Spectroscopy of short-lived radioactive molecules: A sensitive laboratory for new physics
R.F. Garcia Ruiz, R. Berger, J. Billowes, C.L. Binnersley, M.L. Bissell, A.A. Breier, A.J. Brinson, K. Chrysalidis, T. Cocolios, B. Cooper, K.T. Flanagan, T.F. Giesen, R.P. de Groote, S.Franchoo, F.P. Gustafsson, T.A. Isaev, A. Koszorus, G. Neyens, H.A. Perrett, C.M. Ricketts, S.Rothe, L. Schweikhard, A.R. Vernon, K.D.A. Wendt, F. Wienholtz, S.G. Wilkins, X.F. Yang
SSpectroscopy of short-lived radioactive molecules:A sensitive laboratory for new physics
R.F. Garcia Ruiz,
1, 2, ∗ R. Berger, † J. Billowes, C.L. Binnersley, M.L. Bissell, A.A. Breier, A.J. Brinson, K. Chrysalidis, T.E. Cocolios, B.S. Cooper, K.T. Flanagan,
4, 7
T.F. Giesen, R.P. de Groote, S.Franchoo, F.P. Gustafsson, T.A. Isaev, ´A. Koszor´us, G. Neyens,
1, 6
H.A. Perrett, C.M. Ricketts, S.Rothe, L. Schweikhard, A.R. Vernon, K.D.A. Wendt, F. Wienholtz,
1, 13
S.G. Wilkins, and X.F. Yang CERN, CH-1211 Geneva 23, Switzerland Massachusetts Institute of Technology, Cambridge, MA 02139, USA Fachbereich Chemie, Philipps-Universit¨at Marburg,Hans-Meerwein-Straße 4, 35032 Marburg, Germany School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom Laboratory for Astrophysics, Institute of Physics, University of Kassel, 34132 Kassel, Germany KU Leuven, Instituut voor Kern- en Stralingsfysica, B-3001 Leuven, Belgium Photon Science Institute, The University of Manchester, Manchester M13 9PY, United Kingdom Department of Physics, University of Jyv¨askyl¨a, Survontie 9, Jyv¨askyl¨a, FI-40014, Finland Institut de Physique Nucleaire d’Orsay, F-91406 Orsay, France NRC ”Kurchatov Institute”-PNPI, Gatchina, Leningrad district 188300, Russia Institut f¨ur Physik, Universit¨at Greifswald, Greifswald, Germany Institut f¨ur Physik, Johannes Gutenberg-Universit¨at Mainz, D-55128 Mainz, Germany Institut f¨ur Physik, Universit¨at Greifswald, D-17489 Greifswald, Germany School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100971, China (Dated: October 30, 2019)
The study of molecular systems provides ex-ceptional opportunities for the exploration of thefundamental laws of nature and for the search forphysics beyond the Standard Model of particlephysics [1–3]. Measurements of molecules com-posed of naturally occurring nuclei have providedthe most stringent upper bounds to the electronelectric dipole moment (eEDM) to date [1], andoffer a route to investigate the violation of fun-damental symmetries with unprecedented sensi-tivity [2, 4]. Radioactive molecules - where oneor more of their atoms possesses a radioactivenucleus - can contain heavy and deformed nu-clei, offering superior sensitivity for EDM mea-surements as well as for other parity- and time-reversal-violation effects [5, 6]. Radium monoflu-oride, RaF, is of particular interest as it is pre-dicted to have an appropriate electronic structurefor direct laser cooling [6], thus paving the way forhigh-precision studies on cold trapped molecules.Furthermore, some Ra isotopes are known to bepear shaped (octupole deformed) [7], thereby re-sulting in a large enhancement of their symmetry-violating nuclear moments [5, 8, 9]. Until now,however, no experimental measurements of RaFhave been performed, and their study is im-peded by major experimental challenges, as nostable isotopes of radium exist. Here, we presenta novel experimental approach to study short- lived radioactive molecules using the highly sensi-tive collinear resonance ionisation method. Withthis technique we have measured, for the firsttime, the energetically low-lying electronic statesfor each of the isotopically pure RaF molecules
RaF,
RaF,
RaF,
RaF, and
RaF atthe ISOLDE radioactive beam facility at CERN.Our results provide strong evidence of the exis-tence of a suitable laser-cooling scheme for thesemolecules and constitute a pivotal step towardshigh-precision studies in these systems. Our find-ings open up new opportunities in the synthesis,manipulation and study of short-lived radioac-tive molecules, which will have a direct impact inmany-body physics, astrophysics, nuclear struc-ture, and fundamental physics research.
Molecular systems are versatile laboratories to explorethe atomic nucleus, as well as the properties and inter-actions of the building blocks of matter (electrons andquarks) [1, 2, 10]. In molecules, electron-nucleon andnucleon-nucleon interactions are dominated by the elec-tromagnetic and strong forces, respectively. The weakforce, although much smaller in magnitude, can add mea-surable contributions to these interactions. Most impor-tantly, the weak force is known to violate the symmetrywith respect to spatial inversion of all particle coordi-nates (known as parity violation), giving rise to variousintriguing phenomena. Some of these parity-violating ef-fects have been measured with high accuracy for only a r X i v : . [ nu c l - t h ] O c t RFQ cooler and buncher T = 10 ms
High-resolutionmass separator
355 nm600-780 nm
Ion sourceActivated Uraniumcarbide target
Electrostatic deflectors Neutralizationcell e - RaFDetectorDumped remaining ions 1.2 m (TOF=6.7 μ s) RaF + Na RaF( Σ ) CF RaF+
RaF+
RaF( Σ ) + Na
0 mirror o RaF + Σ RaF+
RaF @ 40 keV+
TiSaDye2Dye1
CERN Proton SynchrotronBooster (PSB) + n m n m n m Ionisationpotentia l (780 nm)12820 cm (step 2)(step 1) -1-1 FIG. 1. Radioactive radium isotopes were created by impinging 1.4-GeV protons from the CERN Proton Synchrotron Booster(PSB) on a uranium carbide (UC x ) target. Radium monofluoride cations (RaF + ) were produced by passing tetrafluoromethane(CF ) gas through the activated UC x target at 1300 o C. Molecular ions were extracted from the source, mass-selected, andinjected into a helium-filled radio-frequency trap, where they were accumulated for 10 ms. Bunches of molecular ions wereextracted and neutralised in-flight by charge exchange with neutral Na atoms. Neutral RaF molecules were overlapped withdifferent laser beams in a collinear geometry. Resonantly reionised molecules were deflected onto a particle detector. Theresonance ionisation scheme is shown on the top right. Molecular orbitals are shown schematically. Nuclear positions withinthe molecules are indicated by a grey sphere (Ra) and green sphere (F), whereas the sigma bond between the atoms is indicatedby a grey cylinder (see text for more details). a few atomic systems [10–12], contributing to the moststringent low-energy tests of the Standard Model. In cer-tain molecules, effects resulting from both parity viola-tion (P-odd) and time-reversal violation (T-odd) are sig-nificantly enhanced with respect to atomic systems [5, 8–10], offering the means to explore unknown aspects of theweak and strong forces. As the strengths of these inter-actions scale with the atomic number, the nuclear spinand nuclear deformation, molecular compounds of heavyradioactive nuclei are predicted to exhibit unprecedentedsensitivity, with an enhancement of more than two or-ders of magnitude for both P-odd and P,T-odd effects[5, 6, 8, 9, 13].However, the experimental knowledge of radioactivemolecules is scarce [14], and quantum chemistry calcu-lations often constitute the only source of information.Molecules possess complex quantum level structures,which renders spectroscopy of their structure consider-ably more challenging when compared to atoms. More-over, major additional experimental challenges must beovercome to study molecules containing heavy and de-formed short-lived nuclei. These radioactive nuclei donot occur naturally and must therefore be produced ar-tificially at specialised facilities such as the Isotope Sep- arator On-line Device (ISOLDE) at CERN. As compar-atively little is known about the properties and chemicalbonds of radioactive molecules, the techniques to synthe-sise and manipulate them are not fully understood [14].Furthermore, molecules containing short-lived isotopescan only be produced in quantities smaller than 10 − grams (typically with rates of less than 10 particles/s).Thus, spectroscopic studies require particularly sensitiveexperimental techniques adapted to the properties of ra-dioactive ion beams and conditions present at radioac-tive beam facilities. Here, we present a new approach forperforming laser spectroscopy of short-lived radioactivemolecules, providing the first spectroscopic informationof radium monofluoride (RaF). To our knowledge, this isthe first laser spectroscopy study ever performed on witha molecule containing short-lived isotopes.Since the theoretical suggestion for direct cooling ofmonofluoride molecules with lasers [15] has been experi-mentally demonstrated [16], a great deal of experimentaland theoretical attention has been focussed on molecularsystems with similar structures [17–21]. The laser coolingof polyatomic molecules has been proposed and criteria toidentify suitable candidates have been outlined [22]. Thishas triggered a wealth of studies on the opportunities re-sulting from laser cooling techniques in molecular physics[23]. In contrast to other heavy-atom molecules, RaF ispredicted to have highly closed excitation and re-emissionoptical cycles, which would make it ideal for laser cool-ing and trapping [6]. Moreover, due to the recently dis-covered pear-shaped nuclear deformation of certain Raisotopes [7], the interactions of the electrons with the P-odd nuclear anapole moment as well as with the P,T-oddnuclear Schiff and magnetic quadrupole moments are pre-dicted to be enhanced by more than two orders of magni-tude [4, 5, 13, 24]. Hence, these molecules could providea unique laboratory to measure these symmetry-violatingnuclear moments.Figure 1 shows a diagram of the experimental setupused to produce and study the RaF molecules. Asa first step, radium isotopes were produced by evap-oration of an irradiated target (see section Methods -Production of RaF molecules). RaF + molecular ionswere then formed upon injection of CF gas into thetarget material. Molecular ions were extracted fromthe ion source by applying an electrostatic field, andmolecules containing one specific radium isotope wereselected with a high-resolution magnetic mass separator(∆ m/m ∼ / + with a 4- µ s temporal width werereleased and accelerated to 39998(1) eV, before enter-ing into the Collinear Resonance Ionisation Spectroscopy(CRIS) setup [25, 26].At the CRIS beam line, the ions were first neutralisedin-flight by passing through a collision cell filled withsodium vapour, inducing charge-exchange according tothe reaction RaF + + Na → RaF + Na + . As the ion-isation energy of RaF is estimated to be close to thatof Na (5.14 eV) [27], the neutralisation reaction domi-nantly populates the RaF X Σ + electronic ground state.Molecular orbitals are shown schematically in Figure 1.The lowest unoccupied molecular orbital in RaF + , whichis essentially of non-bonding character, becomes occupiedby an unpaired electron (symbolised in Figure 1 by a redsphere together with an arrow representing the electronspin) upon neutralisation. This is shown schematicallyas an isodensity surface, with lobes in slightly transpar-ent blue and transparent red indicating different relativephases of the single-electron wavefunction.After the charge-exchange reaction, non-neutralisedRaF + ions were deflected out of the beam, and the re-maining bunch of neutral RaF molecules was overlappedin time and space by several (pulsed) laser beams ina collinear arrangement, along the ultra-high-vacuum(10 − mbar) interaction region of 1.2-m length. Laserpulses (step 1) of tunable wavelength were used to reso-nantly excite the transition of interest, and a high-power 355-nm laser pulse (step 2) was used to subsequentlyionise the excited RaF molecules into RaF + (see insetof Figure 1). The resonantly ionised molecules were thenseparated from the non-ionised molecules by deflectingthe ions onto a particle detector. When the excitationlaser is on resonance with a transition in the molecule(step 1 in Figure 1), the second laser pulse ionises themolecule, producing a signal at the detector. Molecularexcitation spectra were obtained by monitoring the ioncounts as a function of the wavenumber of the first laser.As only theoretical predictions were available for theexcitation energies of RaF, finding the transition exper-imentally required scanning a large wavelength range( > − ). The prediction for the A Π / − X Σ + (0,0) transition, for example, was 13300 cm − with an ac-curacy estimated to be within 1200 cm − [6, 24]. Giventhe bandwidths of laser available ( < − ), thescan of such a large wavelength region on samples pro-duced at rates below 10 molecules/s represents a signif-icant experimental challenge. In order to optimize thesearch of molecular transitions, three broadband laserswere scanned simultaneously (see section Methods - Lasersetup), and a zero degree mirror at the end of the beamline was used to reflect the laser light anti-collinearlywith respect to the travelling direction of the RaF bunch.Thus, each of the three scanning lasers covered two dif-ferent wavenumber regions separated by 15.7 cm − in themolecular rest frame due to the Doppler shift present forthe fast RaF molecules (see section Methods). The pos-sibility of using multiple high-power broadband lasers toscan large wavenumber ranges both collinearly and anti-collinearly is a marked advantage of the CRIS technique[26] compared with optical detection techniques, whichwould suffer from a large background due to the pres-ence of intense photon densities delivered close to thephotodetectors.The predicted region for the A Π / ← X Σ + transi-tion was scanned (with the three lasers for the first stepsimultaneously and both collinearly and anti-collinearly)at a speed of 0.06 cm − /s, covering a 1000 cm − rangein only 5 hours. After a few hours of scanning on a beamof RaF, a clear sequence of vibronic absorption sig-nals was recorded. The measured spectrum assigned tothe ( v (cid:48) , v (cid:48)(cid:48) ) vibrational transitions (0,0), (1,1), (2,2), (3,3)and (4,4) of the A Π / − X Σ + band system is shownin Figure 2a. Weaker band structures found around 440cm − s higher and lower with respect to the (0,0) bandwere assigned to the ∆ v = ± v (cid:48) , v (cid:48)(cid:48) ) = (1,0),(1,2), (2,1), (3,2), (4,3), (5,4) and (0,1), (1,2), respec-tively (Figures 2b and 2c). The quantum number assign-ment for ∆ v = − A Π / − X Σ + band system, wefound spectroscopic signatures of electronic transitions tohigher-lying states. Some examples of recorded spectraare shown in Figures 2d-f, along with the energy-levelscheme. We assign the observed transitions as follows:The band system around 15325 cm − (Figure 2d) is at-tributed to the A Π / − X Σ + transition due to thecomplex rovibrational structure expected to arise fromintense satellites that are possible in these transitions.As the bands are comparatively strong, they are as-signed to the ∆ v = 0 band system. Whereas the in-dividual assignments to vibrational transitions must beconsidered tentative as per the congested structure ofthe Franck–Condon profile, the ∆ v = 0 assignment issupported by the fact that no additional structure waslocated within a ±
400 cm-1 region. The band systemlocated around 15142.7 cm − (Figure 2e) is tentativelyassigned to the B ∆ / − X Σ + transition by virtue ofthe good agreement with the computed excitation ener-gies to the Ω = 3 / / Π character [6, 24].This mixing provides intensity to the one-photon transi-tion from a Σ state into the ∆ manifold. The computedBorn-Oppenheimer potentials for this Ω = 3 / B ∆ / − X Σ + transition in BaH andBaD were reported to have a perturbed character dueto mixing between electronic levels [28]. Thus, in thepresent case, a vibrational profile that is richer than ex-pected from adiabatic potentials can not be ruled out apriori. The band system with origin at 16175 . − (Figure 2f) is assigned to the C Σ + − X Σ + transitionbased on the observed Franck–Condon profile, which isin good agreement with the computed harmonic vibra-tional energy spacings as well as the expected intensitydistribution and is in a wavenumber region that is onlyslightly lower than predicted [6, 24]. All measured andassigned vibronic bands of the four electronic transitionsare listed in Table I.The measured A Π / − X Σ + (0,0) band center,˜ T e = 13287 . − is in excellent agreementwith the ab initio calculated value of 13300(1200) cm − [24]. In accordance with theoretical predictions [6],we found vibronic transitions with ∆ v =0 to be muchstronger than those of ∆ v = ±
1. For most of the mea-surements the power density used for the resonant stepwas 100(5) µ J cm − per pulse as measured at the entrywindow of the CRIS beam line. Reducing the power by50 % did not significantly reduced the resonant ionisationrate, indicating that these transitions were measured wellabove saturation. The much weaker vibrational transi-tions with ∆ v = ± µ J cm − power density per pulse (bandwidthof 0.1 cm − ). As the ∆ v = ± I (0 , /I (0 ,
0) was derived, indicating highly diagonal FCfactors, an essential property for laser cooling [6].By measuring the resonant ionisation rate for differenttime delays between the excitation and ionisation laserpulses, an upper limit for the lifetime of the excited state Π / ( v (cid:48) =0), T / ≤
50 ns, was obtained. The measure-ments were performed with the wavenumber of the reso-nant laser fixed at the resonance value of the transition( v (cid:48) , v (cid:48)(cid:48) ) = (0,0). The resonant ionisation rate dropped bymore than 70 % for time delays above 50 ns. This shortlifetime corresponds to a large spontaneous decay rate( > × s − ), which would allow for the application ofstrong optical forces for laser cooling. An additional con-cern for the suitability of laser cooling is related to theexistence of metastable states lying energetically belowthe Π / level, which could prevent the application of aclosed optical cooling loop, a major problem encounteredfor BaF [6]. In contrast to BaF, all other predicted elec-tronic states ( Π / , ∆ / and Σ) in RaF were foundto be energetically above the Π / state. This demon-strates a marked advantage of RaF as its electronic struc-ture will allow for efficient optical-cooling cycles.From combination differences of energetically low-lyingvibronic transitions in the band system A Π / − X Σ + we have derived experimental values for the harmonicfrequency, ˜ ω e , and the dissociation energies, ˜ D e , us-ing a Morse potential approximation. Results aregiven in Table II, and further details of the analysis canbe found in the section Methods - Spectroscopic analysis.Furthermore, the A Π / ← X Σ + vibronic spectraof the short-lived isotopologues RaF,
RaF,
RaF,
RaF and
RaF, were measured (Figure 3). All vibra-tional transitions were clearly observed, including thoseof the molecule with the shortest-lived Ra isotope stud-ied,
RaF ( T / = 3 . > molecules/s.Our results have established the energetically low-lyingelectronic structure of these molecules, and constitute apivotal step towards precision measurements in this sys- ν = 1 ν = 2 ν = 3 ν = 4 ν = 1 ν = 2 ν = 3 ν = 4 ν = 0 ν = 0 n m -1 n m n m n m n m n m b)a)
0 0 1 1 2 2 3 3 4 4 1 0 2 1 3 2 4 3 5 4 ν ’’’’’’ ’’’’’’’’’ c m - c m - c m - c m - c m -
439 cm -1 T <50 ns RaF + RaF c) (0 1)(1 2) RaF d) (0 0)(1 1)(2 2) f)
1 1 2 2 3 3 0 0 e)
1 1 2 2 3 3 0 0 ( )( )
FIG. 2. Measured vibronic spectra for
RaF. Wavenumbers in the spectra are in the rest frame of the molecule. The countson the particle detector were measured as a function of the laser wavenumber of the resonant step. A fixed wavelength (355 nm)was used for the ionisation step. Panel a) shows the observed peaks corresponding to the vibronic spectra of the ∆ v =0 bandsystem of v (cid:48)(cid:48) =0, 1, ..4, scanned by the grating Ti:Sapphire laser. The pulsed dye laser was used to scan electronic transitionsin different wavelength ranges: b) the ∆ v =+1 band system of the A Π / ← X Σ + transition with v (cid:48)(cid:48) =0, 1, ..4, and c) the( v (cid:48) , v (cid:48)(cid:48) ) = (0,1) and (1,2) band. The corresponding transitions to other electronic states are shown in panels: d) A Π / ← X Σ + , e) B ∆ / ← X Σ + (tentatively assigned), and f) C Σ + ← X Σ + . The shape of the spectra is due to populationdistribution of different rotational states. The solid lines show the fit with skewed Voigt profiles. Three essential propertiesfor laser cooling of RaF molecules were identified: i) the short lifetime of the excited states Π / ( T / <
50 ns) will allow forthe application of strong optical forces, ii) dominant diagonal transitions, (∆ v =0)/(∆ v = ± > .
97, indicate a large diagonalFranck-Condon factor, and iii) the expected low-lying electronic states B ∆ / , A Π / , and C Σ + were found to be above the A Π / states, which will allow efficient optical cooling cycles to be applied. tem. Three essential properties for the laser cooling ofRaF molecules were identified: i) the short lifetime ofthe excited states A Π / ( T / <
50 ns) will allow forthe application of strong optical forces, ii) dominant di-agonal transitions, indicating a large diagonal Franck-Condon factor, and iii) the expected low-lying electronicstates B ∆ / , A Π / , and C Σ + states were foundto be above the A Π / states, which will allow efficientoptical cooling cycles to be applied.The ability to produce, mass-select, and spectroscop-ically study radioactive molecules is expected to pro-foundly impact several fields of research. For example,astronomical observations have recently suggested thepresence of the long-lived radioactive molecule AlF,based on theoretical predictions of its molecular structure[29]. Our experimental method will enable spectroscopystudies of this radioactive molecule. These studies can beextended to other radioactive compounds of astrophysi-cal interest (e.g. CO).The new experimental technique can also be employedfor the laser spectroscopy of a wide variety of neutralmolecules and molecular ions, including those with veryshort-lived isotopes ( ≤ I , of their constituent isotopes. In the case ofRaF molecules, for example, Ra isotopes with a varietyof nuclear spins are available, such as the I = 0 nuclei Ra,
Ra,
Ra, the I = 1 / Ra,
Ra,the I = 3 / Ra,
Ra, and the I = 5 / Ra. Future high-precision measurements will allow forthe study of nuclear structure effects, as well as still un-explored subatomic properties such as the P-odd T-evennuclear anapole moments, the P,T-odd nuclear Schiff mo-ment and magnetic quadrupole moments.Currently, most of our knowledge of nuclear ground-stateelectromagnetic properties of unstable nuclei has beenobtained from the study of radioactive atoms [30–32],but very little is known about the nuclear weak struc-
TABLE I. Measured vibronic transitions of
RaF from the X Σ + electronic ground state to excited A Π and B ∆states. The values indicate the band head positions. Com-bined statistical and systematic uncertainties are included inparentheses.Transition v (cid:48) ← v (cid:48)(cid:48) ∆˜ ν/ cm − A Π / ← X Σ + − . − . − . − . − . − . − . − . − . − . −
1) 12846 . −
2) 12843 . B ∆ / ← X Σ + ) 0 − . − . − . − . A Π / ← X Σ + (0 −
0) 15344 . −
1) 15325 . −
2) 15309 . C Σ + ← X Σ + − . − . − . − . RaF Morse potential parameters for X Σ + electronic ground and A Π / excited states.Parameter X Σ + /cm − A Π / /cm − ˜ ω e D e /10 ture. Further precision studies of radioactive moleculeswill offer a new window in the exploration of the atomicnucleus and its fundamental constituents. Our resultsopen up new opportunities to study fundamental physics,nuclear structure, and quantum chemistry of the heaviestelements. Thus, we expect that these findings will moti-vate new avenues of research at the increasingly capableradioactive-ion-beam facilities around the world. Acknowledgements. — This work was supported bythe ERC Consolidator Grant No.648381 (FNPMLS);Deutsche Forschungsgemeinschaft (DFG, German Re-search Foundation) – Projektnummer 328961117 –SFB 1319 ELCH; STFC grants ST/L005794/1 andST/L005786/1 and Ernest Rutherford Grant No.
T = 3.6 d R a ( m a ss ) RaF
RaF
RaF
RaF
RaF
T = 11.4 d
T = 14.9 d
T = 5.7 y
T = 1600 y c o un t s [ a . u ] W a v e nu m b e r - c m - FIG. 3. Measurements of the vibronic absorption spec-tra A Π / ← X Σ + of the isotopologues RaF,
RaF,
RaF,
RaF, and
RaF.
ST/L002868/1; projects from FWO-Vlaanderen GOA15/010 from KU Leuven and BriX IAP Research Pro-gram No. P7/12; the European Unions Grant Agree-ment 654002 (ENSAR2); the Russian Science Foun-dation under grant N 18-12-00227; the BMBF grants05P15HGCIA and 05P18HGCIA. We thank J. P. Ramosand T. Stora for their support in the production of RaFmolecules. We would also like to thank the ISOLDEtechnical group for their support and assistance. Wethank D. Budker for comments and suggestions as wellas Alexander Petrov for discussions on ∆ states. R.B.acknowledges I. Tietje for early discussions on variousexperiments at CERN and is indebted to A. Welker forsharing knowledge on isotope production and separa-tion as well as for initial discussions of the RaF studies.R.B. acknowledges discussions with K. Gaul on molecu-lar properties and with D. Andrae on finite nuclear sizeeffects. R.B. and T.A.I acknowledge S. Hoekstra andL. Willmann for early discussions on production of RaF.T.A.I. is grateful to A. Zaitsevskii for discussions on thecoupled-cluster method.
Author contributions — R.F.G.R. led the experimen-tal part and R.B. led the theoretical support. R.F.G.R.,R.B., C.B., M.L.B., K.C., B.S.C., K.T.F., R.P.G, S.F.,F.P.G., A.K., H.A.P., C.M.R., S.R., A.R.V., F.W. andS.G.W performed the experiment. R.F.G.R., R.B.,A.A.B., A.J.B. and T.F.G. performed the data analysis.R.F.G.R. prepared the figures. R.B. and T.A.I performedtheoretical calculations that motivated the experimentalproposal and analysis of the results. R.F.G.R, R.B. pre-pared the initial draft of the manuscript with input fromA.A.B., A.J.B., K.T.F., T.F.G., T.A.I., G.N. and S.G.W.All authors discussed the results and contributed to themanuscript at different stages.
Data availability.
All the relevant data supportingthe findings of these studies are available from the corre-sponding author upon request. ∗ [email protected] † [email protected][1] V. Andreev et al. , “Improved limit on the electric dipolemoment of the electron,” Nature , 355 (2018).[2] E. Altunta¸s et al. , “Demonstration of a sensitive methodto measure nuclear-spin-dependent parity violation,”Phys. Rev. Lett. , 142501 (2018).[3] R. Berger and J. Stohner, “Parity violation,” WIREsComput. Mol. Sci. , 0 (2019).[4] V. V. Flambaum, D. DeMille, and M. G. Kozlov, “Time-reversal symmetry violation in molecules induced by nu-clear magnetic quadrupole moments,” Phys. Rev. Lett. , 103003 (2014).[5] V.V. Flambaum, “Enhanced nuclear schiff moment andtime reversal violation in Th-containing molecules,”Phys. Rev. C , 035501 (2019).[6] T. A. Isaev, S. Hoekstra, and R. Berger, “Laser-cooledRaF as a promising candidate to measure molecular par-ity violation,” Phys. Rev. A , 052521 (2010).[7] L. Gaffney et al. , “Studies of pear-shaped nuclei usingaccelerated radioactive beams,” Nature , 199 (2013).[8] N. Auerbach, V. V. Flambaum, and V. Spevak, “Collec-tive t- and p-odd electromagnetic moments in nuclei withoctupole deformations,” Phys. Rev. Lett. , 4316–4319(1996).[9] A. D. Kudashov et al. , “Ab initio study of radiummonofluoride (RaF) as a candidate to search for parity-and time-and-parityviolation effects,” Phys. Rev. A ,052513 (2014).[10] M. S. Safronova et al. , “Search for new physics withatoms and molecules,” Rev. Mod. Phys. , 025008(2018).[11] C.S Wood et al. , “Measurement of parity nonconserva-tion and an anapole moment in cesium,” Science ,1759 (1997).[12] D. Antypas et al. , “Isotopic variation of parity violationin atomic ytterbium,” Nature Phys. , 120 (2019).[13] K. Gaul, S. Marquardt, T.A. Isaev, and R. Berger, “Sys-tematic study of relativistic and chemical enhancementsof P,T-odd effects in polar diatomic radicals,” Phys. Rev.A , 032509 (2019).[14] A. Formanuik et al. , “Actinide covalency measured bypulsed electron paramagnetic resonance spectroscopy,”Nature chem. , 578 (2017).[15] M. D. DiRosa, “Laser-cooling molecules,” Eur. Phys. J.D , 395–402 (2004).[16] E.S. Shuman et al. , “Laser cooling of a diatomic molecule,” Nature , 820 (2010).[17] J.J. Hudson et al. , “Improved measurement of the shapeof the electron,” Nature , 493 (2011).[18] J.F. Barry et al. , “Magneto-optical trapping of a diatomicmolecule,” Nature , 286 (2014).[19] S. Truppe et al. , “Molecules cooled below the dopplerlimit,” Nature Phys. , 1173 (2017).[20] J. Lim et al. , “Laser cooled YbF molecules for measuringthe electron’s electric dipole moment,” Phys. Rev. Lett. , 123201 (2018).[21] L. Anderegg et al. , “Molecules cooled below the dopplerlimit,” Nature Phys. , 890 (2018).[22] T. A. Isaev and R. Berger, “Polyatomic candidates forcooling of molecules with lasers from simple theoreticalconcepts,” Phys. Rev. Lett. , 063006 (2016).[23] Timur A. Isaev and Robert Berger, “Towards ultracoldchiral molecules,” Chima , 375–378 (2018).[24] T. A. Isaev and R Berger, “Lasercooled radium monoflu-oride: A molecular all-in-one probe for new physics,”arXiv:1302.5682 (2013).[25] K. T. Flanagan et al. , “Collinear resonance ionizationspectroscopy of neutron-deficient francium isotopes,”Phys. Rev. Lett. , 212501 (2013).[26] R. F. Garcia Ruiz et al. , “High-precision multiphoton ion-ization of accelerated laser-ablated species,” Phys. Rev.X , 041005 (2018).[27] T. A. Isaev et al. , “Ion neutralisation mass-spectrometryroute to radium monofluoride,” arXiv:1310.1511 (2013).[28] A. Bernard et al. , “The 5 d states of barium hydride; BaHand BaD,” Mol. Phys. , 1–18 (1989).[29] T. Kaminski et al. , “Astronomical detection of radioac-tive molecule AlF in the remnant of an ancient explo-sion,” Nature Astro. , 778 (2018).[30] R. F. Garcia Ruiz et al. , “Unexpectedly large charge radiiof neutron-rich calcium isotopes,” Nature Phys. , 594(2016).[31] P. Campbell, I.D. Moore, and M.R. Pearson, “Laserspectroscopy for nuclear structure physics,” Prog. Part.and Nucl. Phys. , 127 – 180 (2016).[32] B. Marsh et al. , “Characterization of the shape-staggering effect in mercury nuclei,” Nature Phys. ,1163 (2018).[33] T.T. Bohlen et al. , “The FLUKA code: Developmentsand challenges for high energy and medical applications,”Nucl. Data Sheets , 211 – 214 (2014).[34] S. Kreim et al. , “Recent exploits of the isoltrap massspectrometer,” Nucl. Inst. Meth. B , 492500 (2013).[35] R.N. Wolf et al. , “Isoltrap’s multi-reflection time-of-flightmass separator/spectrometer,” Int. J. Mass Spec. , 123 – 133 (2013). METHODS
Production of RaF molecules:
Radium isotopeswere produced 33 days before the laser-spectroscopy mea-surements by impinging 1.4-GeV protons on the cold ura-nium carbide target material. The target was exposed topulses of 10 protons/pulse over a period of 2 days. Af-ter irradiation with a total of 8 × protons, the target Counts / 800ps
T i m e o f f l i g h t / u s
B i F R a F + 2 2 9 T h O + FIG. 4. Time-of-flight spectrum of the
RaF + ( A =245)beam as delivered from ISOLDE after 1000 revolutions in theMR-ToF MS. A mass resolving power 1 . × was achievedwhich allowed the isobaric beam composition to be analysed.Only Ra F + ions were detected. The position of the mostlikely accompanying ions are highlighted by dotted verticallines. was kept in a sealed chamber filled with Ar gas. Afterday 33, the target was connected to the High-ResolutionSeparactor (HRS) front end at ISOLDE. FLUKA [33]simulations predicted 2 × atoms of Ra in the tar-get material (7.5 × − grams), following proton irradi-ation. The target was pumped down to pressures below10 − mbar, and the target holder and ion source weregradually heated up to about 1300 o C. A leak valve at-tached to the target was used to inject CF into the tar-get environment. RaF molecules were formed by reactivecollisions of CF molecules with Ra atoms [27] present in-side the irradiated target material.The RaF + ( A =245) beam extracted from theISOLDE target unit was sent to the ISOLTRAP setup[34], where the molecular ions were captured, cooled andbunched by a RFQ trap and subsequently analysed usinga multi-reflection time-of-flight mass spectrometer (MR-ToF MS) [35]. A measured mass spectrum is shown inFigure 4. After 1000 revolutions in the device, a massresolving power ( R = m/ ∆ m ) of 1 . × was achieved,which allowed the isobaric beam composition to be anal-ysed. The only mass peak detected was identified as thesignal of Ra F + , confirming the purity of the beamfrom ISOLDE. Laser setup.
The resonant ionisation schemes usedfor the study of RaF molecules are shown in Fig. 1.Three different laser systems were prepared to cover thescanning range from 12800 cm − to 13800 cm − : i) a dye laser system (Dye1: Spectron Spectrolase 4000) pro-vided pulses of 100(5) µ J with a linewidth of 10 GHz(0.3 cm − ). ii) a dye laser (Dye2: Sirah Cobra) witha narrower linewidth of 2.5 GHz (0.09 cm − ) producedpulses of similar energy. The lasers were loaded witheither Styryl 8 or DCM dyes to provide wavenumberranges 12800-14000 cm − and 15150-16600 cm − , respec-tively. Both dye lasers were pumped by 532-nm pulses at100 Hz, obtained from two different heads of a twin-headNd:YAG laser (Litron LPY 601 50-100 PIV). iii) a grat-ing Ti:Sapphire laser system with a linewidth of 2 GHz(0.07 cm − ) produced pulses of 20(1) µ J, pumped by 532-nm pulses at 1 kHz from a Nd:YAG laser (LDP-100MQLEE laser). The non-resonant ionisation step was ob-tained by 355-nm pulses of 30 mJ at 100 Hz, producedby the third-harmonic output of a high-power Nd:YAGlaser (Litron TRLi).The release of the ion bunch was synchronised with thelaser pulses by triggering the flash-lamps and Q-switch ofthe pulsed lasers with a Quantum Composers 9528 digi-tal delay pulse generator.Dye laser wavelengths were measured with a WS-6 wave-length meter. Ti:Sapphire laser wavelengths were mea-sured by a WSU-2 HighFinesse wavelength meter cali-brated by measuring a reference wavelength provided bya stabilised diode laser (TopticaDLC DL PRO 780).
Collinear and anti-collinear excitation.
For amolecule travelling at velocity v , the laser wavenumberin the laboratory frame, ˜ ν , is related to the wavenum-ber in the molecule rest frame, ˜ ν , by the expression˜ ν = 1 + β cos θ (cid:112) − β ˜ ν , with β = v/c and θ being the anglebetween the direction of the laser beam and the veloc-ity of the molecule. For RaF molecules at 39998(1) eV( v ∼ .
18 m/ µ s), a difference of 15.7 cm − is obtainedbetween the laser pulse sent out collinearly (cos θ = 1)and anti-collinearly (cos θ = −
1) with respect to the di-rection of the molecule’s velocity.
Spectroscopic analysis.
The vibrational transitionsin Fig. 2 show asymmetric line profiles with a maximumlocated towards higher wavenumbers. Since the bandcenters cannot be determined directly from the measuredline profiles, we used the wavenumber positions of themaxima in our data analysis. Table I lists the maximumpeak positions and estimated uncertainties are given inparentheses. The wavenumber difference, ∆˜ ν , of vibra-tional levels in the electronic Σ + ground state and in the Π / excited state were derived from combination differ-ences of the recorded RaF spectra (see Table III).In our analysis we used vibrational energy terms E v / ( hc ) of a Morse potential according to: E v / ( hc ) = ˜ ω e (cid:18) v + 12 (cid:19) − ˜ ω e D e (cid:18) v + 12 (cid:19) . (1) TABLE III.
RaF vibrational transitions in the electronic X Σ + ground state and A Π / excited state derived fromcombination differences. Uncertainties are given in parenthe-ses. v (cid:48) ← v (cid:48)(cid:48) Σ + ∆ ˜ ν/ cm − Π / ∆˜ ν/ cm − · · · Energy level differences( E v +1 − E v ) / ( hc ) = ˜ ω e − ˜ ω e D e ( v + 1) , (2)were used to derive the Morse potential parameters ˜ ω e and ˜ D e from a least-squares fit analysis. The derivedenergy level differences are given in Table III, whereas Table II contains the molecular parameters from the fit.The harmonic vibration frequencies ˜ ω e of the Σ + and Π / states are almost identical and correspond well tothe theoretical predictions with a deviation of less than5 %, see Table IV. The same holds for the estimated dis-sociation energy ˜ D e , which is in better agreement withthe values of Ref. [6] as therein also the low-energy partof the potentials were used to estimate the dissociationenergy.In the case of the two low-lying Π fine-structure lev-els, the observed origins T , agree well with the calcu-lated values based on the RCC-ANO basis set. From theenergy difference of the fine-structure components the ef-fective spin-orbital coupling parameter A is derived. Forthe Π states the experimental value of 2068(5) cm − is ingood agreement with the calculated value. The band ori-gins are in reasonable agreement with results from RCC-ANO basis set calculation, if one attributes the Ω = 3 / / and ∆ / character in this order of energies. Areverse assignment also gives better agreement with ex-periment.0 TABLE IV. Molecular parameters of
RaF from vibrational analysis of the electronic ground- ( X Σ + ) and excited states( A Π, B ∆, C Σ + ). Experimental results are compared with theoretical calculations.˜ ω e /cm − ˜ T e /10 cm − A /10 cm − ˜ D e /10 cm − Ref X Σ + a
431 4.26 [24], theo. b A Π / / Π / a b B ∆ / / ∆ / a b C Σ 430.9(2) 1.61806(1) 2.78(9) this work a Fock-space coupled cluster singles and doubles (FS-CCSD), Dyall basis set and smaller active space bb