S-factors of capture reactions important for astrophysics from {\it ab initio} wave functions

Nuclear structure of $^3$He, $^4$He, $^7$Be, $^8$B, $^{10}$Be and $^{11}$Be is studied within the {\it ab initio} no-core shell model (NCSM). Starting from realistic inter-nucleon interactions, wave functions for these nuclei are obtained in basis spaces up to $12\hbar\Omega$ and then used to calculate cluster form factors (overlap functions) for the bound states of $^8$B with $^7$Be+p, $^7$Be with $^3$He$+^4$He and $^{11}$Be with $^{10}$Be+n as a function of the separation between the two interacting clusters. Due to the use of the harmonic oscillator basis, the overlap functions have incorrect asymptotics. To fix this problem, we perform a least-square fit of Woods-Saxon potential solutions to the NCSM overlap functions in the range from 0 fm up to about 4 fm under the constraint that the experimental separation energy is reproduced. The corrected overlap functions are then used for the $^7$Be(p,$\gamma$)$^8$B, $^3$He($\alpha$,$\gamma$)$^7$Be and $^{10}$Be(n,$\gamma$)$^{11}$Be S-factor calculations. Support from the LDRD contract No. 04-ERD-058 as well as partial support from the DOE grants SCW0498 and DE-FG02-04ER41338 is acknowledged.