content_image/362333.jpg content_image/362332.jpg content_image/362331.jpg content_image/362330.jpg
## Acknowledgments 

We would like to acknowledge the CNPq, FAPERJ, FAPESP, the PRONEX program, under contract No E-26/171.528/2006, and the International Atomic Energy Agency, under research contract No. 14568, for partial financial support. This work was supported in part by the National Science Foundation under Grant Nos. PHY-0606007 and INT-0228058. AWS is supported by the Joint Institute for Nuclear Astrophysics at MSU under NSF PHY grant 08-22648 and also by NSF grant PHY 08-00026. 

## Appendix A: Evaluation of the phase space integral 

We wish to evaluate the final density of states given by the extended Fermi breakup integral of Eq.(9), which is repeated below, 

<img src='content_image/362333.jpg'>

We begin by using the formal relation between the densities of states ω$_{j}$ ( ε$_{j}$ ) and the corre- sponding internal Helmholtz free energies f ∗ j ( β$_{j}$ ) [25] 

<img src='content_image/362332.jpg'>

We invert the Laplace transform to obtain an expression for the density of states ω$_{j}$ ( ε$_{j}$ ) as 

<img src='content_image/362331.jpg'>

where c$_{j}$ is a positive number to the right of all singularities in the complex plane. Since the density of states ω$_{j}$ ( ε$_{j}$ ) normally grows as exp ( 2 √ aε$_{j}$ ) , the constant c$_{j}$ in the inverse Laplace transform could be taken to zero without any effect on the result. (The integral defining f ∗ j ( β$_{j}$ ) converges for any β$_{j}$ with ℜ [ β$_{j}$ ] > 0 .) However, to facilitate the evaluation of intermediate results, it is convenient to leave it free for the moment. Substituting for the densities, we have 

<img src='content_image/362330.jpg'>

