## Abstract

A new citation index \(h_{\mathrm{PI}}\) for principal investigators (PIs) is defined in analogy to Hirsch’s index *h*, but based on renormalized citations of a PI’s papers. To this end, the authors of a paper are divided into two groups: PIs and non-PIs. A PI is defined as an assistant, associate or full professor at a university who supervises an individual research program. The citations for each paper of a certain PI are then divided by the number of PIs among the authors of that paper. Data are presented for a sample of 48 PIs of physics and physics-related engineering departments from a private research-oriented U.S. university using the ISI Web of Science citations database. The main result is that individual rankings based on *h* and \(h_{\mathrm{PI}}\) differ substantially. Also, to a good approximation across the sample of 48 PIs, one finds that \(h_{\mathrm{PI}} = h \,/ \sqrt{<}N_{\mathrm{PI}}{>}\) where \({<}N_{\mathrm{PI}}{>}\) is the average number of principal investigators for the papers of the PI in question. Similarly, \(h_{\mathrm{PI}} = \frac{1}{2} \sqrt{C_{\mathrm{tot}}\,/<N_{\mathrm{PI}}>}\), where \(C_{\mathrm{tot}}\) is the total number of the PI’s citations. Approaches to broadending the scope of *h* or \(h_{\mathrm{PI}}\) with regard to highly cited papers are compared, and a new metric called \(h_x\) is introduced for such papers which represents the average number of citations exceeding the minimum of \(h^2\) in the *h*-core. A recent proposal to determine an optimum h-index is also discussed in relationship to actual citation data.

## Keywords

Citations h-Index Principal investigator Multiple authors## References

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