Beam energy determination via collinear laser spectroscopy

An approach to determine the kinetic beam energy at the ${10}^{\ensuremath{-}5}$ level is presented, which corresponds to an improvement by more than one order of magnitude compared with conventional methods. Particularly, collinear fluorescence and resonance-ionization spectroscopy measurements on rare-isotope beams, where the beam energy is a major contribution to the uncertainty, can benefit from this method. The approach is based on collinear spectroscopy and requires no special equipment besides a wavelength meter, which is commonly available. Its advent is demonstrated in a proof-of-principle experiment on a Ni beam. In preparation for the energy measurement, the rest-frame transition frequencies of the $3{d}^{\phantom{\rule{0.16em}{0ex}}9}4s{\phantom{\rule{0.16em}{0ex}}}^{3}{D}_{3}\ensuremath{\rightarrow}3{d}^{\phantom{\rule{0.16em}{0ex}}9}4p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{2}$ transitions in neutral nickel isotopes have been identified to be ${\ensuremath{\nu}}_{0}{(}^{58}\mathrm{Ni})=850\phantom{\rule{0.16em}{0ex}}343\phantom{\rule{0.16em}{0ex}}678\phantom{\rule{0.16em}{0ex}}(20)$ MHz and ${\ensuremath{\nu}}_{0}{(}^{60}\mathrm{Ni})=850\phantom{\rule{0.16em}{0ex}}344\phantom{\rule{0.16em}{0ex}}183\phantom{\rule{0.16em}{0ex}}(20)$ MHz.