Decay-Assisted Laser Spectroscopy of Neutron-Deficient Francium

K.M. Lynch, J. Billowes, M. L. Bissell, I. Budinc̆ević, T. E. Cocolios, R. P. De Groote, S. De Schepper, V. N. Fedosseev, K. T. Flanagan, S. Franchoo, R. F. Garcia Ruiz, H. Heylen, B. A. Marsh, G. Neyens, T. J. Procter, R. E. Rossel, S. Rothe, I. Strashnov, H. H. Stroke, and K. D. A. Wendt School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom ISOLDE, PH Department, CERN, CH-1211 Geneva-23, Switzerland Instituut voor Kernen Stralingsfysica, KU Leuven, B-3001 Leuven, Belgium EN Department, CERN, CH-1211 Geneva 23, Switzerland Institut de Physique Nucléaire d’Orsay, F-91406 Orsay, France Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55128 Mainz, Germany Department of Physics, New York University, New York, New York 10003, USA (Received 6 January 2014; published 28 March 2014)


I. INTRODUCTION
Recent advances in high-resolution laser spectroscopy have resulted in the ability to measure short-lived isotopes with yields of less than 100 atoms/s [1,2].The Collinear Resonance Ionization Spectroscopy (CRIS) experiment [3], located at the ISOLDE facility, CERN, aims to push the limits of laser spectroscopy further, performing hyperfine-structure measurements on isotopes at the edges of the nuclear landscape.It provides a combination of highdetection efficiency, high resolution, and ultralow background, allowing measurements to be performed on isotopes with yields below, in principle, 1 atom/s.
The first optical measurements of francium were performed in 1978.Liberman et al. identified the 7s 2 S 1=2 → 7p 2 P 3=2 atomic transition, performing hyperfine-structure and isotope-shift measurements first with low-resolution [4] and later with high-resolution laser spectroscopy [5].The wavelength of this transition λðD2Þ ¼ 717.97ð1Þ nm was in excellent agreement with the prediction of Yagoda [6], made in 1932 before francium was discovered.Further measurements of francium followed in the next decade.High-resolution optical measurements were performed on both the 7s 2 S 1=2 → 7p 2 P 3=2 atomic transition [7][8][9] and the 7s 2 S 1=2 → 8p 2 P 3=2 transition [10], along with transitions into high-lying Rydberg states [11].The CRIS technique, a combination of collinear laser spectroscopy and resonance ionization, was originally proposed by Kudriavtsev and Letokhov in 1982 [12], but the on-line experimental realization of the technique was not performed until 1991 on ytterbium atoms [13].
The ability to study the neutron-deficient francium (Z ¼ 87) isotopes at the CRIS beam line offers the unique opportunity to answer questions arising from the study of the nuclear structure in this region of the nuclear chart.As the isotopes above the Z ¼ 82 shell closure become more neutron deficient, a decrease in the excitation energy of the ðπ1i In 185 Bi (Z ¼ 83) and 195 At (Z ¼ 85), the ðπ3s −1 1=2 Þ 1=2 þ deformed-intruder state has been observed to be the ground state [14,15].
Recent radioactive-decay measurements suggest the existence of a ðπ3s −1 1=2 Þ 1=2 þ proton-intruder state for 203 Fr and, with a lower excitation energy, for 201 Fr, suggesting that this state may become the ground state in 199 Fr [16,17].The intruder configurations polarize the nucleus, creating significant deformation.From the study of the nuclear structure of the neutron-deficient francium isotopes toward 199 Fr (by measuring the magnetic dipole moments and change in mean-square charge radii of the ground and isomeric states), the quantum configuration of the states and the shape of the nuclei can be investigated.
Radioactive-decay measurements on the neutrondeficient francium isotopes have aimed to determine the level structure of the low-lying nuclear states, but their exact nature is still unknown [16][17][18][19].High-resolution collinear laser spectroscopy has allowed determination of the ground-state properties of 204;205;206 Fr [20], confirming the tentative spin assignments.The spin of 205 Fr was measured to be 9=2 − , the ground-state spins of 204;206 Fr were confirmed as 3 ðþÞ , but the low-lying spin (7 þ ) and (10 − ) isomers are still under investigation.
General methods of isomer identification have already been achieved with in-source laser spectroscopy (see Ref. [21] and references therein).In the case of 68;70 Cu [22], following the selection of isomeric beams, experiments such as Coulomb excitation [23] and mass measurements [24] have been performed.However, these experiments suffered from isobaric contamination, as well as significant ground-state contamination due to the Doppler broadening of the hyperfine resonances of each isomer [1].One way of addressing the difficulties of in-source laser spectroscopy (isobaric contamination, Doppler broadening, pressure broadening) is selecting the ground or isomeric state of interest by resonance ionization in a collinear geometry.
In a sub-Doppler geometry, the process of isomerselective resonance laser ionization [21] can result in a high-purity isomeric beam.Deflection of the pure-state ion beam to the decay-spectroscopy station allows identification of the hyperfine component with alpha-decay spectroscopy.

II. EXPERIMENTAL TECHNIQUE
Radioactive ion beams of francium are produced at the ISOLDE facility, CERN [25], by impinging 1.4-GeV protons onto a thick uranium carbide (UC x ) target (up to 2-μA integrated proton current).The radioisotopes are surface ionized through interaction with the rhenium coating on the hot (2400-K) tantalum transfer line and extracted from the target-ion source at 50 keV.The isotope of interest is mass selected using the high-resolution separator and bunched (at 31.25 Hz) with the radio-frequency ISOLDE cooler (ISCOOL) [26,27].The bunched-ion beam is deflected into the CRIS beam line and transported through a potassium-vapor charge-exchange cell (420-K, approximately 10 −6 -mbar chamber pressure, 6 × 10 −4 -mbar vapor pressure [28]) to be neutralized.In the 1.2-m-long interaction region, the arrival of the atomic bunch is synchronized with two copropagating pulsed laser beams to excite the state of interest followed by ionization in a stepwise scheme.The temporal length of the atomic bunch is 2-3 μs, corresponding to a spatial length of 45-70 cm.To reduce the background signal resulting from nonresonant collisional ionization, the interaction region aims at ultrahighvacuum (UHV) conditions.A pressure of < 10 −8 m bar is achieved during this experiment.A schematic diagram of the CRIS beam line is shown in Fig. 1.

A. Collinear resonance ionization spectroscopy
The resonant-excitation step from the 7s 2 S 1=2 electronic ground state to the 8p 2 P 3=2 state is probed with 422.7-nm light.The laser light of this resonant step is provided by a narrow-band Ti:sapphire laser of the resonance ionization laser ion source (RILIS) installation [29,30], pumped by the second harmonic output of a neodymium-doped yttrium aluminum garnet (Nd:YAG) laser (model: Photonics Industries DM-60-532, 10 kHz).The fundamental output from the tunable Ti:sapphire laser is frequency doubled using a barium borate crystal to produce the required 422.7nm laser light.The light is fiber coupled into the CRIS beam line through 35 m of multimode optical fiber (approximately 100-mW output).The laser linewidth of 1.5 GHz limits the resolution achieved in the present experiment, allowing only the lower-state (7s 2 S 1=2 ) splitting to be fully resolved.The second (nonresonant) transition from the 8p 2 P 3=2 state to the continuum is FIG. 1. Schematic diagram of the CRIS beam line.Laser ions can be deflected to a copper plate, and the corresponding secondary electrons can be detected by the MCP or implanted into a carbon foil for alpha-decay spectroscopy.Inset: The DSS "windmill" system for alpha-decay tagging.
driven using 1064-nm light.This light is produced by a fundamental Nd:YAG laser (model: Quanta-Ray LAB 130, operated at 31.25 Hz) next to the CRIS setup, temporally overlapped with the 422.7-nm laser beam and aligned through the laser-atom interaction region.The standard repetition rate of the RILIS lasers (10 kHz) limits the repetition rate of the 1064-nm laser light to 31.25 Hz. (One out of every 320 pulses of 422.7-nm laser light is utilized.)The bunching of the ion beam with ISCOOL is matched to the lower repetition rate of 31.25 Hz to overlap the atom bunch with the two laser pulses every 32 ms.
The synchronization of the first-and second-step laser pulses and the release of the ion bunch from ISCOOL are controlled by a Quantum Composers digital-delay generator (model: QC9258).The 10-kHz pulse generator of the Ti:sapphire pump laser acts as the master clock, triggering the delay generator to output a sequence of transistortransistor logic pulses to synchronize the 1064-nm laser light and the ion bunch with the 422.7-nm light, allowing resonance ionization of the francium atoms to occur.The laser ions are detected by a microchannel plate (MCP) housed in the decay-spectroscopy station (DSS).The electronic signal from the MCP is digitized by a LeCroy oscilloscope (model: WavePro 725Zi, 2-GHz bandwidth, 8-bit analogue-to-digital converter, 20 giga-samples/s), triggered by the digital-delay generator.The data are transferred from the oscilloscope using a LabVIEW program.
The frequency of the resonant-excitation step, the 422.7-nm laser light, is scanned to study the 7s 2 S 1=2 → 8p 2 P 3=2 atomic transition.The scanning and stabilization of the frequency are controlled by the RILIS Equipment Acquisition and Control Tool (REACT), a LabVIEW control program package that allows for remote control, equipment monitoring, and data acquisition [31].The scanning is achieved by controlling the etalon tilt angle inside the Ti:sapphire laser resonator to adjust the laser wavelength, which is measured with a HighFinesse wave meter (model: WS7) and calibrated with a frequencystabilized HeNe laser.The francium experimental campaign at CRIS marks the first implementation of the REACT framework for external users.The remote-control LabVIEW interface for the Ti:sapphire laser runs locally at the CRIS setup, allowing independent laser scanning and control.

B. Decay-assisted laser spectroscopy
The technique of decay-assisted collinear laser spectroscopy is further developed at the CRIS beam line to take advantage of the ultrapure ion beams produced by resonance ionization in a collinear geometry [32].The selectivity from resonance ionization of an isotope is a result of the selectivity of the Lorentzian profile of the natural linewidth (approximately 12.5 MHz) of the state and the Gaussian profile of the laser linewidth (approximately 1.5 GHz).At a frequency separation of 4 GHz, the Gaussian component falls to 1% of its peak intensity and the selectivity is dominated by the natural linewidth of the state.Thus, the maximum selectivity from resonance ionization is given by Eq. ( 1): where Δω AB is the separation in frequency of the two states (A and B), Γ n is the FWHM of the natural linewidth of the state, S n is the selectivity of the transition, and N is the number of transitions used.The total selectivity of a resonance ionization process is given by the product of the individual selectivities.In the case of the two states being the ground state and isomer, the selectivity can be calculated from Eq. ( 1).When the two states are the isotope of interest and contamination from a neighboring isotope, additional selectivity can be gained from the kinematic shift since the laser is overlapped with an accelerated beam.
In addition to hyperfine-structure studies with ion detection, the decay-spectroscopy station can be used to identify the hyperfine components of overlapping structures.The DSS allows the hyperfine structure of two states to be separated by exploiting their characteristic radioactivedecay mechanisms.The separation results in a smaller error associated with the hyperfine parameters and a better determination of the extracted nuclear observables.
The DSS consists of a rotatable-wheel implantation system [33].It is based on the design from KU Leuven [34] (Fig. 1 of Ref. [35]), which has provided results in a number of successful experiments (see Ref. [36] and references therein).The wheel holds nine carbon foils, produced at the GSI target laboratory [37], with a thickness of 20ð1Þ μg cm −2 (approximately 90 nm) into which the ion beam is implanted (at a depth of approximately 25 nm).
Two Canberra passivated implanted planar silicon (PIPS) detectors for charged-particle detection (e.g., alpha, electron, fission fragments) are situated on either side of the implantation carbon foil, as shown in Fig. 1.One PIPS detector (model: BKA 300-17 AM, thickness 300 μm) sits behind the carbon foil and another annular PIPS (APIPS) (model: BKANPD 300-18 RM, thickness 300 μm, with an aperture of 4 mm) is placed in front of the carbon foil.The detectors are connected to charge-sensitive Canberra preamplifiers (model: 2003BT) via a UHV type-C subminiature electrical feedthrough.
Laser-produced ions from the interaction region in the CRIS beam line are deflected to the DSS by applying a potential difference between a pair of vertical electrostatic plates; see Fig. 1.The deflected ion beam is implanted into the carbon foil, after passing though a collimator with a 4-mm aperture and the APIPS detector.The collimator shields the APIPS detector from direct implantation of radioactive ions into the silicon wafer; see Fig. 1.Decay products from the carbon foil can be measured by either the APIPS or PIPS detector, with a total solid-angle coverage of 63% (simulated, assuming a uniform distribution of implanted activity).Operation of the single APIPS detector during the experiment gives an alpha-detection efficiency of 25%.An electrical contact is made to the collimator, allowing the current generated by the ion beam when it strikes the collimator to be measured and the plate to be used as a beam-monitoring device.When it is not in use, it is electrically grounded to avoid charge buildup.A Faraday cup is installed in the location of one of the carbon foils.This copper plate (thickness 0.5 mm, diameter 10 mm) is electrically isolated from the steel wheel by polyether ether ketone (PEEK) rings and connected by a spot-welded Kapton cable attached to a rotatable Bayonet Neill-Concelman (BNC) connection in the center of the wheel [33].
The alpha-decay-spectroscopy data are acquired with a digital data-acquisition system, consisting of XIA digital gamma-finder (DGF) revision-D modules [38].Each module has four input channels with a 40-MHz sampling rate.Signals fed into the digital data-acquisition system are self-triggered with no implementation of master triggers.
Because of the reflective surface of the inside of the vacuum chambers, a significant fraction of 1064-nm laser light is able to scatter into the silicon detectors.Despite the collimator in front of the APIPS detector to protect it from ion implantation (and laser light), the infrared light causes a shift in the baseline of the signal from the silicon detector.The resulting shift requires the parameters for the DGF modules to be adjusted to account for this effect on-line, since the reflections are due to the particular setup of the experiment (power and laser-beam path).
The low energy resolution of the APIPS detector is associated with the necessity of optimizing the DGF parameters on-line with the radioactive 221 Fr [t 1=2 ¼ 4.9ð2Þ min].In addition, a fluctuating baseline resulting from the changing power of the 1064-nm laser light means that only a resolution of 30 keV at 6.341 MeV is achieved.The energy resolution, however, is sufficient to identify the characteristic alpha decays of the neutron-deficient francium isotopes under investigation.

III. RESULTS
The hyperfine structures of the neutron-deficient francium isotopes 202-206 Fr are measured with collinear resonance ionization spectroscopy, with respect to the reference isotope 221 Fr.This paper follows the recent publication reporting the hyperfine-structure studies of 202;203;205 Fr [39].During the experimental campaign, the neutron-rich francium isotopes 218m;219;229;231 Fr are also studied.A detailed description of the nature of these isotopes will be the topic of a future publication [40].
The resonance spectrum of the 7s 2 S 1=2 → 8p 2 P 3=2 transition is fit with a χ 2 -minimization routine.The hyperfine A P 3=2 factor is fixed to the ratio of the 7s 2 S 1=2 → 8p 2 P 3=2 transition of A P 3=2 =A S 1=2 ¼ þ22.4=6209.9,given in the literature [10].For the 8p 2 P 3=2 state, the hyperfine B P 3=2 factor is small enough to have no impact on the fit to the data and is consequently set to zero [41].
The intensities of the hyperfine transitions S FF 0 between hyperfine levels F and F 0 (with angular momenta J and J 0 , respectively) are related to the intensity of the underlying fine-structure transition S JJ 0 [2].The relative intensities of the hyperfine transitions are given by where the curly brackets denote the Wigner 6-j coefficient.
Although these theoretical intensities are only strictly valid for closed two-level systems, and there is jitter on the temporal overlap of the two laser pulses in the interaction region, they are used as the currently most reliable estimate.
The A S 1=2 factor and the centroid frequency of the hyperfine structure are determined for each scan individually.For isotopes with multiple scans, a weighted mean for the A S 1=2 factor and the centroid frequency are calculated based on the error of the fits.The uncertainty attributed to the A S 1=2 factor is calculated as the weighted standard deviation of the values.The isotope shifts are determined relative to 221 Fr, with the uncertainty propagated from the error of the fits, the scatter, and the drift in the centroid frequency of the 221 Fr reference scans [41].

A. Spectroscopic studies of 204 Fr
The hyperfine structure of 204 Fr is shown in Fig. 2 the lower-state splitting is resolved (associated with the 1.5-GHz linewidth of the scanning laser), two hyperfine resonances are expected per nuclear (ground or isomeric) state.Consequently, Fig. 2 contains the hyperfine structure of three long-lived states in 204 Fr, with one of the resonances unresolved (labeled E).In order to identify the states of the hyperfine resonances, laser-assisted alphadecay spectroscopy is used.
The radioactive decay of the low-lying states in 204 Fr is presented in Fig. 3.The characteristic alpha decay of each nuclear state in 204 Fr is utilized to identify the hyperfinestructure resonances of Fig. 2. The laser is tuned on resonance with each of the first three hyperfine resonances (labeled A, B, and C), and alpha-decay spectroscopy is performed on each.The alpha-particle energy spectrum of these three states is illustrated in Fig. 4. The energy of the alpha particles emitted when the laser is on resonance with an atomic transition of the hyperfine spectrum characteristic of 204g Fr is shown in blue.This transition occurs at 11.503 GHz (peak A of Fig. 2) relative to the centroid frequency of 221 Fr.Similarly, the alpha-particle energy spectra for 204m1 Fr and 204m2 Fr are shown in green and red, when the laser is detuned by 8.508 and 18.693 GHz (peaks B and C) from the reference frequency, respectively.Present in the alpha-particle energy spectrum are the alpha particles emitted from the decay of the 204 Fr states (6950-7050 keV) in addition to those emitted from the nuclear states in the daughter isotope 200 At (6400-6500 keV).Each state in 204 Fr has a characteristic alpha-particle emission energy: 7031 keV for 204g Fr, 6969 keV for 204m1 Fr, and 7013 keV for 204m2 Fr.The identification of the state is confirmed by the presence of the corresponding daughter decays of 200g At (6464 keV), 200m1 At (6412 keV), and 200m2 At (6537 keV) in the alphaparticle energy spectrum.
An additional alpha-decay measurement is performed on peak D in the hyperfine spectrum of 204 Fr (see Fig. 2) at 43.258 GHz relative to the centroid frequency of 221 Fr.The observation of 7013-keV alpha particles allows this state to be identified as 204m2 Fr.Identification of peak D means the identity of all five hyperfine-structure peaks can be allocated to a state in 204 Fr (hence, the hyperfine-structure peak E is the overlapping structure of 204g Fr and 204m1 Fr), allowing analysis of the hyperfine structure of each state.
In addition to the 7031-keV alpha particles of 204m2 Fr, alpha particles of 6969 keV from the decay of 204m1 Fr are also observed when the laser is on resonance with the 204m2 Fr state.The decay of the (10 − ) state to 204m1 Fr via an E3 internal transition (IT) has been predicted [18] but only recently observed [17]; see Fig. 3.In the study, the conversion electrons from the internal conversion of 204m2 Fr were tagged with the emitted 6969-keV alpha particles of 204m1 Fr that followed (with a 5-s correlation time).The coincidences allowed the predicted energy of the 275-keV isomeric transition to be confirmed.During the CRIS experiment, an additional alpha-decay measurement is performed on 204m2 Fr, with the laser detuned by 43.258 GHz relative to the centroid frequency of 221 Fr; see Fig. 5.This spectrum confirms the presence of the 6969-keV alpha particle (denoted by Ã), emitted from the decay of 204m1 Fr.The ultrapure conditions of this measurement allow the first unambiguous extraction of the branching ratios in the decay of 204m2 Fr: B α ¼ 53ð10Þ% and B IT ¼ 47ð10Þ% [42].
Decay-assisted laser spectroscopy is also performed on the hyperfine structure of the low-lying states of 204 Fr.Just as the laser frequency of the resonant 422.7-nm ionization step is scanned and resonant ions are detected in the collinear resonance ionization spectroscopy of 204 Fr, the same technique is repeated with the measurement of alpha FIG. 3. The radioactive decay of 204 Fr and its isomers [16,18,19].FIG. 4. Alpha-particle spectroscopy of (blue) 204g Fr, (green) 204m1 Fr, and (red) 204m2 Fr allow the hyperfine peaks in Fig. 2 to be identified.The laser is detuned by 11.503 GHz (peak A, 204g Fr), 8.508 GHz (peak B, 204m1 Fr), and 18.693 GHz (peak C, 204m2 Fr) relative to the centroid frequency of 221 Fr. particles.At each laser frequency, a radioactive-decay measurement of 60 s is made at the DSS, measuring the alpha particles emitted from the implanted ions.Figure 6 (top) shows the hyperfine peaks associated with each state in 204 Fr.Measurement of the alpha decay as a function of laser frequency allows production of a matrix of alphaparticle energy versus laser frequency; see Fig. 6.
In order to separate hyperfine structures for each state, an alpha-energy gating is used to maximize the signal-to-noise ratio for the alpha particle of interest.The alpha-energy gates are chosen to be 7031-7200 keV for 204g Fr, 6959-6979 keV for 204m1 Fr, and 7003-7023 keV for 204m2 Fr.
By gating on the characteristic alpha-particle energies of the three states in 204 Fr, the hyperfine structures of individual isomers become enhanced in the hyperfine spectrum.Figure 7(a) shows the hyperfine structure of 204g Fr, Fig. 7(b) shows 204m1 Fr, and Fig. 7(c) shows 204m2 Fr.The presence of 204m2 Fr can be observed in the spectra of 204g Fr due to the overlapping peaks of the alpha energies: The tail of the 7013-keV alpha peak is present in the gate of the 204g Fr alpha peak.The presence of 204m2 Fr in the hyperfine-structure spectrum of 204m1 Fr is attributed to the E3 IT decay of 204m2 Fr to 204m1 Fr: Alpha particles of energy 6969 keV are observed when on resonance with 204m2 Fr.Additionally, 204g Fr is present in the 204m2 Fr spectra due to the similar energies of the 7031-and 7013-keV alpha particles.However, despite the contamination in the hyperfine spectra, each peak is separated sufficiently in frequency to be analyzed independently.
From the resulting hyperfine structures of Fig. 7 produced by the alpha-tagging process (in comparison to the overlapping ion data of Fig. 2), each state of 204 Fr can be analyzed individually and the hyperfine factors extracted with better accuracy and reliability.The estimated error of the A S 1=2 factors is 30 MHz on account of the scatter of A S 1=2 values for 221 Fr.Likewise, an error of 100 MHz is assigned to the isotope shifts.alpha-decay spectroscopy.According to the literature, the radioactive decay of 202g Fr [t 1=2 ¼ 0.30ð5Þ s] emits an alpha particle of energy 7241(8) keV, whereas 202m Fr [t 1=2 ¼ 0.29ð5Þ s] emits an alpha particle of energy 7235 (8) keV [44].The radioactive decay of the ground and isomeric states of 202 Fr is presented in Fig. 9.
The laser is tuned onto resonance with peak A ( 202g Fr, 13.760 GHz relative to the centroid frequency of 221 Fr) and peak B ( 202m Fr, 20.950 GHz relative to the centroid frequency of 221 Fr) of Fig. 8 obtained from ion detection.For each position, an alpha-decay measurement is performed, shown in Fig. 10.The alpha particles emitted when the laser is on resonance with an atomic transition characteristic to 202g Fr are shown in blue, and 202m Fr in red.Because of the limited statistics of our measurement, and the similarity in energies of the alpha particles (within error), it is impossible to say that alpha particles of different energies are observed in Fig. 10.
Firm identification of the hyperfine components can be achieved, however, by studying the alpha particles emitted by the daughter isotopes 198g;m At.Evident in the spectrum of 202g Fr are the alpha particles emitted from the decay of the daughter nucleus 198g At with an energy of 6755 keV.Similarly, present in the 202m Fr spectrum are the alpha particles from the decay of 198m At with an energy of 6856 keV.The difference in energy of these two alpha peaks illustrates the ability of the CRIS technique to separate the two states and provide pure ground-state and isomeric beams for decay spectroscopy.data for the francium isotopes 202−206;221 Fr are taken in run I, and the data for 202−205;221 Fr are taken in run II.Consistency checks are carried out, allowing 206 Fr to be evaluated with respect to the rest of the data set from run II.A detailed description of this analysis can be found in Ref. [42].In run I, no alpha tagging is available, and consequently, the peaks in the ion-detected hyperfine spectrum need to be identified in a different way.Recent measurements of the ground-state hyperfine structure of 206g Fr provide the A S 1=2 factor for the splitting of the 7s 2 S 1=2 state [20].One peak of the (7 þ ) isomeric state is also identified in this experiment [see Fig. 1(c) of Ref. [20]], allowing the positions of the overlapping resonances to be determined.Therefore only the identities of peaks A and B (shown in Fig. 11) are unknown.Figure 11(a) presents the hyperfine structures when peak A is assigned to 206m2 Fr and peak B to 206m1 Fr. Figure 11(b) shows the fit when peak A is 206m1 Fr and peak B is 206m2 Fr.The suggested identity of the two resonances (based on mean-square charge radii and g-factor systematics) is discussed in Sec.IV.

D. Yield measurements
The yields of the neutron-deficient francium isotopes 202-206 Fr are presented in Table I.The quoted yields, scaled ISOLDE-database yields based on an independent yield measurement of 202 Fr, can be expected to vary by a factor of 2 due to different targets.The quoted value for 204 Fr is estimated based on francium-yield systematics.The composition of the beam for 202;204;206 Fr is calculated from the ratio of hyperfine-peak intensities (based on the strongest hyperfine-structure resonance) from the CRIS ion data.The composition of the beam for 202 Fr is confirmed with the alpha-decay data measured with the DSS.

E. King-plot analysis
The atomic factors F and M are evaluated by the Kingplot method [45].The technique combines the previously measured isotope shifts by Coc et al. [7] of the 7s 2 S 1=2 → 7p 2 P 3=2 transition, with 718-nm laser light, with those made by Duong et al. [10] of the 7s 2 S 1=2 → 8p 2 P 3=2 transition (422.7 nm).The isotope shifts of δν 207;221 and δν 211;221 from this work are combined with δν 220;221 and δν 213;212 from Ref. [10].These values are plotted against the corresponding isotope shifts from Coc et al. [7], shown in Fig. 12.The linear fit of the data, and using where GHz amu [46].The mass factor is the linear combination of two components: the normal mass shift K NMS and the specific mass shift K SMS , and is dependent on the frequency of the transition probed.Subtraction of the normal mass shift of the 422.7-nm transition (K NMS 422 ¼ þ389 GHz amu) from the mass factor M 422 allows for calculation of the specific mass shift, giving K SMS 422 ¼ þ360ð330Þ GHz amu.The specific mass shift for the 718-nm line is determined by Dzuba et al. to be K SMS 718 ¼ −314ð113Þ GHz amu [46].

F. Hyperfine-structure observables
Table II presents the hyperfine A S 1=2 factor, isotope shift, change in mean-square charge radius, and magneticmoment values extracted from the CRIS data for the francium isotopes 202-206 Fr with reference to 221 Fr.Additional data for 207;211;220 Fr (used in the creation of the King plot of Fig. 12) are included for completeness.All values are deduced using the nuclear spins presented.
The hyperfine A S 1=2 factor is defined as with μ I the magnetic dipole moment of the nucleus and B e the magnetic field of the electrons at the nucleus.For each isotope, it is calculated from the weighted mean of A S 1=2 values for isotopes where more than one hyperfinestructure scan is present.A minimum error of 30 MHz is attributed to the A S 1=2 -factor values due to the scatter of the measured A S 1=2 for the reference isotope 221 Fr [41,53].The isotope shift δν A;A 0 between isotopes A and A 0 is expressed as As with the A S 1=2 values, the isotope shifts are calculated as the weighted mean of all isotope shifts for a given nucleus.The error on the isotope shift is determined to be 100 MHz due to the long-term drift of the centroid frequency of 221 Fr as the experiment progresses and the scan-to-scan scatter in centroid frequency.When the calculated weighted standard deviation of the isotope shift is higher than 100 MHz, this error is quoted instead.Combining the extracted F and M atomic factors from the King-plot analysis with the measured isotope shifts, evaluation of the change in mean-square charge radii δhr 2 i A;A 0 between francium isotopes can be performed; see Eq. ( 6).
The magnetic moment of the isotopes under investigation can be extracted from the known moment of another isotope of the element, using the ratio In this work, calculation of the magnetic moments is evaluated in reference to the magnetic moment of 210 Fr, measured by Gomez et al.
1ð4Þ MHz [7,52]].The calculation represents the most accurate measurement of the magnetic moment of a francium isotope to date, due to probing the 9s 2 S 1=2 hyperfine splitting that has reduced more electron-correlation effects than that of the ground state.
The current evaluated magnetic moments of the francium isotopes are made in reference to the magnetic moment of 211 Fr of Ekström et al. [54].
The hyperfine anomaly for the francium isotopes is generally considered to be of the order of 1% and is included as a contribution to the error of the hyperfine A S 1=2 factors and magnetic moments [55].
Table II presents the experimental results alongside comparison to the literature of the hyperfine A S 1=2 factor, change in mean-square charge radius, and magneticmoment values.The literature values for 204-206 Fr have been taken from Ref. [20] and 207;211;220;221 Fr from Ref. [7].The magnetic-moment values from the literature have been recalculated in reference to μð 210 FrÞ [52], the most accurate measurement to date.The changes in mean-square chargeradii values for 207;211;220 Fr have been taken from Ref. [46].All experimental results are in broad agreement with those of the literature.

A. Charge radii of the neutron-deficient francium
Located between radon and radium, francium (Z ¼ 87) has five valence protons occupying the π1h 9=2 orbital, according to the shell model of spherical nuclei.Below the N ¼ 126 shell closure, the neutron-deficient francium isotopes are studied down to 202 Fr (N ¼ 115).The changes in mean-square charge radii for the francium and lead isotopes are presented in Fig. 13.The data of francium show the charge radii of 207-213 Fr reevaluated by Dzuba et al. [46] alongside the CRIS values, which extends the data set to 202 Fr.The blue data points show the francium ground states, while the (7 þ ) isomeric states are in green and the (10 − ) states in red.The error bars attributed to the CRIS values are propagated from the experimental error of the isotope shift and the systematic error associated with the atomic factors F 422 and M 422 .The systematic error is the most significant contribution to the uncertainty associated with the mean-square charge radii and not that arising from the isotope shift.The francium data are presented with the lead data of Anselment et al. [56] to illustrate the departure from the spherical nucleus.The changes in mean-square charge radii of the francium isotopes have been overlapped with the charge radii of the lead isotopes, by using 213 Fr (N ¼ 126) and 208 Pb (N ¼ 126) as reference points.The dashed isodeformation lines represent the prediction of the droplet model for the francium isotopes [57].The data are calibrated using β 2 ð 213 FrÞ ¼ 0.062, evaluated from the energy of the 2 þ 1 state in 212 Rn [58].The doubly magic 208 Pb represents a model spherical nucleus, with the shape of the nucleus remaining spherical with the removal of neutrons from the closed N ¼ 126 shell.This trend is observed until N ¼ 114, where a small deviation from the spherical droplet model (isodeformation line β 2 ¼ 0.0) is interpreted as enhanced collectivity due to the influence of particle-hole excitations across the Z ¼ 82 shell closure [59].The change in mean-square charge radii for the francium isotopes shows agreement with the lead data as the ν3p 3=2 , ν2f 5=2 , and ν3p 1=2 orbitals are progressively depleted.The deviation from sphericity at N ¼ 116 with 203 Fr marks the onset of collective behavior.The spectroscopic quadrupole moments are not measured in this work, since they require a laser linewidth of < 100 MHz.Measurement of the quadrupole moment will provide information on the static deformation component of the change in mean-square charge radii, allowing better understanding of this transition region.
Recent laser-spectroscopy measurements on the groundstate properties of 204;205;206 Fr suggest this deviation occurs earlier, at 206 Fr (N ¼ 119) [20].In Ref. [20], a more pronounced odd-even staggering is observed in relation to the lead isotopes, where the mean-square charge radius of 205 Fr is larger than that of 206 Fr.The CRIS experiment observes a smaller mean-square charge radius of 205 Fr in comparison to 206 Fr, the deviation from the lead isotopes occurring at 203 Fr instead.However, both experiments are in broad agreement within errors down to N ¼ 117.
Figure 13 presents the two options of the mean-square charge radii of 206m1 Fr and 206m2 Fr (as defined by their hyperfine-peak identities in Fig. 11).Option 1 is favored over option 2 due to the smaller mean-square charge radii of 206m1 Fr (compared to 206g Fr) agreeing with the systematics of the states in 204 Fr.As seen in Fig. 13, 206g Fr (N ¼ 119) overlaps with the lead data within errors.The large change in the mean-square charge radius of 206m2 Fr suggests a highly deformed state for the (10 − ) isomer.FIG. 13.Mean-square charge radii of the francium (circle) isotopes [54] presented alongside the lead (diamond) isotopes [56].The dashed lines represent the prediction of the droplet model for given isodeformation [57].The data are calibrated by using β 2 ð 213 FrÞ ¼ 0.062, evaluated from the energy of the 2 þ 1 state in 212 Rn [58].Options 1 and 2 for the (7 þ ) and (10 − ) states in 206 Fr are based on the isomeric identification given in Fig. 11.
The mean-square charge radii of francium are overlaid with the radon (Z ¼ 86) charge radii of Borchers et al.
(down to N ¼ 116, with the exception of N ¼ 117) [60] in Fig. 14.The mean-square charge radii of radon have been calibrated to the francium pair δhr 2 i 211;213 to account for the uncertainty in F and M for the optical transition probed.(The original isotope shifts are presented graphically.)Despite the uncertainty, the agreement between the mean-square charge radii of the francium and radon data is clear.The addition of a single π1h 9=2 proton outside the radon even-Z core does not affect the charge-radii trend, suggesting the valence proton acts as a spectator particle.
Table III presents a comparison of β 2 values with the literature.The droplet model [57] is used to extract the rms values for β 2 (column 3) from the change in mean-square charge radii [calibrated using β 2 ð 213 FrÞ ¼ 0.062, as before].Column 4 presents β 2 values extracted from the quadrupole moments of Ref. [20].The larger β 2 values extracted from the mean-square charge radii, compared to those extracted from the quadrupole moments, suggest that the enhanced collectivity observed in Figs.In Fig. 15, the blue line represents the empirical g factor (g emp ) of the odd-A isotopes for the single-particle occupation of the valence proton in the π1h 9=2 orbital.g emp ðπ1h 9=2 Þ is determined from the magnetic moment of the single-particle state in 209 Bi [61].Similarly, g emp ðπ3s 1=2 Þ is estimated from the magnetic moment of the single-hole ground state in 207 Tl [62].From N ¼ 126 to 116, every isotope has a g factor consistent with the proton occupying the π1h 9=2 orbital.The g factor indicates that the 9=2 − state remains the ground state, and the ðπ3s −1 1=2 Þ 1=2 þ proton-intruder state has not yet inverted.This lowering in energy of the π3s 1=2 state to become the ground state would FIG.14. Mean-square charge radii of the francium (circle) isotopes [54] presented alongside the radon (diamond) isotopes [60].The dashed lines represent the prediction of the droplet model for given isodeformation [57].The data are calibrated using β 2 ð 213 FrÞ ¼ 0.062, evaluated from the energy of the 2 þ 1 state in 212 Rn [58].Options 1 and 2 for the (7 þ ) and (10 − ) states in 206 Fr are based on the isomeric identification given in Fig. 11.FIG. 15. g factors for francium (solid blue line and symbols) [52,54] and thallium (dot-dashed red line and symbols) isotopes with odd A [63].The g factors for the π3s 1=2 and π1h 9=2 proton orbitals have been calculated empirically.See the text for details.[57] is used to extract the rms values for β 2 from the change in mean-square charge radii.The charge-radii values are calibrated using β 2 ð 213 FrÞ ¼ 0.062, as before.Literature: β 2 values are extracted from the quadrupole moments of Ref. [20].See the text for details.be apparent in the sudden increase in g factor of the ground state, as illustrated by the black g emp ðπ3s 1=2 Þ line.
Figure 15 highlights the robustness of the Z ¼ 82 and N ¼ 126 shell closure with a shell-model description valid over a range of isotopes.A close-up of g emp ð1π1h 9=2 Þ in Fig. 16 illustrates that the g factor is sensitive to bulk nuclear effects.The departure from the g emp ð1π1h 9=2 Þ line shows the sensitivity of the g factor to second-order core polarization in the odd-A thallium, bismuth, and francium isotopes.The systematic decrease in g factor of francium is attributed to second-order core polarization associated with the presence of five valence particles, compared to one particle (hole) in the bismuth (thallium) isotopes, enough to significantly weaken the shell closure.The linear trend observed in bismuth, thallium, and francium (until N ¼ 118) is suggested to be related to the opening of the neutron shell, yet allowing for more neutron and protonneutron correlations.
Further measurements toward the limit of stability are needed to better understand the prediction of the inversion of the π3s 1=2 intruder orbital with the π1h 9=2 ground state.A remeasurement of 203 Fr could determine the presence of the spin 1=2 þ isomer [t 1=2 ¼ 43ð4Þ ms [19]], which is not observed during this experiment.
The g factors for the odd-odd francium isotopes are presented in Fig. 17.With the coupling of the single valence proton in the π1h 9=2 orbital with a valence neutron, a large shell-model space is available.The empirically calculated g factors for the coupling of the π1h 9=2 proton with the valence neutrons are denoted by the colored lines.These g factors are calculated from the additivity relation as outlined by Neyens [64].The empirical g factors of the odd valence neutrons are calculated from the magnetic moments of neighboring nuclei: 201 Po for the blue 213 Ra for the black g emp ðπ1h 9=2 ⊗ ν3p 1=2 Þ line, and 211 Ra for the green g emp ðπ1h 9=2 ⊗ ν2f 5=2 Þ line [67].The empirical g factors for the valence proton in the π1h 9=2 orbital are calculated from the magnetic moment of the closest odd-A francium isotope ( 203 Fr and 213 Fr, respectively) from the CRIS data.The ground states of 202;204;206 Fr display similar g factors, with the valence proton and neutron coupling to give a spin 3 ðþÞ state.The tentative configuration in the literature of ðπ1h 9=2 ⊗ ν2f 5=2 Þ 3 þ for 202g Fr is based on the configuration of the (3 þ ) state in 194 Bi (from favored Fr-At-Bi alpha-decay chain systematics) [44].Similarly, the assignment of the same configuration for 204g Fr and 206g Fr is based on the alpha-decay systematics of neighboring nuclei 196;198 Bi.However, the initial assignment of 194g Bi is declared to be either ðπ1h [68].From the g factors of the ground states of 202;204;206 Fr, it is clear that the configuration of these states is indeed ðπ1h Figure 17 also presents the g factors of 206m1 Fr and 206m2 Fr for options 1 and 2 (see Fig. 11).The first isomeric states of 204;206 Fr (7 þ ) have a valence neutron that occupies the ν2f 5=2 state.This coupling of the proton and particle with the neutron and hole results in a ðπ1h 9=2 ⊗ ν2f 5=2 Þ 7 þ configuration [69].For 202m Fr, 204m2 Fr, and 206m2 Fr, the particle-proton-neutron-hole coupling results in a tentative ðπ1h 9=2 ⊗ ν1i 13=2 Þ 10 − configuration assignment for each isomer [70].However, while the agreement of the g factors FIG.16.Close-up of the g factors for francium (blue line and symbols) [52,54], bismuth (green symbols) [63], and thallium (red symbols) isotopes [65] with odd A. The g factor for the π1h 9=2 proton orbital has been calculated empirically.See the text for details.FIG. 17. g factors for francium isotopes with even A [54]: ground state (solid blue line and symbols), spin (7 þ ) state (dotted green line and symbols), and spin (10 − ) state (dashed red line and symbols).The g factors for the coupling of the proton and neutron orbitals have been calculated empirically.See the text for details.
of the spin (10 − ) state in 202;204 Fr points to a ν1i 13=2 occupancy, the observed value for 206m2 Fr is in disagreement with the g factor of such a (10 − ) state.The charge radius of 206m2 Fr indicates a highly deformed configuration, where the single-particle description of the nucleus is no longer valid.The value of the charge radius is consistent with the g factor of this state: It is no longer obeying a simple shell-model description.The observation leads to the conclusion that while a ðπ1h 9=2 ⊗ ν1i 13=2 Þ 10 − configuration for 206m2 Fr is suggested, the charge radii and magnetic moment point to a drastic change in the structure of this isomeric state.
The agreement of the experimental and empirical g factors, as shown in Figs.15-17, illustrates the suitability of the single-particle description of the neutron-deficient francium isotopes, with the exception of the (10 − ) state in 206m2 Fr.A model-independent spin and spectroscopic quadrupole-moment determination is needed to clarify the nature of this isomeric state.The neutron-deficient francium isotopes display a single-particle nature where the additivity relation is still reliable.

V. CONCLUSION AND OUTLOOK
The hyperfine structures and isotope shifts of the neutron-deficient francium isotopes 202-206 Fr with reference to 221 Fr were measured with collinear resonance ionization spectroscopy, with the change in mean-square charge radii and magnetic moments extracted.The selectivity of the alpha-decay patterns allowed the unambiguous identification of the hyperfine components of the low-lying isomers of 202;204 Fr for the first time.
The resonant atomic transition of 7s 2 S 1=2 → 8p 2 P 3=2 was probed and the hyperfine A S 1=2 factor measured.A King-plot analysis of the 422.7-nm transition in francium allowed the atomic factors to be calibrated.The field and mass factors were determined to be F 422 ¼ −20.670ð210ÞGHz= fm 2 and M 422 ¼ þ750ð330Þ GHz amu, respectively.
The novel technique of decay-assisted laser spectroscopy in a collinear geometry was performed on the isotopes 202;204 Fr.The decay-spectroscopy station was utilized to identify the peaks in the hyperfine spectra of 202;204 Fr.Alpha tagging the hyperfine-structure scan of 204 Fr allowed the accurate determination of the nuclear observables of the three low-lying isomeric states and the determination of the branching ratios in the decay of 204m2 Fr.
Analysis of the change in mean-square charge radii suggests an onset of collectivity that occurs at 203 Fr (N ¼ 116).However, measurement of the spectroscopic quadrupole moment is required to determine the nature of the deformation (static or dynamic).The magnetic moments suggest that the single-particle description of the neutrondeficient francium isotopes still holds, with the exception of the (10 − ) isomeric state of 206m2 Fr.Based on the systematics of the region, the tentative assignments of the hyperfinestructure peaks in 206 Fr result in magnetic moments and mean-square charge radii that suggest a highly deformed state.Laser-assisted nuclear-decay spectroscopy of 206 Fr would unambiguously determine their identity.
The occupation of the valence proton in the π1h 9=2 orbital has been suggested for all measured isotopes down to 202 Fr, indicating the ðπ1s −1 1=2 Þ 1=2 þ intruder state does not yet invert with the π1h 9=2 orbital as the ground state.Further measurements of the very neutron-deficient francium isotopes toward 199 Fr are required to fully determine the nature of the proton-intruder state.A laser linewidth of 1.5 GHz was enough to resolve the lower-state (7s 2 S 1=2 ) splitting of the hyperfine structure and measure the A S 1=2 factor.In the future, the inclusion of a narrow-band laser system for the resonantexcitation step will enable the resolution of the upper-state (8p 2 P 3=2 ) splitting, providing the hyperfine B P 3=2 factor.Measurement of the upper-state splitting will allow extraction of the spectroscopic quadrupole moment and determination of the nature of the deformation.
Successful measurement of 202 Fr was performed during this experiment, with a yield of 100 atoms/s.By pushing the limits of laser spectroscopy, further measurements of 201 Fr (with a yield of 1 atom/s) and 200 Fr (less than 1 atom/s) are thought to be possible.The ground state (9=2 − ) of 201 Fr has a half-life of 53 ms and its isomer (1=2 þ ) a half-life of 19 ms.By increasing the sensitivity of the CRIS technique, the presence of the 1=2 þ isomers in 201;203 Fr can be confirmed.A positive identification will lead to nuclearstructure measurements that will determine (along with the verification of nuclear spin) the magnetic moments that are sensitive to the single-particle structure and thus to the ðπ3s 1=2 Þ 1=2 þ proton-intruder nature of these states.With sufficient resolution (< 100 MHz), the spectroscopic quadrupole moment of these neutron-deficient states (with I ≥ 1) will be directly measurable and the time-averaged static deformation can be determined.
The successful measurements performed by the CRIS experiment demonstrate the high sensitivity of the collinear resonance ionization technique.The decay-spectroscopy station provides the ability to identify overlapping hyperfine structures and eventually perform laser-assisted nucleardecay-spectroscopy measurements on pure ground-and isomeric-state beams [32,73].
FIG. 2. Collinear resonance ionization spectroscopy of204 Fr relative to221 Fr.The hyperfine structure of the 3 ðþÞ ground state of 204g Fr is shown in blue, the 7 þ state of 204m1 Fr is shown in green, and the (10 − ) state of 204m2 Fr is shown in red.

B
FIG. 5. Alpha-particle spectroscopy of the (10 − ) state of 204m2 Fr.The decay of 204m2 Fr to 204m1 Fr via an E3 IT is observed through the presence of 204m1 Fr alpha particles of 6969 keV (denoted by Ã).The laser is detuned by 43.258 GHz relative to the centroid frequency of 221 Fr.

C
FIG. 8. Collinear resonance ionization spectroscopy of 202 Fr relative to 221 Fr.The hyperfine structure of the (3 þ ) ground state of 202g Fr is shown as a solid blue line, and the (10 − ) state of 202m Fr is shown as a dashed red line.
Figures 15 and 17  show the experimental g factors for odd-A and even-A francium isotopes, respectively.These plots present the CRIS data alongside the data from Ekström et al.[54].The Ekström et al. data have been reevaluated with respect to the μð 210 FrÞ measurement of Gomez et al.[52].In Fig.15, the blue line represents the empirical g factor (g emp ) of the odd-A isotopes for the single-particle occupation of the valence proton in the π1h 9=2 orbital.g emp ðπ1h 9=2 Þ is determined from the magnetic moment of the single-particle state in 209 Bi[61].Similarly, g emp ðπ3s 1=2 Þ is estimated from the magnetic moment of the single-hole ground state in 207 Tl[62].From N ¼ 126 to 116, every isotope has a g factor consistent with the proton occupying the π1h 9=2 orbital.The g factor indicates that the 9=2 − state remains the ground state, and the ðπ3s −1 1=2 Þ 1=2 þ proton-intruder state has not yet inverted.This lowering in energy of the π3s 1=2 state to become the ground state would alpha-decay gated hyperfine-structure scan of 204 Fr.See the text for details.b Based on the isomeric identity of the hyperfine resonances of option 1. See the text for details.c Based on the isomeric identity of the hyperfine resonances of option 2. See the text for details.

TABLE I .
Yields of the neutron-deficient francium isotopes at the ISOLDE facility (1.4-GeV protons on a UC x target).The nuclear-state compositions of the radioactive beams for 202;204;206 Fr are presented.
[46]Literature value taken from Ref.[20]c Literature magnetic-moment values recalculated in reference to μð 210 FrÞ[52].dBased on the isomeric identity of the hyperfine resonances of option 1. See the text for details. e Based on the isomeric identity of the hyperfine resonances of option 2. See the text for details.f Literature value taken from Ref.[7].gLiteraturevalue taken from Ref.[46].

TABLE III .
Extracted β 2 values.Experiment: The droplet model