Invariant-mass spectroscopy in projectile fragmentation reactions

The fragmentation of a projectile into a number of pieces can lead to the creation of many resonances in different nuclei. We discuss application of the invariant-mass method to the products from such reactions to find some of the most exotic resonances located furthest beyond the proton drip line. We show examples from fragmentation of a fast $^{13}$O beam including the production of the newly identified $^9$N resonance. In extracting resonance parameters from invariant-mass spectra, accurate estimates of the background from non-resonant prompt protons are needed. This is especially important in determining the widths of wide resonances typically found at the edge of the chart of nuclides. An event-mixing recipe, where the mixed events have reduced weighting for the smaller invariant-masses, is proposed to describe this background. The weighting is based on the measured correlations of heavier hydrogen isotopes with the resonances or the projectile residues.