We extend the pioneering work of J. E. Hirsch, the inventor of the h-index, by proposing a simple and seemingly robust approach
for comparing the scientific productivity and visibility of institutions. Our main findings are that i) while the h-index
is a sensible criterion for comparing scientists within a given field, it does not directly extend to rank institutions of
disparate sizes and journals, ii) however, the h-index, which always increases with paper population, has an universal growth
rate for large numbers of papers; iii) thus the h-index of a large population of papers can be decomposed into the product
of an impact index and a factor depending on the population size, iv) as a complement to the h-index, this new impact index
provides an interesting way to compare the scientific production of institutions (universities, laboratories or journals).
We develop and discuss the theoretical basis of a new criterion for ranking scientific institutions. Our novel index, which
is related to the h-index, provides a metric which removes the size dependence. We discuss its mathematical properties such
as merging rules of two sets of papers and analyze the relations between the underlying rank/citation-frequency law and the
h-index. The proposed index should be seen as a complement to the h-index, to compare the scientific production of institutions
(universities, laboratories or journals) that could be of disparate sizes.