Among the various indices for academic productivity/impact in the respective field, which is most accepted one?
You can see some productivity measures, used in academia, here and here
This question is inspired by the comment here and should not be confused with this
Clarification: The word accepted meant to be taken as accepted in the respective field of activity, for various requirements, say appointments, career advancements, selection for awards, invitation as an examiner, editor, reviewer etc. These measures might not have much impact on the general public, and that is not being asked.
Answer
There is no accepted numerical measure for an individual's academic productivity. The available measures can sometimes be useful, but they all have serious weaknesses and many detractors. In particular, there is no widely accepted or safe choice: if you make any public use of a productivity measure, many people will react angrily, no matter which measure you choose (and their anger may well be justified).
Added in edit: In my experience, citation and publication counts are sometimes mentioned in letters of recommendation, but just as a crude numerical measure, rather than with any serious importance attached to them; most letters do not mention them. (I've never seen an h-index mentioned in a letter or job application, but perhaps it is more common in physics.) Hiring committee members occasionally impose minimal numerical standards, but just to rule out inappropriate cases ("we won't consider anyone for a tenure-track job unless they have at least two publications", say). In the departments I'm familiar with, nobody uses them to choose between serious candidates. Like Dan C says, they just aren't that useful: they add a small amount of information, with a lot of noise and even systematic bias.
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