Laser and decay spectroscopy of the short-lived isotope 214 Fr in the vicinity of the N = 126 shell closure

G. J. Farooq-Smith,1,2,* T. E. Cocolios,1,2 J. Billowes,1 M. L. Bissell,1,2 I. Budinčević,2 T. Day Goodacre,1,3 R. P. de Groote,2 V. N. Fedosseev,3 K. T. Flanagan,1 S. Franchoo,4 R. F. Garcia Ruiz,1,2 H. Heylen,2 R. Li,4,† K. M. Lynch,2,5 B. A. Marsh,3 G. Neyens,2 R. E. Rossel,3,6 S. Rothe,1,3 H. H. Stroke,7 K. D. A. Wendt,6 S. G. Wilkins,1 and X. F. Yang2 1School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom 2KU Leuven, Instituut voor Kernen Stralingsfysica, B-3001 Leuven, Belgium 3EN Department, CERN, CH-1211 Geneva 23, Switzerland 4Institut de Physique Nucléaire d’Orsay, F-91406 Orsay, France 5ISOLDE, PH Department, CERN, CH-1211 Geneva 23, Switzerland 6Institut für Physik, Johannes Gutenberg-Universität, D-55128 Mainz, Germany 7Department of Physics, New York University, New York, New York 10003, USA (Received 10 August 2016; published 4 November 2016; publisher error corrected 17 November 2016)


I. INTRODUCTION
As one of the first elements studied at the isotope separator online device (ISOLDE) facility at CERN [1], francium has played an important role in explaining the variety of nuclear behavior that exists around the Z = 82 and N = 126 magic shell closures. High-profile studies have already documented the phenomena of shape coexistence and octupole deformations in isotopes located in the neutron-deficient and -rich regions, respectively [2,3]. However, for the case of 214 87 Fr 127 , which resides between these two regions next to the N = 126 shell closure, little information is known. In this paper we focus on the charge radii in the trans-lead region and in particular, the characteristic increase in the gradient that is observed at a shell closure crossing. This is often referred to as a "kink" [4] and has already been seen at N = 126 in the neighboring isotopes from thallium to radium [5][6][7][8][9][10][11][12].
The interpretation of the kink at N = 126 remains a challenge for nuclear models. Many groups have investigated this region with mean-field calculations [13][14][15][16][17] but no general consensus exists on how to reproduce the correct magnitudes. Until now, limited experimental input has been available regarding the gradient of the kink at this particular shell closure. Although data for the trans-lead region is available from N = 132 onwards, little is known for N = 127-131 due to the short lifetime of the isotopes immediately after the N = 126 shell closure. Only four N = 127 isotones have been studied: 81 Tl [5], 82 Pb [6], 83 Bi [7], and 84 Po [18]. With five protons located in the π 1h 9/2 orbital, 214 Fr offers an additional test of the robustness of the Z = 82 shell closure.
The collinear resonance ionization spectroscopy (CRIS) setup at CERN-ISOLDE has recently explored isotopes across the francium chain [11,[19][20][21][22]. In particular, new developments at the decay spectroscopy station (DSS) [23] have allowed combined decay and laser spectroscopy techniques to be performed. A recent example of this includes the identification of ground and isomeric states in 202 Fr, 204 Fr, and 206 Fr [20,22], from overlapping hyperfine structures. In this article, we report the first measurements of 214 Fr at the CRIS beam line. With a half-life of only 5.0(2) ms [24], 214 Fr represents the shortest-lived isotope to have been measured online with laser spectroscopy. The change in the mean-square charge-radii and the gyromagnetic factor will be presented, alongside a discussion on recent mean-field calculations performed in the area. Based on these considerations, the implications on the behavior exhibited past the N = 126 shell closure will be discussed.

II. EXPERIMENTAL SETUP
The 214 Fr ion beam was produced at the ISOLDE facility [25] via spallation reactions, by impinging 1.4 GeV protons from the proton-synchrotron booster (PSB) onto a thick UC x target [26]. The PSB duty cycle delivered proton pulses separated by integral multiples of 1.2 s, resulting in release profiles that could be defined empirically [27]. The short half-life of 214 Fr meant that the release profile was primarily dominated by the decay losses. This increased the importance of operating the experimental setup at a fast duty cycle comparable to the half-life, in order to minimize these losses.
The resulting reaction products were surface-ionized in a high temperature (∼2200 K) tantalum hot cavity ion source and extracted at 40 keV. The isotopes of interest were mass separated by the high resolution mass separator (HRS) [25]. Cooling and bunching of the ions was performed with the use of the ISCOOL radio-frequency gas-filled linear Paul trap [28,29]. The release time for these bunches was synchronized with the duty cycle of the laser system. In order to limit the 214 Fr decay losses from within the trap, a 200 Hz repetition rate was used. After reaccelerating to 40 keV, the ion bunches were electrostatically deflected into the CRIS beam line [20,30,31], where they were first neutralized through a charge exchange cell (CEC) filled with potassium vapor (445-455 K) with a neutralization efficiency of ∼50%. Any remaining nonneutralized ions were deflected out of the atomic beam in the differential pumping region situated just after the CEC.
The neutralized atomic bunches then entered an ultra high vacuum (UHV) interaction region (kept at a pressure of 9 × 10 −9 mbar), where they were collinearly overlapped with laser light both spatially and temporally. The ionization scheme consisted of two steps: a 422.7-nm step to excite the 7s 2 S1/2 → 8p 2 P3/2 transition at 23 658.306 cm −1 , and a nonresonant 1064-nm step, which was subsequently used to ionize the atoms. The 422.7-nm laser light was produced by frequency-doubling light from a 10 kHz Ti:Sa narrowband (1 GHz) laser provided by the resonance ionization laser ion source (RILIS) laser laboratory [32,33], in which the laser frequency could be stepped by using a data acquisition routine [34]. It was transported to the CRIS beam line using a 35-m long multimode optical fiber. The 1064-nm light was produced with a Litron LPY-601 Nd:YAG system (consisting of two lasers running at 100 Hz each) that could operate at 200 Hz, situated next to the CRIS beam line. By opening the beam gate 10 ms after proton impact with the target and setting its temporal width to several 214 Fr half-lives, the amount of 214 Fr available for study was maximized. This also limited the isobaric contamination present (mainly 214 Ra), which was constantly released from the target. The low pressure maintained within the interaction region minimized the background due to nonresonant ionization with gas molecules. After the resonant excitation and reionization processes, the ions were deflected onto a biased copper plate (held at −270 V), where ejected secondary electrons were guided onto a micro-channel plate (MCP) detector. Separate α-decay spectroscopy could also be performed by implanting the ions into carbon foils on a rotatable wheel. Emitted α particles could be detected within the DSS [20,23], located at the end of the CRIS beam line.

A. Laser spectroscopy of 214 Fr
The magnetic dipole moment was extracted from the hyperfine structure shown in Fig. 1 by means of a χ 2minimization fitting routine [4]. The center of gravity of the hyperfine spectrum of 214 Fr was compared to the reference isotope, 221 Fr, for extraction of the isotope shift. All other measured observables were determined relative to 210 Fr, using: A ref (7s 2 S1/2) = +7195.1(4) MHz [35], I π = 6 + [36], and μ ref = +4.38 (5) μ N [37]. The changes in the mean-square charge radii were extracted by using the equation where A and A are assigned to the reference and measured isotopes, respectively. The parameters M 422 = +750(330) GHz.amu and F 422 = −20.67(21) GHz/fm 2 represent the atomic factors and contain all the optical dependence for the 422.7-nm transition [20]. The hyperfine anomaly for francium has been measured as <1% [40,41], which was beyond the resolution of the technique used in this work. The data were analyzed with a constant ratio of A(7s 2 S1/2)/A(7p 2 P3/2) = +0.0036 and the B(7p 2 P3/2) hyperfine parameter was set to zero [30]. The 1.5-GHz line width of the 422.7-nm RILIS Ti:Sa laser produced pure Gaussian line shapes. Only the lower-state splitting could be resolved, preventing the extraction of the nuclear spin and quadrupole moment. However, the comparison of measured peak intensity ratios with those expected from angular-momentum coupling meant that tentative spin assignments were possible. The low resolution available, along with J = 1/2 for the 7s 2 S1/2 state, meant that the normal relation for the hyperfine transition intensities, S FF , between states of F and F (with angular momentum J and J , respectively) could be simplified to where I represents the nuclear spin of the isotope. Fitting routines applied to the data shown in Fig. 1 suggested a ratio of 1.7(3) for the intensities of the two structures. In conjunction with Eq. (2), this was consistent with a low-spin assignment. In order to assess the ratio of ground and isomeric states within the beam and their contribution to the structure of Fig. 1, additional decay spectroscopy measurements were performed. A systematic error of 30 MHz was established for A(7s 2 S1/2) based on the scatter observed in the measured A factors of the 221 Fr reference scans [11,30]; however, this uncertainty was mainly dominated by the limited resolution of the laser system. For the isotope shift, a minimum instrument error of 150 MHz was set. This accounted for the drift and fluctuations of the centroid frequency of 221 Fr, and the precision of the HighFinesse/Ångstrom WS7 wavelength meter. When the calculated weighted standard deviation of the isotope shift or A(7s 2 S1/2) parameter was greater than the minimum errors, these were quoted instead.

B. Decay spectroscopy of 214 Fr
Laser-assisted nuclear decay spectroscopy was performed for the 214 Fr ion beam in order to determine its ground and isomeric state content. Figures 2(a) and 2(b) show the α-decay spectra from the implantation of the full A = 214 beam, as well as the purified laser-ionized beam of 214 Fr into the carbon foils, for a collection time of 30 min. Relative to the centroid frequency of 221 Fr, the Ti:Sa laser frequency was detuned to 18.3 and 22.1 GHz, respectively, for each hyperfine structure observed in Fig. 1. The laser-ionized spectrum in Fig. 2(b) represents the sum of the two separate spectra obtained from this method. A selectivity of 3.3 [20] meant that the content of each peak could be analyzed separately at the DSS. The presence of 214 Ra as an isobaric contaminant was reduced from the laser-ionized spectrum by beam gating (see Sec. II). However, the impinging of its daughter isotope 210 Rn (t 1/2 = 2.4(1) h [39]) with the surface of the silicon detectors occurred whenever full 214 Fr beams were examined. This meant that its decay could still be seen when analyzing the laser-ionized beam, allowing the 210 Rn peak to be used for calibrating the energy scale for both spectra.
All expected α decays from Fig. 3 were observed for both 214g Fr and 214m Fr when the ion deflector after the CEC was switched off, with a ratio of approximately 8:1. However, the implantation of the laser-ionized beam resulted in lower statistics and a nonoptimal energy resolution for the silicon detectors, due to the influence of the laser light on the baseline of the detector signal. In addition, data taking for this measurement was stopped before it could be completed (as this was performed at the end of the experiment), resulting in only a partial data set being obtained. Nonetheless, 10 counts were observed that corresponded to the decay of 214g Fr, and none were seen for 214m Fr. Given the observed 214g Fr: 214m Fr ratio of 8:1 with the full beam, a statistical analysis concluded there was a 100% confidence that the ground state was present in the laser-ionized beam. Additionally, there was an 82.5% confidence that no isomeric state was present in the laserionized beam. Although the possibility of a ground/isomeric state mix could not be ignored a priori, any existence of an FIG. 3. The radioactive decay scheme of 214g,m Fr. The solid arrows represent the main α-decay paths [38] and the shaded arrows depict the allowed γ -ray transitions between given states.

FIG. 4. Extracted 214g
Fr g factors for (1 − ) and (2 − ) spin assignments, alongside those for the tentative assignments of 218m Fr [11]. Associated error bars are smaller than the data points. The g factors for a pure (π 1h 9/2 ⊗ ν2g 9/2 ) configuration and those with (π 1h 9/2 ⊗ ν1i 11/2 ) configuration mixing have been calculated empirically. See text for details. isomeric state in Fig. 1 would have been suppressed by a factor of eight with respect to the ground state. This was consistent with background, meaning the isomeric state contribution could be neglected.

IV. DISCUSSION
To first order, odd-odd 214g Fr involves the coupling of an unpaired valence proton located in the π 1h 9/2 orbital with a single valence neutron above the N = 126 shell gap, where ν2g 9/2 is the next spherical shell model orbital. This leads to possible ground state spin assignments of (0,1,2, . . .) − , considering the lowest spin states from this multiplet. The observed hyperfine structure of the ground state in Fig. 1 automatically rules out a I = (0 − ) spin assignment, due to the observation of two peaks. Therefore, the use of I = (1 − ) and I = (2 − ) low-spin assignments were considered for the laser spectroscopy analysis following the observations presented above. Earlier α-decay spectroscopy studies have also ruled out the (0 − ) spin assignment and suggest a (1 − ) spin/parity, based on analogy with the isotone 210 Bi [44][45][46]. The extracted g-factor values for the (1 − ) and (2 − ) spin assignments are presented in Table I and shown graphically in Fig. 4. The calculation of the expected empirical g factor (represented by the purple solid line in Fig. 4) can be obtained from the additivity relation [47]. For the case where the proton and neutron spins are the same, the g factor of the weakly coupled pn configuration is independent of the spin to which they couple to. Individual empirical g factors for π 1h 9/2 and ν2g 9/2 were taken from the magnetic moments of the closest odd-A isotopes available: 213 Fr [35] and 211 Po [48], respectively.
Additionally, the ν1i 11/2 and ν2g 7/2 orbitals are also in the near vicinity [15] and their contributions to the total g factor due to configuration mixing with the ν2g 9/2 orbital need to be considered. With respect to the ν1i 11/2 orbital, only linear contributions are expected and this is reflected in Fig. 4. The experimental g( 214g Fr I=(1 − ) ) = +0.241(16) is consistent with a relatively pure (π 1h 9/2 ⊗ ν2g 9/2 ) 1 − configuration. It also compares to the g factors obtained for the tentative I = (8 − ) or I = (9 − ) assignments of 218m Fr at N = 131, which is suggested to have a similar single-particle configuration with the protons and neutrons aligned [11]. The contribution due to configuration mixing with the ν1i 11/2 orbital (using the calculated magnetic moment for 209 Pb [49]) is relatively small, at 3.8%. However, in contrast, ν1i 11/2 configuration mixing accounts for 33.5% of the 214 Fr ground state assignment when I = (2 − ), with g( 214g Fr I=(2 − ) ) = +0.144 (10). In either case, evidence of a contribution from the ν1i 11/2 orbital supports previous theoretical studies that require this in order to reproduce the kink in the mean square charge-radii values at the N = 126 shell closure [14,15,17]. For the ν2g 7/2 orbital, mixing calculations have been performed using the same empirical values as mentioned above for the π 1h 9/2 , ν2g 9/2 , and ν2g 7/2 orbitals, as well as the calculated B(M1) value connecting the ν2g 9/2 and ν2g 7/2 orbitals [49]. These have shown that a 3.8% admixture of this type is sufficient to describe the measured g factor for 214 Fr in the case of I = (1 − ). For the I = (2 − ) assignment, however, the ν2g 7/2 orbital cannot contribute to the total g factor. Further study is required to confirm the ground-state spin and to investigate any possible shell effects that might be present, which will serve to test the robustness of the N = 126 shell closure.
The change in the mean-square charge-radii is interpreted in Fig. 5. Comparing the difference in the mean-square chargeradii before and after N = 126 offers an alternative way of isolating the effect seen at N = 126. This difference can be calculated by using with N , N representing the neutron numbers 125, 126 and 126, 127, for the differences before and after the shell closure respectively. The values for Hg-Ra are given in Table II and   TABLE I. The A(7s 2 S 1/2 ) factors, isotope shifts, g factors, and the change in the mean-square charge-radii for 214 Fr with respect to 221 Fr, for assumed (1 − ) and (2 − ) spin assignments. The statistical and systematic uncertainties for δ r 2 221,214 are separated, enclosed within parentheses and brackets, respectively.  [ 18] - [ 9] This work, [10] [ 43] neutron numbers are used in the mean-square charge-radii superscripts to highlight the crossing of the N = 126 shell closure.
A first observation is that the gradient in the charge radii between the N = 125 and N = 126 isotones is smaller than the gradient between N = 126 and N = 127. The latter leads to the well-known kink in the radii values [4]. A second observation is that the change in the radii below N = 126 is more or less constant for all isotopes from Hg (Z = 80) up to Ra (Z = 88), while an increase of the slope in the kink is observed with an increasing number of protons beyond Z = 82. It should be noted that for the cases of 83 Bi and 84 Po, large systematic uncertainties on the atomic parameters could affect this interpretation [50]. However, in accordance with Eq. (1) these uncertainties scale with the mass difference. Therefore, the close proximity of the charge-radii values in Fig. 5 with their references minimizes these systematic effects. Despite this, the francium data points for both spin assignments lie far away from this trend. Further studies on 214 Fr in higher resolution is needed to confirm this result and draw conclusions about the influence of the valence protons outside Z = 82 on the slope of the kink. Additionally, data from the 80 Hg, 85 At, 86 Rn, and 88 Ra isotones are needed in order to fully establish the systematics in this region. FIG. 5. The difference in the mean-square charge radii for before (red circles) and after (blue stars) the N = 126 shell closure, across the N = 125 and N = 127 isotone chains, using the values in Table II. The shell closure at Z = 82 is highlighted with a dashed line.
The question of how this mechanism arises is still debated. Modifications to the spin-orbit interaction in mean-field calculations have successfully reproduced the kink in the Pb and Po isotope chains [14,15,17]. Other studies suggest the inclusion of a density-dependent term to the spin-orbit term [13,16], with the latter also proposing the inclusion of three-nucleon (3N ) interactions in mean-field calculations. However, mean-field theory is primarily limited to eveneven nuclei. Such calculations are difficult to perform for nuclei with odd numbers of protons and neutrons such as 214 87 Fr 127 , and this poses a major challenge for theoretical nuclear physics [51]. Recently, modified mean-field methods have allowed calculations to extend to odd-A nuclei, giving reasonable descriptions to light-mass nuclei such as 25 Mg [52]. Density functional theory (DFT) has also been developed in recent years and it is hoped that this can be applied across the entire nuclear landscape [53]. At present, a limited framework exists for mean-field calculations in this area of the nuclear chart and the mechanism remains an open question. Further studies are required to expand on the current nuclear theory constraints and it is anticipated that future developments of DFT calculations can be extended to include calculations for heavy-mass nuclei. Experimentally, the study of other N = 127 isotones is desirable in order to further assert whether a dependence exists between the magnitude of these kinks and the proton number.

V. CONCLUSION
The neutron-deficient isotope 214 Fr has been studied at the CRIS beam-line at ISOLDE. With a half-life of 5.0(2) ms, 214g Fr represents the shortest-lived isotope studied online with laser spectroscopic techniques. A comparison between empirical and experimentally obtained g factors suggest that whilst the possible I = (1 − ) assignment is dominated by a (π 1h 9/2 ⊗ ν2g 9/2 ) configuration, the alternative I = (2 − ) assignment involves more configuration mixing with the ν1i 11/2 orbital. Further investigation into possible shell effects involving this orbital is required for a definitive assignment. The charge-radii value past the N = 126 shell closure shows the expected kink and is comparable to the behavior exhibited in the neighboring isotones.