We identify reactions which destroy ^ { 7 } Be and ^ { 7 } Li during big bang nucleosynthesis ( BBN ) in the scenario of BBN catalyzed by a long-lived sub-strongly interacting massive particle ( sub-SIMP or X particle ) .
The destruction associated with non radiative X captures of the nuclei can be realized only if the interaction strength between an X particle and a nucleon is properly weaker than that between two nucleons to a degree depending on the mass of X .
Binding energies of nuclei to an X particle are estimated taking the mass and the interaction strength to nuclei of the X as input parameters .
Nuclear reaction rates associated with the X are estimated naively , and adopted in calculating evolutions of nuclear abundances .
We suggest that the ^ { 7 } Li problem , which might be associated with as-yet-unrecognized particle processes operating during BBN , can be solved if the X particle interacts with nuclei strongly enough to drive ^ { 7 } Be destruction but not strongly enough to form a bound state with ^ { 4 } He of relative angular momentum L = 1 .
Justifications of this scenario by rigorous calculations of reaction rates using quantum mechanical many-body models are highly desirable since this result involves many significant uncertainties .