On the relationship between citations of publication output and Hirsch index h of authors: conceptualization of tapered Hirsch index h(T), circular citation area radius R and citation acceleration a.

The nature of the empirical proportionality constant A in the relation L = Ah(2) between total number of citations L of the publication output of an author and his/her Hirsch index h is analyzed using data of the publication output and citations for six scientists elected to the membership of the Royal Society in 2006 and 199 professors working in different institutions in Poland. The main problem with the h index of different authors calculated by using the above relation is that it underestimates the ranking of scientists publishing papers receiving very high citations and results in high values of A. It was found that the value of the Hirsch constant A for different scientists is associated with the discreteness of h and is related to the tapered Hirsch index h(T) by A(1/2) ≈ 1.21h(T). To overcome the drawback of a wide range of A associated with the discreteness of h for different authors, a simple index, the radius R of circular citation area, defined as R = (L/π)(1/2) ≈ h, is suggested. This circular citation area radius R is easy to calculate and improves the ranking of scientists publishing high-impact papers. Finally, after introducing the concept of citation acceleration a = L/t(2) = π(R/t)(2) (t is publication duration of a scientist), some general features of citations of publication output of Polish professors are described in terms of their citability. Analysis of the data of Polish professors in terms of citation acceleration a shows that: (1) the citability of the papers of a majority of physics and chemistry professors is much higher than that of technical sciences professors, and (2) increasing fraction of conference papers as well as non-English papers and engagement in administrative functions of professors result in decreasing citability of their overall publication output. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s11192-012-0805-7) contains supplementary material, which is available to authorized users.