We study the production of neutron-rich hypernuclei ~(12)∧Be, ~(16)∧C, and ~(10)∧ Li by the (π~-, K~+) and (K~-, π~+) reactions in flight and treat two different mechanisms of production. The first mechanism is a two-step process with meson charge exchange (e.g., π~-p→π~0n, π~0p→K~+∧). The other mechanism is one-step production (π~-p→K~+∑~-) proceeding via a small ∑~- component, arising in ∧ hypernuclei due to ∧N-∑N coupling, as a doorway state. Typically, the two-step mechanism is more productive. The forward differential cross section of the ~(10)B(π~-, K~+)~(10)∧Li(2) reaction is about 70 nb/sr at an incident momentum of 1.05 GeV/c. On the other hand, the one-step process can serve as a direct measurement of the ∑ admixture if the two-step contribution is suppressed by a suitable choice of the reaction kinematics.
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