A new beamline for laser spin-polarization at ISOLDE

W. Ginsa,∗, R. D. Hardingb,c, M. Baranowskid, M. L. Bisselle, R. F. Garcia Ruiza,1, M. Kowalskab, G.Neyensa,b, S. Palladab, N. Severijnsa, Ph. Veltena, F. Wienholtzb, Z. Y. Xua, X. F. Yanga, D.

Zakouckyg

aKU Leuven, Instituut voor Kern- en Stralingsfysica, Leuven, BelgiumbEP Department, CERN, Switzerland

cUniversity of York, York, United KingdomdFaculty of Physics, Adam Mickiewicz University, Poznan, Poland

eSchool of Physics and Astronomy, The University of Manchester, Manchester, United KingdomfPoznan University of Technology, Poznan, Poland

gNPI, Czech Academy of Sciences, Rez, Czech Republic

Abstract

A beamline dedicated to the production of laser-polarized radioactive beams has been constructedat ISOLDE, CERN. We present here different simulations leading to the design and construction ofthe setup, as well as technical details of the full setup and examples of the achieved polarizationsfor several radioisotopes. Beamline simulations show a good transmission through the entire line, inagreement with observations. Simulations of the induced nuclear spin-polarization as a function ofatom-laser interaction length are presented for 26,28Na, [1] and for 35Ar, which is studied in this work.Adiabatic spin rotation of the spin-polarized ensemble of atoms, and how this influences the observednuclear ensemble polarization, are also performed for the same nuclei. For 35Ar, we show that multiple-frequency pumping enhances the ensemble polarization by a factor 1.85, in agreement with predictionsfrom a rate equations model.

Keywords: beamline, laser polarization, β-asymmetry, adiabatic rotation

1. Introduction

Spin-polarized radioactive nuclei have been astaple of nuclear and particle physics researchsince the discovery of parity violation [2]. Withthe use of polarized nuclei as a probe in fieldsranging from fundamental interactions to mate-rial and life sciences [3, 4, 5], an initiative fora dedicated experiment at ISOLDE was started,and a beamline was built and commissioned. Re-sults from the commissioning of the new beamline

∗Corresponding authorEmail addresses: wouter.gins@fys.kuleuven.be

(W. Gins), robert.harding@cern.ch (R. D. Harding)1Current affiliation: EP Department, CERN, CH-1211

Geneva 23, Switzerland

have been reported in Ref. [1]. The present articledocuments the technical aspects of the beamline.

Section 2 describes the mechanism of laserpolarization through optical pumping and howthe induced nuclear polarization can be observedthrough the asymmetry in the nuclear β-decay.Section 3 reports on the different parts of thebeamline, followed by Section 4 dedicated to theion-optical simulations. The magnetic fields gen-erated by the setup are discussed in Section 5.The successful use of multiple-frequency opticalpumping to achieve higher polarization for 35Aratoms, to be used in future fundamental inter-actions studies [5], is described in Section 6 andcompared with experimental data. Calculationsof the adiabatic rotation of the spin-polarized en-sembles of 26,28Na and 35Ar in the magnetic fields

Preprint submitted to NIM A September 13, 2018

arX

iv:1

809.

0438

5v1

[ph

ysic

s.in

s-de

t] 1

2 Se

p 20

18

J=1/2

J=3/2

I=1

F=1/2

F=3/2mF-3/2

mF-1/2

mF1/2

mF3/2

F=1/2F=3/2

F=5/2

mF-5/2

mF-3/2

mF-1/2

mF1/2

mF3/2

mF5/2

σ+

Figure 1: Optical pumping scheme in the D2 line of 28Na.Excitations using σ+ polarized light are drawn with solidlines, while the dashed lines indicate decay paths throughphoton emission.

are presented in Section 7 and compared to theobserved asymmetries. Conclusions are given inSection 8.

2. Optical pumping and β-asymmetry

The hyperfine interaction couples the nuclearspin ~I and the electron spin ~J together to a totalatomic spin ~F = ~I + ~J , which splits a fine struc-ture level into several hyperfine levels. Atomicpopulation can be resonantly transferred fromone hyperfine level to a radiatively coupled levelthrough interaction with a narrowband laser. Inthis process, conservation of angular momentumdictates that the atomic spin ~F can only changeby maximally one unit. The left side of Figure 1illustrates the 5 allowed hyperfine transitions forthe D2 line in 28Na (32S1/2 → 32P3/2) as solidlines. The term “optical pumping” is used whenresonant excitations and decay drive the atomicpopulation towards a specific (magnetic sub)state[6].

When the laser light is circularly polarized (σ+

or σ−), conservation of angular momentum fur-ther imposes the restriction ∆mF = 1 or −1 (in-dicated as solid lines on the right side of Fig-ure 1). The decay back to the lower state ishowever not bound to this rule and can proceedwith ∆mF = 0,±1 (indicated by dashed lines)[7]. By maximizing the number of such exci-tation/decay cycles, the population of a specificF-state is pushed towards substates with eithermaximal or minimal mF quantum numbers in thelowest level.

The number of excitation/decay cycles canbe increased by either increasing the laser pho-ton density or by having a longer interaction

time. In a collinear geometry (as used inhigh-resolution collinear laser spectroscopy exper-iments [8]), where the particle and CW laser beamare spatially overlapped, such an enhanced inter-action time is achieved by choosing an appropriatelength of the laser-particle interaction region.

The resulting atomic polarization is then trans-ferred to a polarization of the nuclear spinthrough the hyperfine interaction. The nuclearpolarization in such an ensemble of nuclei is de-fined as

P =∑mI

w (mI)mII

, (1)

with w (mI) the probability that the |I,mI〉 quan-tum state is populated after the optical pumpingprocess.

The nuclear polarization can be observed by de-tecting the asymmetry in the β-decay of radioac-tive isotopes, due to the parity violation in nuclearβ-decay [2]. The β-decay of a polarized ensemblehas a specific angular distribution that can be re-duced to W (θ) ∼ 1 + AP cos (θ) for allowed β-transitions [9], where θ is the angle between theemitted electron momentum and the nuclear spinorientation. A is the asymmetry parameter of thedecay which depends on the initial and final spinof the nuclear states involved in the β-decay, andP is the polarization of the nuclear ensemble withrespect to a quantisation axis. The experimentalasymmetry (as reported in Section 6) is then de-fined as

Aexp =N (0◦)−N (180◦)N (0◦) +N (180◦)

= �AP, (2)

where � represents depolarization effects which de-pend on several experimental factors.

For more details on spin-polarization via opticalpumping, see Ref. [10, 11].

3. Beamline description

The laser-polarization setup, part of the Ver-satile Ion Techniques Online (VITO) beamline atISOLDE, CERN [12], is designed to polarize nu-clei through the application of optical pumping ofan atomic hyperfine transition. More than 1000

2

5 degree deflector

+ beam diagnostics

Charge Exchange

vacuum chamber

Optical detection

Interaction region

with Helmholtz coils

Adiabatic rotation

region

Main magnet

with sample holder

End of beamline

diagnostics

1 m

Ion beam entrance

Laser window

1111

2 3

Figure 2: Schematic overview of the VITO beamline, with the main beamline components indicated. The beam fromISOLDE enters from the top left beampipe, and the start of this beampipe is used as the start for the ion-opticalsimulations. The numbers are used to indicate the coils in Table 1.

radioactive isotopes of more than 70 elements canbe produced at ISOLDE, CERN, via the impactof a 1.4 GeV proton beam on a variety of tar-gets using different types of ion sources [13]. Theion beam is sent into the laser polarization beam-line and overlapped with a circularly polarizedlaser beam to induce nuclear polarization. Afterimplantation in a suitable host, placed betweenthe poles of an electromagnet, the change in β-asymmetry is observed as a function of laser fre-quency, scanned across the hyperfine structure.Although the technique is also applicable to ions[14], the current design is specific for working withatoms. An overview of the layout of the entire op-tical pumping beamline is given in Figure 2.

The first element of the beamline is a 5 degreedeflector equipped with a laser window, where thelaser beam is overlapped with the pulsed radioac-tive ion beam. A beam diagnostics box, contain-ing an adjustable iris to define the beam waist anda readout plate for the ion-current, is placed di-rectly after the deflector. Beamline simulations ofthe 5 degree deflector are discussed in Section 4.

The Charge Exchange Cell (CEC), housed inthe Charge Exchange vacuum chamber of Figure 2and depicted in Figure 3, is placed after the di-agnostic box, where the beam passes through avapor of Na or K and undergoes charge exchange.It contains a reservoir in the middle where solidNa or K is deposited. The stainless steel reser-

21 mm

beam pipe

Liquid cooled heatsink

Reservoir for

Na or K

Opening for

heating rods

Figure 3: 3/4 view of the CAD drawing of the CEC. Thestainless steel reservoir has 6 deep holes to house heat-ing rods. The liquid cooled heatsink clamps onto thebeampipe ends.

voir is heated using six RS-8607016 220 W heat-ing cartridges powered by a DC power supply. Tominimze the diffusion of the Na or K vapor tothe rest of the beamline, the ends of the pipe arekept at a lower temperature. This is achievedusing a heatsink cooled with circulating Galden R©

PFPE down to 90◦ C, below the evaporation tem-perature of Na or K in vacuum. This minimizesthe loss of vapor to the rest of the beamline andensures a high vapor density in the middle. Non-neutralized ions are deflected from the beam after

3

the CEC using an electrostatic deflector. A spe-cially designed electrode arrangement (referred toas voltage scanner, design details in Section 4)is attached to this cell and modifies the kineticenergy of the incoming ion beam. This changesthe velocity of the beam, and induces a Dopplershift of the laser frequency. The relation betweenthe labframe νrest frequency and the frequencyνobs observed by this accelerated (or decelerated)beam is

νobs = νrest

√1− β1 + β

, (3)

β =

√1− (mc2/ (mc2 + qEkin))2. (4)

This allows a fast scanning of the hyperfine struc-ture by changing the acceleration voltage. In Fig-ure 4 we show the electrical diagram of the wiringthat enables this voltage scanning. The data ac-quisition system (DAQ) can provide a controlledvoltage of up to ±10 V, which is amplified by aKepco amplifier by a factor of 100. This voltageof ±1 kV (and typical precision of 0.02 V) is thenapplied to the secondary windings of an isolatingtransformer. The insulating transformer suppliesthe 230 V line voltages on the secondary side toa DC power supply which is then also floated bythe ±1 kV. Since the biased electrode of the volt-age scanner is connected to the base of the CECand thus to the lower output of the power sup-ply, both elements are biased to ±1 kV relativeto the beamline ground while a constant voltageis applied over the heating rods.

Following the CEC is the optical detection re-gion, which is a copy of the light collection regionused in the COLLAPS setup [15]. The photomul-tiplier tubes in this detection area are used fordetermining the resonant laser frequency throughoptical detection of the fluorescence decay from astable isotope of the element of interest, prior tostarting β-asymmetry measurements on the lessabundant radioactive species.

In the interaction region, where the opticalpumping takes place, Helmholtz coils provide amagnetic field on the order of 2 mT along thebeamline axis pointing in the beam direction.This magnetic field defines a quantisation axis

DAQ (±10 V)

x100

DC supply

Heating rods

80 V

Biasedelectrodeof voltagescanner

Beamline ground

Figure 4: Simplified diagram of the electrical wiring for thevoltage scanning. The voltage scanning provides a float-ing potential for a secondary circuit, where an isolatingtransformer supplies power to a DC power supply for theheating rods mentioned in Section 3. The data acquisitionprogram can supply ±10V, which is amplified by a factor100.

0 1000 2000Frequency offset [MHz]

0

20

40

60

80

Nucle

ar p

olar

izatio

n [%

]

(a)

0.0 0.8 1.6Interaction length [m]

(b)

26Na28Na35Ar

Figure 5: (a) Simulated hyperfine spectrum for pumping26Na in the D2 line using σ+ polarized light at a typicallaser power of 80 mW/cm2. The interaction time corre-sponds to an interaction length of 1.6 m for a 50 keV beam.(b) The calculated polarization in the strongest componentof the hyperfine spectrum (indicated with a dashed line in(a)) as a function of interaction length for the differentnuclear species discussed in this paper.

and avoids coupling of the atomic spins to pos-sible stray fields in the environment. The min-imal length of this interaction region is deter-mined by the time needed for the pumping pro-cess. The process of optical pumping can bemodelled through the formation of rate equationsbased on the Einstein formalism [16, 17, 10]. By

4

Electric

poten

tial[k

V]

Figure 6: Simplified beamline geometry as used in the COMSOL simulations. The electrodes are colored with the appliedelectric potential when the scanner is set to 1 kV (color online). The other (grounded) beamline elements present in thesimulation are colored gray. The trajectories of the particles are drawn in black.

solving this system of differential equations, thedegree of nuclear polarization P (Eq. (1)) canbe calculated for any interaction time. The D2line in Na [1] was used as the case study. Fig-ure 5(a) shows a the hyperfine spectrum gener-ated with this method, while in (b) the polariza-tion in the highest peak is calculated as a func-tion of the laser-atom interaction time (translatedinto a beam line length assuming a 50 keV beam).Based on these calculations, a length of 1.6 m wasselected as a compromise between achievable po-larization and available space in the ISOLDE hall.Although the length needed to fully polarize anensemble depends on the Einstein A parameter ofthe transition, 1.6 m will give a sufficiently longinteraction time for most strong transitions whereA has a value in the order of 107 − 108 Hz. Thisis illustrated in Figure 5(b) for 26,28Na and 35Ar,the first isotopes that have been polarized withthe new set-up.

A series of solenoids and a large electromagnetare placed after the interaction region, with thefield of the solenoids acting along the beam direc-tion and the electromagnet generating a field per-pendicular to it. The combination of these fieldsadiabatically rotates the atomic spin in the hori-zontal plane, orienting it in the same direction asthe field of the electromagnet. The field of theelectromagnet is sufficiently strong to decouplethe nuclear from the electron spin. The details ofthis adiabatic spin rotation and decoupling of the

nuclear spin from the electron spin are discussedin Section 7. A removable sample holder and β-detectors are installed inside the electromagnet,where the polarized ensemble is implanted in asuitable host material. This β-detection setup hasbeen used before in β-NMR studies on Mg iso-topes [14].

A diagnostics box containing a wire scanner andFaraday cup, as detailed in [13] (supplementedwith a plate to detect atomic beams), is installedafter this region to provide beam diagnostics.

4. Ion optics

Ion-optical beam transmission simulations wereperformed to benchmark the effect that the deflec-tor and voltage scanner have on the shape of the

Horizontal deflector

Vertical steerer

40.0 mm

R2 m

TOP VIEW

Beam direction

Figure 7: CAD drawing of the 5 degree ion-deflector. Ionbeam coming from ISOLDE (left) is bent 5 degrees with aradius of 2 m to overlap the ion/atom beam with the laserbeam.

5

1

2 SECTION SIDE VIEW

CONFIG 1 CONFIG 2

364.0 mm212.0 mm

Beam direction

(a)

0 10 20 30Distance [cm]

0.0

0.2

0.4

0.6

0.8

1.0

Volta

ge [k

V]

59.0

59.2

59.4

59.6

59.8

60.0

Kinetic energy of particles [keV]

(b)

0 5 10 15 20Distance [cm]

0.0

0.2

0.4

0.6

0.8

1.0

Volta

ge [k

V]

59.0

59.2

59.4

59.6

59.8

60.0

Kinetic energy of particles [keV]

(c)

Figure 8: (a) 1/2 section view of both configurations for the voltage scanner. The biased electrode is indicated in redand the grounded electrode in green (color online). (b) Electric potential (full line) and the kinetic energy (dashed) ofa 60 keV beam of 39K as a function of distance using configuration 1 when 1 kV is applied to the biased electrode. (c)Same as (b), but for configuration 2.

beam and the transmission that can be expected.

A standard beam of 39K+ with 3 π mm mradbeam emittance is generated for the simulations,as reported for the cooler-buncher ISCOOL [18].The focal point of the beam is, prior to enter-ing the 5 degree deflector, optimized for maximaltransmission using the quadrupole doublet thatis installed in front of it. As the doublet is notincluded in the simulations, the focus is set bychanging the size of the beam and the convergenceof the incoming beam by changing the Twiss pa-rameters [19]. The kinetic energy of the beam isset to 60 keV, which is the maximal beam energythat can be delivered by ISOLDE to the low en-ergy section. For all simulations, the COMSOLmultiphysics software was used [20]. The used ge-ometry is given in Figure 6. First an overview ofall the elements included in the simulations willbe given.

The first electrostatic element of the VITObeamline in the simulations is the 5 degree deflec-tor, which allows a soft bending of the ion beamto overlap it collinearly with the laser light. The5 degree deflector has an internal opening of 40mm and consists of two vertical steerer plates anda pair of electrodes with a machined curve match-ing 2 m (see Figure 7). After this, a voltage scan-ner (the design of which will be treated further inthis section) adjusts the kinetic energy of the ionbeam in a range of ±1 keV. It is mounted insidethe vacuum box where the CEC is also mounted(shaped electrodes and red circle respectively, Fig-ure 6) and the biased electrode is connected to theCEC. The CEC acts as a long collimator with a 2cm opening, followed by another collimator withan opening of 1 cm approximately 2 m furtherdownstream. These small collimators guarantee agood overlap between the particle and laser beam.

6

As the charge exchange process neutralizes thecharged particles, the CEC is the final electro-static element considered in the simulations. Thetubes and chambers forming the beamline up tothis point are also present and are grounded toprovide accurate potential fields.

The design for the voltage scanner deviatesfrom a traditional series of ring electrodes con-nected through a resistor chain [17]. Instead, twospecially shaped electrodes define the equipoten-tial electrical field (Figure 8a). Two configura-tions of this geometrical design of the shaped elec-trodes have been used.

In the first configuration (Config. 1 in Fig-ure 8a), eight triangular spikes are attached toan octagonal mounting base. Overlapping two ofsuch electrodes gives a gradual and nearly-linearchange in potential experienced by the ions, asgiven in Figure 8b. In the second design (Config.2 in Figure 8a), the first electrode is replaced witha cylinder covering the entire scanner, separatedfrom the biased electrode with a teflon insulator.The central beam axis is thus better encapsulated,resulting in a more sigmoidal variation of the elec-tric potential (Figure 8c). To emulate mechani-cal imperfections related to the construction, thegrounding electrode was rotated 0.5◦ relative tothe z-axis as defined in Figure 6. This rotation ispresent in all simulations for both configurations.

The transmission of the beam through thebeam line as a function of scanning voltage hasbeen simulated for the two different designs ofthe voltage scanner (Figure 9a). A second setof simulations were performed with a slightly de-tuned 5 degree deflector (Figure 9b). Both de-signs have been constructed and used in experi-ments, such that the transmission simulations canbe compared to actual data (Figure 9c).

The transmission data for the first configura-tion was gathered in the commissioning experi-ment [1] and were the total β-counts from a 26Nabeam measured as a function of scanning volt-age. During an experiment on β-NMR in liquidsamples performed in May 2018 [4], the secondconfiguration was used for the first time and thedata was gathered in the same way.

The simulations (top 2 panels of Figure 9) and

0

25

50

75

1045 V on 5 degree

Config. 1 Config. 2

0

25

50

75

1050 V on 5 degree

1000 500 0 500 1000Scanner voltage [V]

cou

nts [

arb.

]Tr

ansm

issio

n ef

ficie

ncy

[%]

Figure 9: Transmission efficiency through the beamline,simulated for both configurations of the scanning elec-trodes, as a function of voltage applied to the scanner andfor two different voltages on the deflector. When the op-timal voltage is applied to the 5 degree deflector (1045 V,top plot), the beam is centered on the axis of the biasedelectrode, while a slightly offset voltage (1050 V, middleplot) results in slightly lower transmission since the axes ofthe beam and the electrode no longer coincide. The exper-imental transmission (bottom plot) agrees with the generaltrend predicted by the simulations. The staggering in thedata is due to the structure of the proton supercycle.

the online data (bottom panel of Figure 9) showa very good agreement. The oscillation in thecounts is due to the proton supercycle. In boththe measurements and the simulations, the firstconfiguration has a severe beamsteering effect, re-ducing the transmission efficiency as a function ofscanning voltage. The second configuration hasno such effect, owing to the better encapsulationof the beam axis. The simulations with a detuned5 degree deflector show that this can result ina slight slope for the second configuration and ashift in the peak location for the first. These fea-tures are also present in the data, suggesting an

7

almost perfect beamtune during the experiment.

5. Design of magnetic fields

The magnetic field generated in the beamlineis separated in three separate sections (see Fig-ure 2), each with their own requirements:

1. the interaction region (labelled 1 and 2 inFigure 2).

2. the transitional field region (labelled 3).

3. the main magnet region.

The interaction region has to provide a weak, uni-form magnetic field over the entire beam path thatneeds to compensate for stray fields in order tomaintain the laser-induced atomic spin polariza-tion. The field should be small enough however,not to induce a large splitting of the magnetic sub-states of the hyperfine levels. A magnetic field ofapproximately 2 mT fulfills both requirements.

Once the radioactive beam is implanted, themagnetic field has to be strong enough to decouplethe nuclear spin from random interactions withpotential (defect-associated) electric field gradi-ents in the crystal. The installed electromagnetcan generate a field of up to 0.7 T. This value de-pends on both the current supplied to the magnetas well as the distance between the magnet poles,which can be varied. With a maximal pole dis-tance of 8 cm, different setups for holding samplesand placing detectors can be accommodated.

Since the field generated by the electromagnetis perpendicular to the beamline axis (which isalso the atomic spin orientation axis), the transi-tional field region has to be tuned to provide adi-abatic rotation of the oriented atomic spins. Thefield previously designed for the β-NMR setup atCOLLAPS (see Ref. [21]) was used as the modelfield.

For the design of the magnetic field of boththe interaction and the transitional region, sim-ulations were made in COMSOL. As a designchoice, 4 octagonal coils arranged in a Helmholtzconfiguration are used for the interaction region(see Figure 2). Due to geometrical concerns, asolenoid with 11.25 cm radius extends the inter-action region. Several smaller solenoids directly

0.5 0.4 0.3 0.2 0.1 0.0Distance from magnet center [m]

10 1

100

101

102

Mag

netic

fiel

d no

rm [m

T]

Transitional field onTransitional simulation (scaled by 89%)Main magnet field onBoth on

Figure 10: Comparison between the simulation (solid line)and measurements (markers) of the magnetic field. Thesimulation is scaled down by a global factor to account fora difference between the read out current and the currentapplied to the coils. The discrepancy above -0.2 m is dueto the residual magnetization of the magnet.

wound onto a beampipe continue past this pointand form the transitional field. The final param-eters of all solenoids are given in Table 1.

In order to compare the simulated magneticfield profile with reality, magnetic field measure-ments with a 3D Hall probe were made in threecircumstances: the transitional field and the mainmagnet on (red wide diamonds in Figure 10),only the main magnet powered (green dots) andonly the transitional field powered (blue thin di-amonds). Due to the unknown configuration inthe main magnet, only the transitional field couldbe simulated in COMSOL (full line). The goodagreement between simulation and measurementssuggests a good correspondence between the coilparameters in the simulation and the physicalcoils.

6. Multiple-frequency pumping

This can be overcome by using multi-frequencyoptical pumping to simultaneously excite morethan one hyperfine transitions. The same con-cept has already been applied at the TRIUMFfacility for the polarization of Li, where EOM’swere used to induce side-frequencies in the rangeof ±30 MHz to the main laser beam frequency[22].

8

Table 1: Optimized parameters for the coils as determined with COMSOL simulations. A wire thickness of 0.8 mm wasused through all simulations. For the Helmholtz coils, the radius refers to the inscribed circle. The length refers to thedimension of the coil along the beamline axis. The number after the description refers to the labelling in Figure 2.

Helmholtz coils (1) Large solenoid (2) Small solenoids (3)1 2 3 4 5

Current [A] 1.6 1.0 2Windings [#] 1000 900 10 65 154 1100 225

Radius [mm] 400 112.5 20.5Length [mm] 32 315 40 60 40 154 66

Table 2: The hyperfine parameters of 35Ar, deduced fromthe measured hyperfine parameters of 39Ar in the samelaser transition [23] and the known 35Ar nuclear moments[24].

A [MHz] (calc.) B [MHz] (calc.)

1s5 (J = 2) 265.8(28) 83(25)2p9 (J = 3) 125.6(12) 80(19)

We have verified this experimentally, using a35Ar beam produced by a 1.4 GeV beam ontoa CaO target at ISOLDE. The multi-frequencypumping was realized by using two acousto-opticmodulators (AOMs), which can each produce aside band frequency in the required ranges of 300-400 MHz by applying a fixed RF-frequency to thecrystal inside the AOM. This shifts the frequencyof the incoming laser light by the same value. Fordetails on the setup of the AOMs, see Ref. [11].

The observed hyperfine spectra, using eitherone laser frequency for the scanning or by scan-ning the 3 laser frequencies simultaneously, areshown in Figure 11. The induced nuclear spin-polarization is observed by measuring the asym-metry in the radioactive β-decay after implanta-tion in a suitable crystal, as outlined before. Thespectra shown in Figure 11 have been recorded byimplanting the polarized 35Ar beam into a NaClcrystal kept at a temperature of 15(5) K. The sig-nal height in both spectra is significantly differ-ent, as can be seen clearly in e.g. the 7/2 → 9/2transition, for which the observed asymmetry in-creases by almost a factor of 2.

In order to quantify the observed gain in signal

2000 1500 1000 500 0

0.0

0.7

1.4

2000 1500 1000 500 0f [MHz]

0.0

0.7

1.4

J=3

J=2

I=3/2

F=1/2F=3/2F=5/2

F=7/2

F=3/2F=5/2F=7/2F=9/2

Single frequency pumping

Multi-frequency pumping

Expe

rimen

tal a

sym

met

ry [%

]

Figure 11: Top: Hyperfine structure of the 811 nm tran-sition with indicated allowed transitions. Using the hy-perfine transitions 7/2 → 9/2, 5/2 → 7/2 and 3/2 → 3/2(marked in red) saturates the polarization of the ensemble.Bottom plots: experimental spectra for both single- andmulti-frequency pumping. Both spectra were fitted simul-taneously to the rate equations. The laser power in themain beam was set to be a shared fit parameter, while thehyperfine parameters were fixed to the derived value (seeTable 2). The transitions in the top are connected withtheir location in the single-frequency pumping spectrum.

strength (and thus spin-polarization), the datahave been fitted using the rate equations thatwere implemented using the SATLAS Pythonpackage [25]. In the fitting procedure, the laserpower (determining the linewidths), the centroidof the spectrum and the total signal height (pro-

9

portional to the induced nuclear polarization)were left as free parameters, while the A and Bfactors as given in Table 2 were kept as fixed val-ues. Both spectra were fit simultaneously withthe same value for the laser power, thus ensuringthe correlations due to shared parameters werepropagated correctly when determining the ratioof the signal strength.

An excellent agreement is found between theobserved spectra and the calculated β-asymmetryspectra as a function of the laser frequency, bothfor the single and triple laser-atom interactionsystems. This gives confidence in the predictivepower of this simulation package, such that itcan be used in the future to optimize the laserpolarization experiments. From the fitted signalstrengths in both spectra, we find an increase ofa factor 1.85(3)

7. Adiabatic rotation

In the experimental set-up, the atomic spin-polarization symmetry axis is along the (laser)beam line. On the other hand, for theβ-asymmetry measurements, the nuclear spin-polarization symmetry axis should be along thedirection of the strong holding field in which theimplantation crystal is mounted. This field is per-pendicular to the beam line, in order to allowfor β-detectors to be mounted at 0 and 180 de-grees with respect to the field direction. Fromthe rate equation calculations of the atomic pop-ulation, the nuclear spin polarization is extractedunder the assumption that the decoupling fieldis oriented along the symmetry axis. As we ap-ply a gradually increasing magnetic field in orderto rotate (and decouple) the nuclear and electronspins adiabatically into the main field direction,changes in the nuclear spin polarization due tothe adiabtic rotation process are possible. To thisend, simulations of this adiabatic spin rotationhave been performed. The magnetic field pro-file in the 3 directions has been measured andused in these simulations, for which the total fieldstrength along the beam line was shown in Fig-ure 10.

Quantum mechanical calculations, starting

0.00 0.25 0.50 0.75 1.00 1.25

0

50

100 98.3 %35Ar

Ix Iy Iz

0.00 0.25 0.50 0.75 1.00 1.25

0

50

10077.2 %28Na

0.00 0.25 0.50 0.75 1.00 1.25Time [ s]

0

50

100

50.2 %26Na

Dynamic field Static field

Nucle

ar p

olar

izatio

n [%

]Figure 12: Calculated change in the nuclear spin polar-ization along the x, y and z directions (dotted and dashedand full lines) due to the spin rotation from along the beamaxis (x) to along the main field axis (y).

from the interaction Hamiltonian including thehyperfine interaction and the two Zeemann in-teractions with ~I and ~J , were performed withQuTiP [26]. The state vector is initialized inthe atomic groundstate with populations in the~F and mF states as given by the rate equationsafter the optical pumping process. The interac-tion strength of the magnetic field in the threedirections is made time-dependent, representingthe changing magnetic field as the particle beamtravels through the setup at a certain speed. Thespin dynamics are then calculated by solving theSchrödinger equation. Experimental values fornuclear parameters in these equations were takenfrom Refs. [27] and [24]. The calculated flighttime for the beam from the start of the transi-tional magnetic field to the implantation host isextended to also include a period where the beamis stopped in the host. The first period (the dy-namic field region) is 2/3 of the total time solvedfor, while the implanted period (the static fieldregion) accounts for 1/3 of the time. More detailsof the calculation can be found in Ref. [11].

Table 3 presents the calculated nuclear spin po-larization from both the rate equations and thequantum mechanical calculations. The observedasymmetry ratio between 26Na and 28Na matches

10

Table 3: Calculated and observed nuclear spin polarizationof 26,28Na. Experimental data taken from Ref. [1].

QM calc. Rate equation Experiment

Ratio 1.54 1.43 1.51

the quantum mechanical calculation, although theabsolute number is too high.

Simulations have also been made for the adi-abatic rotation of 35Ar (top panel of Figure 12),which shows no loss in nuclear spin polarizationfrom the rotation process.

8. Conclusion

To answer the demand for accessible spin-polarized radioactive nuclei, the VITO beamlinewas built as a dedicated setup. It is an adaptablebeamline that delivers highly polarized nuclei toa central detection point.

Multi-frequency pumping has been establishedas a viable technique to increase the asymmetrysignal that can be expected from the radioactivespecies. Tests on 35Ar show that the increase andspectrum can be reproduced by the rate equationmodel.

The series of magnetic fields provide an efficientadiabatic rotation and decoupling of the nuclearspin. Rotation calculations agree with the ob-served asymmetry ratios. The rotation calcula-tions can be repeated for different species pro-vided the necessary nuclear parameters are avail-able.

9. Acknowledgments

This work was supported by the ERC StartingGrant no. 640465, FWO-Vlaanderen (Belgium)and GOA 15/010 from KU Leuven, the Scienceand Technology Facilities Council (UK).

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1 Introduction2 Optical pumping and ß-asymmetry3 Beamline description4 Ion optics5 Design of magnetic fields6 Multiple-frequency pumping7 Adiabatic rotation8 Conclusion9 Acknowledgments