Beam energy determination via collinear laser spectroscopy

An approach to determine the kinetic beam energy at the ${10}^{-5}$ 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 $3d^{9}4s{}^3{D}_3\to 3d^{9}4p{}^3{P}_2$ transitions in neutral nickel isotopes have been identified to be ${\nu }_0{(}^{58}\mathrm{Ni})=850343678\left(20\right)$ MHz and ${\nu }_0{(}^{60}\mathrm{Ni})=850344183\left(20\right)$ MHz.

Figure 1

Schematic of the BECOLA beamline. The ion beam is produced in a Penning-ionization-gauge (PIG) source. In the radio-frequency-quadrupole trap (RFQ), the beam is cooled and can be extracted continuously or in bunches. Laser and ion beams are superimposed and aligned through two 3-mm apertures at 2.1 m distance. Fluorescence light is collected by three mirror-based detection units. Further ion optics for beam deflection and collimation are not shown.

Figure 2

Typical resonance spectra of ${}^{60}\mathrm{Ni}$ measured in (a) bunched mode or (b) DC mode. The centroid frequencies could be extracted with uncertainties $\le 0.6$ MHz. The abscissa is relative to the deduced rest-frame transition frequency of 850 344 183.2 MHz. In the bunched mode the background rate is strongly suppressed but also the signal strength is reduced compared with the DC mode since the ion-beam current is limited by the capacity of the RFQ ion trap. Spectra taken in collinear or anticollinear geometry yielded a similar quality. (c) Combining a collinear and an anticollinear measurement, the rest-frame frequency was determined. The inner error bars correspond to the fit uncertainty while the outer error bars include possible voltage drifts between the measurements, which were also considered as a statistical contribution.

Figure 3

Kinetic beam energy deduced by three different approaches relative to the set point of the power supply employed for beam acceleration (29 850 V). The uncertainty of the present method is more than one order of magnitude smaller, and, hence, the results for measurements based on transitions in ${}^{58}\mathrm{Ni}$ and ${}^{60}\mathrm{Ni}$ are also shown in higher resolution in the upper part of the figure. The results based on the isotope shift rely on the same experimental data but yield a higher uncertainty due to the lower sensitivity of this approach. Due to an overdue calibration of the high-voltage divider, only the nominal uncertainty of this approach is plotted.