A ≤ 9, alpha-removal spectroscopic overlaps at A = 7, true scattering in A = 4,5 systems, and scattering at A = 5 using pseudo-bound variational wave functions.