Recent spectroscopic studies have revealed the presence of numerous carbon-enhanced , metal-poor stars with [ Fe/H ] < -2.0 that exhibit strong enhancements of s -process elements . These stars are believed to be the result of a binary mass-transfer episode from a former asymptotic giant-branch ( AGB ) companion that underwent s -process nucleosynthesis . However , several such stars exhibit significantly lower Ba/Eu ratios than solar s -process abundances . This might be explained if there were an additional contribution from the r -process , thereby diluting the Ba/Eu ratio by extra production of Eu . We propose a model in which the double enhancements of r -process and s -process elements originate from a former 8 - 10 M _ { \odot } companion in a wide binary system , which may undergo s -processing during an AGB phase , followed by r -processing during its subsequent supernova explosion . The mass of Eu ( as representative of r -process elements ) captured by the secondary through the wind from the supernova is estimated , which is assumed to be proportional to the geometric fraction of the secondary ( low-mass , main-sequence ) star with respect to the primary ( exploding ) star . We find that the estimated mass is in good agreement with a constraint on the Eu yield per supernova event obtained from a Galactic chemical evolution study , when the initial orbital separation is taken to be \sim 1 year . If one assumes an orbital period on the order of five years , the efficiency of wind pollution from the supernova must be enhanced by a factor of \sim 10 . This may , in fact , be realized if the expansion velocity of the supernova ’ s innermost ejecta , in which the r -process has taken place , is significantly slow , resulting in an enhancement of accretion efficiency by gravitational focusing .