{\it Ab initio} calculations of $p$-$^7$Be scattering and $^7$Be($p$,$\gamma$)$^8$B capture

We build a new {\it ab initio} many-body approach [1] capable of describing simultaneously both bound and scattering states in light nuclei, by combining the resonating-group method [2] with the {\it ab initio} no-core shell model [3]. In this way, we complement a microscopic-cluster technique with the use of realistic interactions, and a microscopic and consistent description of the nucleon clusters. We will present results for the proton scattering on $^7$Be and for the S-factor of the $^7$Be($p$,$\gamma$)$^8$B capture reaction important for astrophysics. Our calculations predict low-lying resonances in $^8$B that have not been clearly identified experimentally so far. Finally, we will also highlight the first results of the $d$-$^3$H and $d$-$^3$He fusion calculation obtained within our {\it ab initio} approach. \\[4pt] [1] S. Quaglioni and P. Navratil, Phys. Rev. Lett. 101, 092501 (2008); Phys. Rev. C 79, 044606 (2009).\\[0pt] [2] K. Wildermuth and Y. C. Tang, A unified theory of the nucleus, (Vieweg, Braunschweig, 1977).\\[0pt] [3] P. Navratil, J. P. Vary, and B. R. Barrett, Phys. Rev. Lett. 84, 5728 (2000).