We investigate the enrichment in elements produced by the slow neutron-capture process ( s -process ) in the globular clusters M4 ( NGC 6121 ) and M22 ( NGC 6656 ) .
Stars in M4 have homogeneous abundances of Fe and neutron-capture elements , but the entire cluster is enhanced in s -process elements ( Sr , Y , Ba , Pb ) relative to other clusters with a similar metallicity .
In M22 , two stellar groups exhibit different abundances of Fe and s -process elements .
By subtracting the mean abundances of s -poor from s -rich stars , we derive s -process residuals or empirical s -process distributions for M4 and M22 .
We find that the s -process distribution in M22 is more weighted toward the heavy s -peak ( Ba , La , Ce ) and Pb than M4 , which has been enriched mostly with light s -peak elements ( Sr , Y , Zr ) .
We construct simple chemical evolution models using yields from massive star models that include rotation , which dramatically increases s -process production at low metallicity .
We show that our massive star models with rotation rates of up to 50 % of the critical ( break-up ) velocity and changes to the preferred ^ { 17 } O ( \alpha , \gamma ) ^ { 21 } Ne rate produce insufficient heavy s -elements and Pb to match the empirical distributions .
For models that incorporate AGB yields , we find that intermediate-mass yields ( with a ^ { 22 } Ne neutron source ) alone do not reproduce the light-to-heavy s -element ratios for M4 and M22 , and that a small contribution from models with a ^ { 13 } C pocket is required .
With our assumption that ^ { 13 } C pockets form for initial masses below a transition range between 3.0 and 3.5 M _ { \sun } , we match the light-to-heavy s-element ratio in the s-process residual of M22 and predict a minimum enrichment timescale of between 240 and 360 Myr .
Our predicted value is consistent with the 300 Myr upper limit age difference between the two groups derived from isochrone fitting .