To state the title question perhaps more precisely:
What is the largest photon energy Eγ and the corresponding mass number A and atomic number Z of a suitable nucleus AZX (presumably in a ground state) such that the hypothetical reaction
AZX+γ→(A−a)(Z−z)Y+whatever remains (with combined charge+z)
is "kinematically" forbidden for any values 1≤a<A and Z≥z≥Z+a−A,
while conforming to the standard model?
Edit
Changed the question title (removed the parenthetical qualification "whether otherwise stable or not"): for any unstable nucleus the stated question and condition is not meaningful and not relevant.
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