The production rates per Ξ via the -atomic states are investigated for the and channels (including their excited channels) within the frame of the doorway double-Λ hypernuclear picture (direct reaction picture). We found that in the stopped reaction (1) the excited double-Λ hypernuclear states for and are produced more strongly than other double-Λ hypernuclei, and (2) the production rates per Ξ depend considerably on the atomic orbital angular momentum of the particle absorbed into nuclei. The calculated production rates per Ξ are discussed in comparison with the KEK-E176 experimental data.