The Target-Power Wall for Element-122 Synthesis: Beam-Intensity and Beam-Power Requirements Implied by the Published ^54Cr+^252Cf Cross Section

Evaporation-residue (ER) cross sections for element 122 have been published: within the dinuclear-system (DNS) model, Zhang et al. (2025) predict  fb for the stable-beam reaction CrCf 122 (3n channel), far below current detection limits. This note takes that published value as input and works out a single consequence the cross-section literature does not state numerically for : the beam power the corresponding luminosity would deposit on the target. For one detected atom per month,  fb requires a Cr beam intensity of order  particle-A — roughly three orders of magnitude above the  design intensity of the world’s leading facility — corresponding to of order  MW of beam power deposited on a milligram-scale actinide target whose facility is rated for  kW. The required power exceeds the rated maximum by about three orders of magnitude across the full range of published and estimated cross sections. The high-power-target problem is itself well known and is actively engineered through rotating, segmented target wheels; the modest contribution here is to write the constraint down explicitly for the element-122 case, showing that target thermal survival, not ion-source current or cross section, sets the wall. The note makes no claim to a novel cross section, a measurement, or a reaction calculation.