{\it Ab initio} no-core shell model with continuum

The {\it ab initio} no-core shell model (NCSM) is a many-body approach to nuclear structure of light nuclei. The NCSM adopts an effective interaction theory to transform fundamental inter-nucleon interactions into effective interactions for a specified nucleus in a selected harmonic oscillator basis space [1]. The method is capable of predicting nuclear structure from inter-nucleon forces derived from quantum chromodynamics by means of chiral effective field theory [2]. NCSM extensions to the microscopic description of nuclear reactions are now under development. In my talk, I will first discuss our recent calculations of the $^4$He total photo-absorption cross section using two- and three-nucleon interactions from chiral effective field theory [3]. I will then outline our effort to augment the NCSM by the resonating group method (RGM) technique to develop a new method capable of describing simultaneously both bound states and nuclear reactions on light nuclei [4]. This approach, which preserves translational symmetry and the Pauli principle, will allow us to calculate cross sections of reactions important for astrophysics and describe weakly-bound systems from first principles. I will present our first phase shift results for neutron scattering off $^3$H, $^4$He and $^7$Li and proton scattering off $^3$He, $^4$He and $^7$Be using realistic nucleon-nucleon potentials. \vspace{3mm} \newline[1] P. Navr\'atil, J. P. Vary and B. R. Barrett, Phys. Rev. C {\bf 62}, 054311 (2000). \newline[2] P. Navr\'atil and V. G. Gueorguiev and J. P. Vary, W. E. Ormand and A. Nogga, Phys. Rev. Lett. {\bf 99}, 042501 (2007). \newline[3] S. Quaglioni and P. Navr\'atil, Phys. Lett. B {\bf 652}, 370 (2007). \newline[4] S. Quaglioni and P. Navr\'atil, arXiv:0712.0855.