Somehow I missed this interesting review by Karl-Heinz Langanke and collaborators Gabriel Martinez-Pinedo and Remco Zegers.
Here is the abstract:
Electron captures on nuclei play an essential role for the dynamics of several astrophysical objects. The capture rate can be derived in perturbation theory where allowed nuclear transitions (Gamow-Teller transitions) dominate, except at the higher temperatures achieved in core-collapse supernovae where also forbidden transitions contribute significantly to the rates. There has been decisive progress in recent years in measuring Gamow-Teller (GT) strength distributions using novel experimental techniques based on charge-exchange reactions. These measurements provide not only data for the GT distributions of ground states for many relevant nuclei, but also serve as valuable constraints for nuclear models which are needed to derive the capture rates for the many nuclei, for which no data exist yet. In particular models are needed to evaluate the stellar capture rates at finite temperatures, where the capture can also occur on excited nuclear states.
There has also been significant progress in recent years in the modelling of stellar capture rates. This has been made possible by advances in nuclear many-body models as well as in computer soft- and hardware. Specifically to derive reliable capture rates for core-collapse supernovae a dedicated strategy has been developed based on a hierarchy of nuclear models specifically adapted to the abundant nuclei and astrophysically conditions present at the various collapse conditions.
This manuscript reviews the experimental and theoretical progress achieved recently in deriving stellar electron capture rates. It also discusses the impact these improved rates have on the various astrophysical objects.
Click the link to access the full preprint