Kinetic-beam-energy determination via collinear laser spectroscopy
Kristian König, Kei Minamisono, Jeremy Lantis, Skyy Pineda, Robert Powel
aa r X i v : . [ phy s i c s . a t o m - ph ] F e b Kinetic-beam-energy determination via collinear laser spectroscopy
Kristian K¨onig, ∗ Kei Minamisono, Jeremy Lantis, Skyy Pineda, and Robert Powel National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, USA (Dated: February 18, 2021)An approach to determine the kinetic beam energy at the 10 − level is presented, which corre-sponds to an improvement by more than one order of magnitude compared to conventional methods.Particularly, collinear fluorescence and resonance ionization spectroscopy measurements on rare iso-tope beams, where the beam energy is a major contribution to the uncertainty, can benefit from thismethod. The approach is based on collinear spectroscopy and requires no special equipment besidesa wavelength meter, which is commonly available. Its advent is demonstrated in a proof-of-principleexperiment on a Ni beam. In preparation for the energy measurement, the rest-frame transitionfrequencies of the 3 d s D → d p P transitions in neutral nickel isotopes have been identifiedto be ν ( Ni) = 850 343 678 (20) MHz and ν ( Ni) = 850 344 183 (20) MHz.
I. INTRODUCTION
Collinear fluorescence and resonance-ionization laserspectroscopy (CLS) are well-established techniques forthe measurement of molecular, atomic, and nuclear ob-servables [1–4]. With widely tunable lasers, opticaltransitions in stable and short-lived isotopes can be ac-cessed in flight at beam energies of typically 10 −
60 keV.The acceleration to this beam energy leads to a strongcompression of the velocity width and enables Doppler-broadening-free measurements with a resonance-peakwidth at the level of the natural linewidth [5]. Further-more, the fast beam velocity and in-flight detection makethis technique, almost exclusively, the method of choiceto access short-lived exotic isotopes. Measurements ofhyperfine spectra of these isotopes are of high interest dueto the direct link to the nuclear charge radius and elec-tromagnetic moments, leading to investigations of, e.g.,the nuclear shell structure [1, 2], the nuclear superfluidity[6], the odd-even staggering in charge radii [7], the halonuclei [8–10], and the nuclear equation of state [11, 12].Due to the collinear geometry, the fast atoms experi-ence a Doppler-shifted laser frequency. Hence, it is ofcritical importance to accurately determine the kineticbeam energy to correctly transform the observed reso-nance spectra into the rest frame of the atomic beam,where the nuclear information can be extracted from theisotope shifts and from the hyperfine splitting. Eventhough the impact of systematic uncertainties largelycancels in these relative measurements, the beam-energyuncertainty remains a dominant contribution. Undertypical conditions, it is of the same order of magnitudeas the statistical uncertainty that is limited by low pro-duction rates of radioactive isotopes (a few 10’s ion/s forthe rarest isotopes that were investigated with CLS sofar [6, 7]). The beam energy is usually determined by adirect measurement of the acceleration potential or indi-rectly by measuring an isotope shift that is well knownfrom literature, allowing for a correction of the beam en- ∗ [email protected] ergy in the analysis. Both approaches, however, are in-trinsically limited in achievable accuracy. Alternatively,beam-energy-independent CLS measurements can be re-alized by performing spectroscopy in collinear and anti-collinear geometry. This has been successfully demon-strated at on-line facilities [13–15] but is not generallyapplied for rare isotope beams due to the twice as longmeasurement time.In a CLS measurement, a high voltage is applied toan ion source. This potential defines the beam energyand can be directly measured using a voltage divider.The obtained accuracy depends on uncertainties of thedivider ratio (typically 10 − relative accuracy), contactvoltages, potential gradients and field penetrations in theion source, leading to an uncertainty of approximately ± − . − . , Ni in thecase of the 3 d s D → d p P transition at 353 nmand a beam energy of 30 keV.Contrarily, the rest-fame transition frequency is ap-proximately two orders of magnitude more sensitive toan energy change (15 MHz/eV for Ni) than the isotopeshift, and hence, is the preferable reference for the energydetermination. For this reason, CLS-based high-voltage-metrology measurements have been proposed [16] to ac-curately measure the acceleration potential, and were re-alized with a relative accuracy of up to a few ppm forwell-known transitions [17–19]. In general, however, rest-frame transition frequencies are known to a few 100 MHzin comparison to a required uncertainty of a few MHz forthe determination of the beam energy at the 1-eV level,which makes this approach practically inapplicable.In this paper we introduce an all-optical approachto determine the kinetic beam energy, which combinesthe advantages of the collinear-anticollinear approachand the high sensitivity of the rest-frame transition fre-quency on the beam energy. It does not require specialequipment like a frequency comb or a precision high-voltage divider, precise literature values nor a longermeasurement time. Proof-of-principle experiments werepreformed on a 30-keV Ni beam reaching 10 − relativeaccuracy, which corresponds to an improvement of atleast one order of magnitude compared to the conven-tional approaches based on a high-voltage divider or anisotope-shift measurement. In particular, collinear flu-orescence and resonance-ionization spectroscopy experi-ments at on-line facilities can strongly benefit from thepresented method. Due to the low production rates ofexotic isotopes, beam-energy independent measurementsvia collinear and anticollinear spectroscopy directly onthese isotopes are generally not feasible due to the lim-ited measurement time, in contrast to off-line facilitieswhere tremendous accuracy has been demonstrated withthat technique [20, 21]. The procedure described here,however, can be realized with an off-line beam in prepa-ration of the on-line experiment and then allows for insitu beam-energy measurements during the on-line runs.Since the beam-energy uncertainty is the dominant con-tribution as descriptively illustrated in [22, 23], this ap-proach can lift on-line CLS measurements on a new levelof accuracy. II. SETUP
A detailed description of the BEam COoling and LAserspectroscopy (BECOLA) facility at the National Su-perconducting Cyclotron Laboratory (NSCL) at Michi-gan State University can be found in [24, 25]. Theparts that are essential for the proposed approach arebriefly presented in this section and visualized in theschematic overview shown in Fig. 1. Ion beams at anenergy of 30 keV are available from either the CoupledCyclotron Facility at NSCL (radioactive isotope beams)or from an off-line Penning-ionization-gauge (PIG) ionsource [26] at BECOLA, which is a discharge plasmasputtering source and produces stable isotope beams ofpredominantly singly-charged ions. The ion beams arefirst transported to the helium-buffer-gas-filled radio-frequency quadrupole ion trap (RFQ) [27], where thebeams are cooled and can be accumulated and extractedas a compressed ion bunch. The bunched beam is re-quired to perform time-resolved resonant fluorescencemeasurements to suppress the constant laser-inducedbackground [28, 29]. The laser beam is introduced in the30 ◦ bender and overlaps with the ion/atom beam overthe following 5-m long straight section. The beamlineincludes several ion optics to ensure a good alignmentbetween laser light and ion beam, which can be checkedby placing two 3-mm-diameter apertures into the beam-line at a distance of 2.1 m. Between the apertures a Na-loaded charge-exchange cell (CEC) [30] and three mirror-system-based fluorescence-detection units (FDU) [24, 31]are installed. The CEC was heated to 410 ◦ C to create collinearlaser beam anticollinearlaser beam30° deflector mirror-basedfluorescence detection regionPIGsource aperture
FIG. 1. Schematic of the BECOLA beamline. The ionbeam is produced in a Penning-ionization-gauge (PIG) source.In the radio-frequency-quadrupole trap (RFQ) the beam iscooled and can be extracted continuously or as bunches. Laserand ion beams are superimposed and aligned through two 3-mm apertures in 2.1 m distance. Fluorescence light is col-lected by three mirror-based detection units. Further ion op-tics for beam deflection and collimation are not shown. a Na vapor leading to a 50 % neutralization efficiency ofthe incoming singly-charged ion beam through electrondonation from the Na vapor. The FDUs collect a largefraction of the fluorescence light and guide it to photo-multiplier tubes that count single photon events with atime resolution of up to 16 ns [25].The CEC is floated from the ground potential and ascanning potential is applied to perform Doppler tuning.Instead of scanning the laser frequency across the reso-nance, the beam velocity is adjusted by applying a smallvoltage U scan with a full scanning width of 40 V that al-ters the beam energy ( E kin = E kin , + eU scan ) and leads todifferent Doppler shifts. When the Doppler-shifted tran-sition frequency matches the laser frequency, the atomsare resonantly excited and emit photons, which are col-lected by the FDUs and counted with attached photomul-tiplier tubes. Compared to scanning the laser frequency,Doppler-tuning enables a faster and more precise scan-ning procedure, chiefly because a higher stability of thelaser system is achieved when operating it at a fixed fre-quency.For the presented measurements, a Ni + ion beam wasgenerated in the PIG source from natural nickel and in-jected into the RFQ. The Ni + beam was extracted fromthe RFQ at an approximate energy of 29.85 keV in twomodes. One was the bunch mode as described above, andthe other was a direct current (DC) mode just passingthrough the RFQ without trapping and bunching. SinceNi + ions are not accessible by laser spectroscopy due tothe lack of transitions in the optical regime, the ionswere neutralized by collisions with sodium vapor insidethe CEC. Through this non-resonant process, variouselectronic states are populated including the metastable3 d s D state [26], from which the atoms were excitedto the 3 d p P state with laser light at 353 nm.The laser light was transported via two fibers to bothends of the beamline so that the ion beam could beirradiated in collinear and anticollinear geometry. Alaser power of 300 µ W was used and the laser light hada diameter of 1 mm at the FDUs. The primary laserwas a continuous-wave Ti-Sapphire laser (Matisse TS,Sirah Lasertechnik) operated at 705 nm and pumped bya frequency-doubled Nd-YAG laser (Millennia eV, Spec-tra Physics). The Ti-Sapphire laser’s short-term stabi-lization was realized by the side-of-fringe locking to areference cavity. For long-term stabilization, the cav-ity length was regulated to a wavelength-meter read-ing (WSU30, HighFinesse), which has a specified 3 σ ac-curacy of 30 MHz and was calibrated every minute toa frequency-stabilized helium-neon laser (SL 03, SIOSMeßtechnik). The 705-nm light was sent to a cavity-based frequency doubler (Wavetrain, Spectra Physics)creating the 353-nm light that was coupled into the op-tical fibers and transported to the CLS beamline. III. METHOD
In collinear (c) or anticollinear (a) laser spectroscopymeasurements the resonant laser frequencies ν c / a are cor-related with the beam energy E kin due to the Dopplereffect ν c / a = ν γ (1 ± β ) ≈ ν (cid:16) ± p E kin /mc (cid:17) (1)where ν is the rest-frame transition frequency, β isthe beam velocity relative to the speed of light c , γ =1 / p − β is the time dilation factor, and m the massof the atom. This correlation becomes more intuitive inthe non-relativistic approximation. The sensitivity of thetransition frequency on the beam energy is ∂ν c / a ∂E kin = 2 ν mc ν / a ν / a − ν ≈ ν √ eU mc ≈ −
30 MHz / eV (2)with the total acceleration potential U and the elec-tric charge e . For typical experimental conditions (10 −
60 keV, visible optical transition, medium mass atoms),a 1-eV change leads to a Doppler shift of the resonancefrequency of approximately 5 −
30 MHz. This is of theorder of the natural linewidth and enables a precise de-termination of the beam energy. Contrarily, in the caseof the isotope shift δν A,A ′ = ν A − ν A ′ , the sensitivityon the beam energy ∂δν A,A ′ /∂E kin is approximately twoorders of magnitude smaller than ∂ν A /∂E kin and mainlyoriginates from the mass difference of both isotopes.Our approach to determine the beam energy is to makeuse of the rest-frame transition frequency ν that wasseparately obtained from the collinear and anticollinearlaser frequencies at resonance ν c and ν a , respectively.The multiplication of ν c and ν a from Eq.1 yields thevelocity- or beam-energy-independent rest-frame transi-tion frequency ν c · ν a = ν γ (1 + β )(1 − β ) = ν . (3) Once the rest-frame transition frequency is deter-mined, it can be used to extract the beam energy in com-bination with any collinear or anticollinear measurementperformed at later times E kin = mc ν − ν c / a ) ν ν c / a . (4)For example, in a typical one week long experiment onexotic isotopes, reference spectra from a stable isotopeare frequently measured to determine the isotope shift.The resonance frequency of the stable isotope can thenbe combined with the pre-determined rest-frame transi-tion frequency to deduce and track the drift of the beamenergy.In the present measurement, Doppler tuning was ap-plied and the beam velocity was varied to scan acrossthe resonance with fixed laser frequencies separately forcollinear and anticollinear measurements. A small scan-ning potential (40 V) was applied to the CEC to varythe otherwise constant beam energy of approximately29.85 keV. The scanning voltage was measured usinga precision voltage divider with a relative accuracy of6 · − , which is negligible compared to the total beam-energy uncertainty. Although the collinear and anti-collinear laser frequencies were chosen to be in resonanceat the same scanning beam energy, a small energy dif-ference remained. To compensate this energy difference,Eq. 4 is modified, correcting one of the resonance frequen-cies to account for the differential Doppler shift derivedin Eq. 3. The corrected rest-frame transition frequencyis now given by ν = s(cid:18) ν c − ∂ν c ∂E kin · e · ∆ U scan (cid:19) · ν a (5)where ∆ U scan is the difference of the scanning energies atresonance, which is typically less than 5 eV. In the analy-sis, ν was determined iteratively starting with insertingthe literature value [32] in Eq. 2. If no precise literaturevalue is available, the beam energy estimated from the setvoltage can be chosen as initial guess. Sufficient conver-gence was already achieved by applying Eq. 5 to deducea first value for ν , inserting it in Eq. 2 and extractingthe final ν from Eq. 5. IV. REST-FRAME TRANSITION FREQUENCYDETERMINATION
The rest-frame frequencies ν of the 3 d s D → d p P transitions in the stable Ni and Ni were de-termined from four collinear and anticollinear CLS mea-surements of each isotope. Thereof, two DC mode andtwo bunch mode measurements were performed. In Fig. 2(a) and (b) typical spectra are depicted. Each measure-ment of ν agreed within their statistical uncertainty -300 -200 -100 0 100 200 3004000500060007000800090001000011000 C oun t s Relative frequency (MHz)
Asym. Voigt fitCol., bunched -300 -200 -100 0 100 200 3006000000620000064000006600000680000070000007200000 C oun t s Relative frequency (MHz)
Asym. Voigt fitAnticol., DC 1 2 3 4850344180850344181850344182850344183850344184850344185850344186850344187 Bunch modeDC mode R e s t - f r a m e f r equen cy ( M H z ) Measurement number (a) (b) (c)
FIG. 2. Typical resonance spectra of Ni measured in bunched mode (a) or DC mode (b). The abscissa is relative to thededuced rest-frame transition frequency of 850 344 183.2 MHz. In the bunched mode the background rate is strongly suppressedbut also signal strength is reduced compared to the DC mode since the ion beam current is limited by the capacity of the RFQion 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 barscorrespond to the fit uncertainty while the outer error bars include possible voltage drifts between the measurements, whichwere also considered as statistical contribution. as shown in Fig. 2 (c) for Ni. The averaged valuesare summarized in Tab. I and are in excellent agreementwith measurements from hollow cathode discharges [32].The largest contribution to the present 20-MHz uncer-tainty originates from the frequency measurement withthe wavelength meter, which will mainly cancel for thebeam-energy determination. Hence, also smaller contri-butions are discussed in detail.The statistically-acting uncertainties given in the firstparentheses in Tab. I consist of: • Fit uncertainty: ≤ . / √ • Voltage drifts: ≤ • Frequency measurement:
20 MHz / 1.4 MHz: TheWSU30 wavelength meter used in the present studyhas a 1 σ uncertainty of 10 MHz, resulting in 20 MHzafter frequency doubling. In [33, 34] this uncer-tainty has been investigated in more detail and itwas found that it can be separated into two parts.The specified uncertainty is caused by a frequencyoffset that is constant over time for measurementsat the same wavelength if regularly calibrated withthe same reference laser. On top of this offset onlyrelatively small variations have been observed. A3-MHz amplitude of these local variations is quotedfor a similar wavelength meter in [34], which is in-terpreted as a 1 σ uncertainty of 1 MHz.A constant offset δν in a collinear-anticollinear fre-quency measurement leads to an identical shift ofthe rest-frame transition frequency( ν c + δν )( ν a + δν ) = ν c ν a + δν ( ν c + ν a ) + δν ≈ ( ν + δν ) (6)with an approximation of ν c + ν a ≈ ν . Inthe later discussion of the beam-energy determina-tion the offset contribution cancels, transferring thefrequency-measurement uncertainty to be causedby the local variations of the wavelength meter.They affect collinear and anticollinear measure-ments independently and hence, the uncertaintywas determined by Gaussian error propagation∆ ν , var = 1 √ ν WM − var · . . (7)To account for the frequency doubling, it was mul-tiplied by a factor of two. • Line shape:
TABLE I. Rest-frame transition frequencies of the3 d s D → d p P transition in the naturallymost abundant neutral nickel isotopes , Ni. The transitionhas been measured before from hollow cathode dischargesbut only the average over all stable isotopes is given [32].Isotope-separated values have been calculated accordingto the natural abundance and the isotope shift from [35],which agree closely with our results when interpreting theuncertainty in [32] of a few mK to be about 100 MHz. Ourstatistical uncertainty is given in the first parentheses whilethe systematic uncertainty is listed in the second parentheses.Isotope This work Literature [32]MHz MHz Ni 850 343 677.6 (1.2) (20.0) 850 343 600 (100) Ni 850 344 183.2 (1.1) (20.0) 850 344 110 (100) in the CEC. Non-matching fit functions can lead toshifts of the extracted resonance centroid frequen-cies, which however, appear in opposite directionsin the collinear and anticollinear measurements andcancel in the extraction of ν . Data fitting was doneby using a symmetric Voigt function, a Voigt withan additional satellite Voigt, and a Voigt with anexponential function [36]. The observed discrepan-cies of ν are below 1 MHz and can still have statis-tical origin but conservatively the largest deviationbetween the different fit models was considered. • Beam alignment: ν ′ = ν a ν c γ (1 + β cos α a ) (1 − β cos α c ) (8)with α c and α a being the angles between atomicbeam and collinear or anticollinear laser light, re-spectively. Calculating the maximum frequency de-viation for the available parameter space that islimited by α c , α a < | α c − α a | < • Other:
Bunch structure:
The rest-frame frequencies ob-tained from measurements in bunch and DC modeagree well within their fit uncertainties, and hencedo not indicate any systematic discrepancy.
Scan voltage:
All measurements were performed ata similar scanning potential and hence, do not have significant contributions due to deflecting or focus-ing the beam, due to the voltage measurement, nordue to the linear approximation in Eq. 5.
Beam overlap:
If the laser beams differ in positionor diameter, they can interact with different partsof the atomic beam. Due to the beam cooling in theRFQ and the resulting homogeneous atomic beam,the estimated impact is negligible.
Photon recoil:
With each laser-atom interaction, adirected moment is transferred to the atom whilethe emittance of fluorescence light is undirected.This leads to an acceleration of the atoms if theatomic and the laser beam are parallel and to adeceleration if both beams have opposite direction,which contradicts to the requirement of a constantbeam energy of Eq. 3. Comparing the ratios of thedifferent detection units for both cases did not showany systematic trend at our current resolution.
Optical population transfer:
The applied transitionis not a two-level system and 10 % of the excitedatoms will decay into a dark state. Hence, multipleinteractions in front of the optical detection regionswill depopulate the ground state, especially for theresonance condition. We assume that we cover thiseffect within the line shape contribution.The total 20-MHz uncertainty of the rest-frame frequencydetermination is dominated by the uncertainty of thelaser-frequency measurement with the wavelength me-ter. The smaller contributions will become significantfor the beam-energy determination, where the frequency-measurement uncertainly can be mostly eliminated.
V. BEAM-ENERGY DETERMINATION
Again, the specified wavelength meter uncertainty isseparated into a constant offset and local variations. In-cluding a frequency offset δν , Eq. 4 yields E kin = mc ν + δν ) − ( ν c / a + δν )) ( ν + δν )( ν c / a + δν )= mc ν − ν c / a ) ν ν c / a + δν ( ν + ν c / a ) + δν (9)where the contribution from δν mostly cancels and fallsbelow the 10 − level, and hence, is not the dominantfactor for the precise determination of the beam energy.The elimination of δν , is based on the use of the samewavelength meter for the determination of ν and theindependent measurements of ν a / c . If a literature value isto be used, the wavelength-meter-offset contribution doesnot cancel, leading to significantly larger uncertainties inthe energy determination.The uncertainty in the frequency difference ( ν − ν c / a )in the numerator of Eq. 4 becomes now the dominantcontribution for the beam-energy determination. Sincethe uncertainties of ν have been discussed in detail inthe previous section, we will now focus on ν c / a : • Fit uncertainty: ≤ . • Line shape: < . < • Local wavelength-meter variations: • He:Ne drift: • Beam alignment: ν , all contributions discussedin section IV except the wavelength-meter offset were in-cluded. Adding these contributions in quadrature, atotal uncertainty of ∆( ν − ν c/a ) = 4 . · − measurement ofthe Ni beam energy at 29.85 keV. VI. DISCUSSION
In Fig. 3, our approach is compared to the conventionalmethods. For demonstration purposes, four Ni and four Ni measurements were performed in alternating orderin collinear geometry. As depicted in the upper part ofthe Fig. 3, the present approach shows consistent resultsfor both isotopes. The deviation between both isotopesvaries between 0.02 eV and 0.2 eV, which is caused bystatistical uncertainties and chiefly voltage drifts betweenthe measurements. After measurement set (2) was a 1-htime break explaining the larger step.In the lower part of the Fig. 3, all methods are com-pared yielding an excellent agreement. However, the un-certainties of the conventional methods are significantlylarger than those of the present approach.To demonstrate the isotope-shift-based approach, theisotope shift between , Ni of the same set of mea-surements was evaluated and the beam energy was ad-justed in the analysis until the isotope shift matched the R e l a t i v e bea m ene r g y ( e V ) Measurement number reference Nireference Ni voltage dividerisotope shift
FIG. 3. Kinetic beam energy deduced by three different ap-proaches relative to the set point of the power supply em-ployed for beam acceleration (29850 V). The uncertainty ofthe present method is more than one order of magnitudesmaller, and hence, the results for measurements based ontransitions in Ni and Ni are also shown in higher res-olution in the upper part of the figure. The results basedon the isotope shift rely on the same experimental data butyield a higher uncertainty due to the lower sensitivity of thisapproach. Due to an overdue calibration of the high-voltagedivider, only the nominal uncertainty of this approach is plot-ted. literature value of δν ( , Ni) = 507 . .
9) MHz [35].The beam energies, for which an agreement betweenthe measured isotope shifts and the literature value wasachieved, are plotted in Fig. 3. Adding the fit uncertainty( ≤ . ·√ ·√
2) and the lineshape (1 MHz) in quadrature to the uncertainty of the lit-erature value, yields a combined uncertainty of ∆ δν AA ′ =3 . E kin = 13 eV due to themuch lower sensitivity of the isotope shift on the beamenergy. Furthermore, this method critically dependson a stable beam energy between the measurements ofboth isotopes, which explains the scatter in Fig. 3. Thebeam-energy differences observed between both isotopeswith the transition-frequency-based approach were in therange of 0.18 eV, which seems to be minor but this is am-plified by ∂ν A /∂E kin · ( ∂δν AA ′ /∂E kin ) − ≈
60 and causesfluctuations of 11 eV in the isotope-shift-based approachin the case of , Ni.Using a high-voltage divider to measure the accelera-tion potential that defines the beam energy, is limited bythe uncertainty of the divider ratio (Ohmlabs HVS-100,originally specified relative accuracy 8 · − ) and of thevoltmeter (Keysight 34465A, 6 · − ). The trapping po-tential well in the RFQ had a nominal depth of -4 V anda release potential of -15 V was applied. Since the fieldpenetration during the extraction of the trapped ions isnot exactly known, a 3-V uncertainty was considered. Inaddition, a 2-V uncertainty was included to regard con-tact and thermal potentials at the RFQ and the hot CEC,leading to a total uncertainty of 4.7 V. The calibration ofthe available high-voltage divider is long outdated and asignificant change of the divider ratio has been observedby comparing it to the set voltage. Hence, the absolutevoltage values could not be accurately evaluated with thisdevice while relative values were still valid and used toestimate the voltage fluctuation over the measurementperiod. Therefore, only the size of the uncertainty basedon a valid calibration is shown in Fig. 3 and the centervalue is defined by the set voltage. VII. CONCLUSION
An approach to determine the kinetic energy of anatom, ion or molecule beam for collinear laser spec-troscopy measurements was demonstrated using a 30-keVNi beam. The rest-frame transition frequencies of , Niwere determined by collinear and anticollinear laser spec-troscopy and used as a reference to deduce the beam en-ergy. This method has several advantages compared toconventional approaches: • High accuracy at the 10 − level, corresponding to an increase by more than one order of magnitude. • No special equipment like a precision voltage di-vider or a frequency comb are required. • No assumptions on energy shifts due to field pene-trations, or due to contact and thermal potentials. • No dependence on literature values. • No additional on-line measurement time as re-quired for the beam-energy-independent measure-ments, e.g., in [8–10].The application of the presented method to determine thekinetic beam energy will significantly improve the accu-racy of collinear fluorescence and resonance-ionization-spectroscopy measurements on rare isotope beams bytransforming the formerly largest systematic uncertaintyinto a minor contribution.
VIII. ACKNOWLEDGEMENTS
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