2 quantum many-body calculations [9]. isotopic ratios for MPSs. These have been deter- mined [18] and a high $^{6}$Li abundance of $^{6}$Li/H ∼ 6 × 10 $^{−}$12 has been suggested. This is ∼ 1000 times higher than the standard BBN prediction. One should be cautious, how- ever, in interpreting these results in that convective mo- tion in stellar atmospheres could cause systematic asym- metries in the observed stellar line profiles and thereby mimic the presence of $^{6}$Li [27]. Nevertheless, several MPSs, continue to exhibit high $^{6}$Li abundances even af- ter carefully correcting for the convection-triggered line asymmetries [28]. Be and B abundances have also observed in MPSs. $^{9}$Be [29–34] and B [35–38] abundances appear to increase roughly linearly as the Fe abundance increases. The ab- sence of a plateau in the abundances of Be and B at low metallicity, however, suggests that these elements are not of primordial origin. Nonthermal nuclear reactions induced by the decay of exotic particles have been studied [39, 40] as a means to provide a cosmological solution to the Li problems. Nonthermal reactions triggered by the radiative decay of long-lived particles can produce $^{6}$Li nuclides up to a level ∼ 10 times larger than the observed level without causing discrepancies in abundances of other light nuclei or the CMB energy spectrum [40]. Another solution to the lithium problems of particu- lar interest here is that due to the presence of negatively charged massive particles X − [41–43] during the BBN epoch. They affect the nucleosynthesis in a different way [1–13]. The X − particles become electromagneti- cally bound to positively charged nuclides with binding energies of ∼ O (0 . 1 − 1) MeV with the largest binding en- ergies for heavier nuclei with larger charges. Since these binding energies are low, the bound states cannot form until late in the BBN epoch. At the low temperatures as- sociated with late times, nuclear reactions are no longer efficient. Hence, the effect of the X − particles is rather small. Interestingly, however, the X − particles can cat- alyze the preferential production of $^{6}$Li [1] along with the weak destruction of $^{7}$Be [5, 6]. A large enhancement of the $^{6}$Li abundance was first suggested [1] to result from an X − bound to $^{4}$He (de- noted as $^{4}$He$_{X}$ ). This enables the X $^{−}$-catalyzed transfer reaction of $^{4}$He$_{X}$ ( d , X $^{−}$) $^{6}$Li, whose cross section could be seven orders of magnitude larger than the corresponding BBN $^{4}$He( d , γ ) $^{6}$Li reaction. The cross section for this re- action, however, was calculated in a more rigorous quan- tum three-body model [4] and shown to be about an or- der of magnitude smaller than the estimate adopted in Ref. [1]. Additional enhancements in X $^{−}$-catalyzed transfer re- action rates for the $^{4}$He$_{X}$ ( t , X $^{−}$) $^{7}$Li, $^{4}$He$_{X}$ ( $^{3}$He, X $^{−}$) $^{7}$Be, and $^{6}$Li$_{X}$ ( p , X $^{−}$) $^{7}$Be reactions were assumed in Ref. [3]. The rates for those reactions are, however, not as greatly enhanced as that of the $^{4}$He$_{X}$ ( d , X $^{−}$) $^{6}$Li because they involve a Δ l = 1 angular momentum transfer and con- sequently a large hindrance of the nuclear matrix ele- ment [6]. This has been confirmed in recent detailed The solution to the lithium problems in this catalyzed BBN model have been explored by solving the full Boltz- mann equations for the recombination and the ioniza- tion of nuclides and X − particles coupled to the nuclear reactions [6–8]. Constraints on specific supersymmetric models through the catalyzed BBN calculation have been obtained in Refs. [3, 11, 12, 44, 45]. Neutral X -nuclei, i.e., p$_{X}$ , d$_{X}$ and t$_{X}$ have also been suggested [8] as a means to produce and destroy Li and Be through two α -induced X − stripping reactions d$_{X}$ ( α , X $^{−}$) $^{6}$Li and t$_{X}$ ( α , X $^{−}$) $^{7}$Li, and three p$_{X}$ induced stripping reactions p$_{X}$ ( $^{6}$Li,$^{3}$He α ) X $^{−}$, p$_{X}$ ( $^{7}$Li,2 α ) X − and p$_{X}$ ( $^{7}$Be,$^{8}$B) X $^{−}$. The result, however, relies on reaction rates calculated within the framework of the Born ap- proximation, which is a poor approximation in this low- energy regime [9, 42]. The rates for those reactions and those for charge-exchange reactions of p$_{X}$ ( α , p ) α$_{X}$ , d$_{X}$ ( α , d ) α$_{X}$ and t$_{X}$ ( α , t ) α$_{X}$ have been calculated in a rigorous dynamical quantum many-body treatment in Ref. [9]. They found that the cross sections for the charge-exchange reactions were much larger than those of the nuclear reactions, and that the neutral bound states p$_{X}$ , d$_{X}$ and t$_{X}$ were immediately changed to α$_{X}$ before they could react with ambient nuclei. The late time pro- duction and destruction of Li and Be, therefore, do not significantly affect the BBN as shown in this letter. The $^{8}$Be$_{X}$ + p → $^{9}$B $^{∗}$a X → $^{9}$B$_{X}$ + γ reaction through the $^{9}$B $^{∗}$a X atomic excited state of $^{9}$B$_{X}$ has also been stud- ied [7]. However this reaction was found to be not operative because its resonance energy is relatively large (see Table 2 of Ref. [7]). A resonant reaction $^{8}$Be$_{X}$ ( n , X $^{−}$) $^{9}$Be through the atomic ground state of $^{9}$Be $^{∗}$(1 / 2 $^{+}$,1.684 MeV)$_{X}$ , i.e., an atom composed of the 1 / 2+ nuclear excited state of $^{9}$Be and an X − particle, has also been suggested as a possible reaction to pro- duce mass 9 nuclides [10]. Kamimura et al. [9], how- ever, adopted a root mean square charge radius for $^{8}$Be of 3.39 fm as a more realistic input. They then found that $^{9}$Be $^{∗}$(1 / 2 $^{+}$, 1.684 MeV)$_{X}$ is not a resonance but a bound state located below the $^{8}$Be$_{X}$ + n threshold. The resonant $^{8}$Be$_{X}$ ( n , X $^{−}$) $^{9}$Be$_{X}$ reaction is thus not likely to contribute. The resonant $^{7}$Be$_{X}$ ( p , γ ) $^{8}$B$_{X}$ reaction through the first atomic excited state of $^{8}$B$_{X}$ was suggested [5] as a means to reduce the primordial $^{7}$Li abundance [51]. A rate for this reaction has been calculated in a rigorous quan- tum three body model [9], which roughly reproduces the value of Ref. [5] but is somewhat inefficient in destroy- ing $^{7}$Be$_{X}$ . The resonant reaction $^{7}$Be$_{X}$ + p → $^{8}$B $^{∗}$(1 $^{+}$, 0.770 MeV)$_{X}$ → $^{8}$B$_{X}$ + γ through the atomic ground state of $^{8}$B $^{∗}$(1 $^{+}$,0.770 MeV)$_{X}$ , i.e., an atom consisting of the 1 + nuclear excited state of $^{8}$B and an X − particle has also been proposed [6] as a process for $^{7}$Be$_{X}$ destruc- tion. From a more realistic estimate of binding energies between nuclides and X − particles [7], this resonant re- action was found to exist, but the resonance energy level is too high to efficiently destroy $^{7}$Be$_{X}$ .