Observations of heavy elements in Red Giant stars clearly show that low-mass AGB stars can provide a nucleosynthesis site of the s -process .
Stellar evolution models produced over the last years indicate that radiative burning of ^ { 13 } \textrm { C } between succeeding thermal pulses in low-mass AGB star models may indeed provide the neutrons for the s -process .
However , although it seems clear that some mixing between the proton-rich envelope and the carbon-rich core may lead to the production of ^ { 13 } \textrm { C } , the physical mechanism responsible for such mixing is not yet unambiguously identified .

We present stellar model calculations which include mixing due to overshoot and rotation .
Overshoot , with a time-dependent and exponentially decaying efficiency , leads to a partial mixture of protons and ^ { 12 } \textrm { C } during the third dredge-up , when the envelope convection zone reaches deep into the core .
According to the depth-dependent ratio of protons and ^ { 12 } \textrm { C } , a small ^ { 13 } \textrm { C } pocket forms underneath a ^ { 14 } \textrm { N } -rich layer .
Overshoot does not allow for any mixing after the envelope convection zone retreats at the end of the third dredge-up after each pulse .

Rotation introduces mixing driven by large angular velocity gradients which form at the envelope-core interface in AGB stars , in particular after a thermal pulse .
This leads to partial mixing after a pulse , as in the case of overshoot .
However , both mechanisms differ during the interpulse phase .
Rotation continues to mix the region of the ^ { 13 } \textrm { C } -pocket with a diffusion coefficient of logD \sim 2 \dots 3 \mathrm { cm ^ { 2 } s ^ { -1 } } .
This does not only spread the ^ { 13 } \textrm { C } -pocket , but also the more massive ^ { 14 } \textrm { N } -rich layer , and finally leads to mixture of both layers .
By the time when the temperature there has risen to about 9 10 ^ { 7 } K and neutron production sets in , the ^ { 14 } \textrm { N } abundance exceeds the ^ { 13 } \textrm { C } abundance by a factor of 5 \dots 10 .
We analyze the role of ^ { 14 } \textrm { N } as a neutron poison by considering the recycling of neutrons via ^ { 14 } \textrm { N } ( \mathrm { n } , \mathrm { p } ) ^ { 14 } \mathrm { C } and ^ { 12 } \textrm { C } ( p, \gamma ) ^ { 13 } \textrm { N } ( \beta ^ { + } ) ^ { 13 } \textrm { C } qualitatively .
We find that as long as X ( ^ { 14 } \textrm { N } ) \ll X ( ^ { 12 } \textrm { C } ) , the s -process will still be possible to occur under radiative conditions .