  We consider the effects of metastable charged sparticles on Big-Bang
Nucleosynthesis (BBN), including bound-state reaction rates and chemical
effects. We make a new analysis of the bound states of negatively-charged
massive particles with the light nuclei most prominent in BBN, and present a
new code to track their abundances, paying particular attention to that of Li7.
Assuming, as an example, that the gravitino is the lightest supersymmetric
particle (LSP), and that the lighter stau slepton, stau_1, is the metastable
next-to-lightest sparticle within the constrained minimal supersymmetric
extension of the Standard Model (CMSSM), we analyze the possible effects on the
standard BBN abundances of stau_1 bound states and decays for representative
values of the gravitino mass. Taking into account the constraint on the CMSSM
parameter space imposed by the discovery of the Higgs boson at the LHC, we
delineate regions in which the fit to the measured light-element abundances is
as good as in standard BBN. We also identify regions of the CMSSM parameter
space in which the bound state properties, chemistry and decays of metastable
charged sparticles can solve the cosmological Li7 problem.
