Photoabsorption spectra of He þ N clusters, N = 5-9, have been calculated using a diatomics-in-molecules like electronic structure model and a path-integral Monte Carlo sampling method. A qualitative change in the calculated spectra has been observed at N = 9, which has been interpreted in terms of a structural transformation in the clusters consisting in a transition from trimer-like ionic cores observed for N � 7 to dimer-like ionic cores prevailing in He þ 9 through an intermediate state (comparable abundances of both types of ionic cores) observed in He þ 8 . The calculated spectra have been thoroughly compared with an earlier calculation on He þ 3 , He þ 4 , and He þ 10 reported from our group and data available for the same cluster sizes from an experiment.