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. We wish to evaluate the final density of states given by the extended Fermi breakup integral of Eq.(9), which is repeated below, 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] We invert the Laplace transform to obtain an expression for the density of states ω$_{j}$ ( ε$_{j}$ ) as 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 14 ω$_{n}$ = k ∏ l =1 1 N$_{l}$ ! n ∏ j =1 ( V$_{n}$ (2 π ℏ ) 3 ) n − 1 ∫ n ∏ j =1 d $^{3}$p$_{j}$ δ ( n ∑ j =1 ⃗ p$_{j}$ ) ( 1 2 πi ) n n ∏ j $_{=1}$( ∫ c$_{j}$ + i ∞ c$_{j}$ − i ∞ dβ$_{j}$ e − β$_{j}$f ∗ $_{j}$( β$_{j}$ ) ) ω$_{j}$ ( ε$_{j}$ ) = 1 2 πi ∫ c$_{j}$ + i ∞ c$_{j}$ − i ∞ dβ$_{j}$ e β$_{j}$$^{ε$_{j}$}$e − β$_{j}$f ∗ $_{j}$( β$_{j}$ ) , (A3) e − β$_{j}$f ∗ $_{j}$( β$_{j}$ ) = ∫ ∞ 0 dε$_{j}$e − β$_{j}$$^{ε$_{j}$}$ω$_{j}$ ( ε$_{j}$ ) . (A2) ω$_{n}$ = k ∏ l =1 1 N$_{l}$ ! ( V$_{n}$ (2 π ℏ ) 3 ) n − $^{1}$∫ n ∏ j =1 d $^{3}$p$_{j}$ δ ( n ∑ j =1 ⃗ p$_{j}$ ) (A1) × ∫ n ∏ j =1 ( ω$_{j}$ ( ε$_{j}$ ) dε$_{j}$ ) δ ( ε$_{0}$ − B$_{0}$ − E$_{c}$$_{0}$ − n ∑ j =1 ( p 2 j 2 m$_{j}$ + ε$_{j}$ − B$_{j}$ − E$_{cj}$ ) . Appendix A: Evaluation of the phase space integral