h_PI: The Citation Index for Principal Investigators
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A new citation index h_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 who are senior faculty members of physics and physics-related engineering departments at 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_PI differ substantially. Also, to a good approximation across the sample of 48 PIs, one finds that h_PI = h / √(<N_PI>) where <N_PI> is the average number of principal investigators on the papers of a particular PI. In addition, h_PI = 1/2√(C_tot /<N_PI>), where C_tot is the total number of citations. Approaches to broadening the scope of h or h_PI are discussed briefly, and a new metric for highly cited papers called h_x is introduced which represents the average number of citations exceeding the minimum of h^2 in the h-core.
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