On the β -decay of 186 Hg
A. Algora, E. Ganio?lu, P. Sarriguren, V.Guadilla, L. M. Fraile, E. Nácher, B. Rubio, J. L. Tain, J. Agramunt, W. Gelletly, J. A. Briz, R. B. Cakirli, M. Fallot, D. Jordán, Z. Halász, I. Kuti, A. Montaner, A. Onillon, S. E. A. Orrigo, A. Perez Cerdan, S. Rice, V. Vedia, E. Valencia
aa r X i v : . [ nu c l - e x ] D ec Highlights
On the β -decay of Hg A. Algora, E. Ganio˘glu, P. Sarriguren, V. Guadilla, L. M. Fraile, E. N´acher, B. Rubio,J. L. Tain, J. Agramunt, W. Gelletly, J. A. Briz, R. B. Cakirli, M. Fallot, D. Jord´an, Z. Hal´asz,I. Kuti, A. Montaner, A. Onillon, S. E. A. Orrigo, A. Perez Cerdan, S. Rice, V. Vedia,E. Valencia • The Gamow-Teller strength distribution of the decay of
Hg into
Au has been deter-mined for the first time using the total absorption gamma spectroscopy technique and hasbeen compared with theoretical QRPA calculations using the SLy4 Skyrme force. Themeasured Gamow-Teller strength distribution and the half-life are described by mixingoblate and prolate configurations independently in the parent and daughter nuclei. The bestdescription of the experimental beta strength is obtained with dominantly prolate compo-nents for both parent
Hg and daughter
Au. The approach also allowed us to determinean upper limit of the oblate component in the parent state, which also describes nicely theexperimental beta strength and provides the best description of the half-life of the decaywithin this framework. • The complexity of the analysis required the development of a new approach in the analysisof the X-ray gated total absorption spectrum. This approach can also be of particularinterest for cases where the β + component of the β -decay can contaminate the X-ray gatedspectra. n the β -decay of Hg A. Algora a,b, ∗ , E. Ganio˘glu c, ∗ , P. Sarriguren d , V. Guadilla a,e , L. M. Fraile f , E. N´acher a,d ,B. Rubio a , J. L. Tain a , J. Agramunt a , W. Gelletly g , J. A. Briz d,h , R. B. Cakirli c , M. Fallot h ,D. Jord´an a , Z. Hal´asz b , I. Kuti b , A. Montaner a , A. Onillon h , S. E. A. Orrigo a ,A. Perez Cerdan a , S. Rice g , V. Vedia f , E. Valencia a a Instituto de F´ısica Corpuscular, CSIC-Univ. de Valencia, E-46071 Valencia, Spain b Institute of Nuclear Research (ATOMKI), P.O.Box 51, H-4001 Debrecen, Hungary c Department of Physics, Istanbul University, Istanbul 34134, Turkey d Instituto de Estructura de la Materia, CSIC, E-28006, Madrid, Spain e Faculty of Physics, University of Warsaw, 02-093, Warsaw, Poland f Univ. Complutense, Grupo de F´ısica Nuclear, CEI Moncloa, E-28040, Madrid, Spain g Department of Physics, University of Surrey, GU2 7XH, Guildford, UK h Subatech, IMT-Atlantique, Univ. de Nantes, CNRS-IN2P3, F-44307, Nantes, France
Abstract
The Gamow-Teller strength distribution of the decay of
Hg into
Au has been determined forthe first time using the total absorption gamma spectroscopy technique and has been comparedwith theoretical QRPA calculations using the SLy4 Skyrme force. The measured Gamow-Tellerstrength distribution and the half-life are described by mixing oblate and prolate configurationsindependently in the parent and daughter nuclei. The best description of the experimental betastrength is obtained with dominantly prolate components for both parent
Hg and daughter
Au. The approach also allowed us to determine an upper limit of the oblate component in theparent state. The complexity of the analysis required the development of a new approach in theanalysis of the X-ray gated total absorption spectrum.
Keywords: beta decay, total absorption spectroscopy, shape coexistence
PACS: + w, 29.30.KvThe existence of eigenstates characterized by di ff erent intrinsic shapes in a particular nucleuscan be considered a unique type of behaviour in finite many-body quantum systems [1]. This phe-nomenon, called shape coexistence, is essentially a quantum mechanical e ff ect that appears veryclearly in specific regions of the nuclide chart [1, 2, 3]. The appearance of co-existent structuresin nuclei has been interpreted as the consequence of the competition of two opposing trends: thestabilizing e ff ect of closed shells or subshells, that drives the nuclear system to sphericity and theresidual interactions between protons and neutrons that drives the system to deformation. The-oretically it has been interpreted in the framework of the shell model or mean-field approaches.The coexisting structures can mix depending on their quantum mechanical properties, and theresulting states can be connected by transitions basically determined by their degree of mixing.The relevant states have been studied conventionally through electromagnetic probes, nuclear ∗ Corresponding authors
Email addresses: [email protected] (A. Algora ), [email protected] (E. Ganio˘glu )
Preprint submitted to Physics Letters B December 21, 2020 ransfer reactions and α -decay, but its possible impact in β -decay has only been studied in a fewcases (for the most recent reviews see [1, 4, 5] and references therein).The region around the neutron-deficient Hg nuclei is considered to be a benchmark for studiesrelated to shape transitions and shape e ff ects. Its study has attracted significant attention inrelation to measurements of the changes in mean-square charge radii ( δ h r i ) [6]. The δ h r i measurements show a characteristic staggering for the Hg isotopic chain, that is not seen soclearly in any other isotopic chain in the nuclide chart [7]. The staggering was interpreted as achange in the ground state structure and consequently on the ground state shape around A = δ h r i in the Hgnuclei down to A =
179 and established firmly the limits of the staggering phenomenon. Thisstudy also confirmed the results of the earlier δ h r i measurements.In this context, β -decay studies can o ff er an insight into nuclear shapes and related phenom-ena in particular cases. The idea, first introduced by I. Hamamoto and coworkers [10] and laterdeveloped by P. Sarriguren et al. [11], is based on the dependence of the β strength of the de-cay on the nuclear shape assumed for the parent state. Information on the deformation of theground state of the decaying nucleus can be obtained from the comparison between experimentand theory in cases where the pattern of the theoretical strength distributions show a clear de-pendence on the shape [12, 13, 14, 15, 16]. For a proper determination of the experimental β strength, these studies require the application of the total absorption gamma-ray spectroscopy(TAGS) technique, that provides β -decay data free from the Pandemonium systematic error [17].These studies have relied mainly on quasiparticle random-phase approximation (QRPA) cal-culations, where the deformation of the parent state and the deformation of the populated statesin the daughter nucleus remain the same. For that reason the method was originally thought to beapplicable mainly to cases where mixing in the ground state of the parent nucleus was assumedto be small. Thus in the case of the β -decay of Kr, where the theoretical description of themeasured β strength was relatively poor compared to the Sr case [12], this was interpreted asevidence of a strongly mixed, ground state configuration in the parent nucleus [13].In this context, the β -decay of Hg can be seen as a one-o ff . From the pattern observed inthe di ff erences in charge-radii, the ground states of even-even Hg isotopes around A =
186 arecompatible with oblate shapes that are in general less common in the nuclide chart [18], whilethe odd- A isotopes below A =
186 are best described with prolate shapes [19]. Similarly, thejump in the charge-radii di ff erences observed in Au isotopes between A =
187 and A = Au and a prolate shape in
Au [20]. Therefore, we face in this case an interesting problem, where a β -decay can connectpartners with deformations that are assumed to be quite di ff erent, at least in their ground states.They are expected to be predominantly oblate in the parent Hg and predominantly prolate inthe daughter
Au. The decay in these cases is expected to be supressed with respect to decaysbetween partners with similar shapes. Actually, this suppression can be observed in the measuredhalf-lives of Hg isotopes, where the trend changes when crossing the decay around A =
186 (seeFig. 1). In this figure the trend observed in the half-lives of the heavier Hg isotopes ( A > < A < ff erent shapes. A smooth trend is recovered in the decayof the lighter Hg isotopes.Theoretical calculations [21, 22] show that in the Hg case there is a clear sensitivity of the β strength of the decay to the shape of the parent nucleus independently of the force employedin the calculations, which justifies such study. Even though the information that can be obtained2
72 174 176 178 180 182 184 186 188 190 192 A -5 -4 -3 -2 -1 T / , e xp ( s ) Hg Figure 1: Systematics of the β -decay half-lives of Hg isotopes. From the figure two trends are visible, and a transitionalregion between A = β -decay study is considered model dependent, it can be complementary to the resultsbased on other techniques such as Coulomb excitation, and can provide independent informationon the prolate or oblate character of the ground state of the parent nucleus, since it is based on adi ff erent probe. This is of particular interest since a direct measurement of the electric quadrupolemoment of the ground state of Hg is not possible. Furthermore, even in the most recent workby Bree et al. [23] it was not possible to obtain information on the sign of the deformation forthe
Hg ground state.This article summarizes the results of the first β -decay investigation of Hg using the totalabsorption technique. The study was challenging both in terms of the analysis and the interpreta-tion, and further details will be given elsewhere [24]. On one hand, the measured total absorptionspectra for the decay is quite exceptional compared to our previous experience, since the mostimportant features of the decay spectrum are concentrated at very low excitation energy in a”comb” like structure (see Fig. 2). The study of this decay required the development of a newapproach in the analysis because of the sizable conversion electron coe ffi cients of the gammatransitions that de-excite the strongly populated 1 + state at 363 keV in Au and to the pene-tration and summing of the X-rays in the total absorption spectrometer employed. On the otherhand, the straightforward interpretation of the experimental data, based on the direct comparisonof the deduced β strength with the theoretical calculations, seems at odds with assumed factsin the region and was further examined (see Fig. 3). In order to obtain a consistent picture ofthe whole phenomenology, an additional assumption, that both parent and daughter states can bemixed in di ff erent degrees was required. The result from this study shows that it is possible tofind a given mixing of oblate and prolate configurations for both parent and daughter nuclei thatis able to reproduce nicely the measured β strength. The theoretical analysis presented here forthe first time in the framework of QRPA calculations should be considered in cases where parentand daughter nuclei are expected to exhibit di ff erent degrees of mixing.The β -decay of Hg was studied at CERN-ISOLDE. In this experiment Hg isotopes wereproduced by bombarding a 50 gcm − UC x target with a beam of 1.4 GeV protons deliveredby the Proton Synchrotron Booster. In the measurements, the RILIS laser ionisation source[25] was used to ionise selectively Hg isotopes before separation in mass ( A ) with the GeneralPurpose Separator (GPS). Then, the mass separated beam was transported to the total absorptionspectrometer (TAS) Lucrecia , where it was implanted outside the spectrometer in the magnetictape of a tape transport system. The tape was used to move the accumulated activity to thecentre of the spectrometer in collection and measuring cycles that were determined by the half-life of the isotope of interest. In the case of the
Hg decay study ( T / = Lucrecia , is made of a cylindrically shaped NaI(Tl) mono-crystal with 38cm diameter and 38 cm length. The total e ffi ciency of this setup has been estimated using MonteCarlo (MC) simulations to be 90 % for mono-energetic gamma rays in the range of 300-3000keV, which gives an approximately 99 % e ffi ciency for gamma cascades of more than one gammaray. In this setup the beam pipe is inserted in a hole of φ = . β -decay of neutron deficient cases, two ancillarydetectors were used: a germanium telescope, that is composed of a Ge planar and a Ge coaxialdetector, together with a thin plastic beta detector. The ancillary detectors allow us to tag theelectron capture (EC) or the β + component of the decay by requesting coincidences of the TAGS4 nergy [keV]0 500 1000 1500 2000 2500 3000 3500 C oun t s TAGS gateR*f+cont.PileupBck gate
Figure 2: Comparison of the analyzed TAGS X-ray gated spectrum (red) and reconstructed (black) spectrum after theanalysis for the
Hg decay. The reconstructed spectrum is calculated with the β -intensities obtained in the analysisand the corresponding response function of the spectrometer. The contributions of the di ff erent contaminants (pileup andbackground) are also presented (blue and pink, respectively). spectrum with the X-rays detected in the planar detector (EC component) or with the β -particlesdetected in the β detector ( β + component). More details on the Lucrecia setup can be found in[14, 15, 27]. In this kind of study, the TAGS spectrum generated in coincidence with the X-raysemitted in the EC process is preferred for the analysis, since the coincidence is element selectiveand provides a very clean decay spectrum.For the analysis of the total absorption spectrum, the d i = P j max j = R i j ( B ) f j + c i ( i = , .., i max )matrix equation has to be solved. Here d i represents the content of bin i in the TAGS spectrum, R i j ( B ) is the response matrix of the setup and represents the probability that a decay that feedslevel j in the daughter nucleus gives a count in bin i of the TAGS spectrum ( d i ), f j is the β feeding to the level j , that has to be determined and c i represents the contribution of possiblecontaminants to the contents of bin i . The TAGS spectrum d , used in the analysis, was generatedby putting a condition on the X-rays of Au, specifically coincidences with the K α and K β lines. The contributions of the X-ray background and pileup to the spectrum d were also takeninto account. The calculation of the response function R i j ( B ) requires the knowledge of thebranching ratio matrix B of the levels in the daughter nucleus. In our conventional analysis thismatrix is first calculated using the information available from high-resolution studies up to acertain threshold energy, in this particular case up to 600 keV. Above that energy threshold andup to the decay Q value (3176(24) keV [28] ) the statistical model is used to generate the gammadecay branches of the levels. The statistical model is based on a Back-Shifted Fermi Gas Modellevel density function [29] and gamma strength functions [30] of E1, M1, and E2 character. Thelevel density function parameters were obtained from fits to the data available in [31, 32, 30].Once the branching ratio matrix is defined, it is possible to calculate the R i j using MC techniquesand solve the equation using an appropriate algorithm [33, 34].The first analysis attempts, that followed the conventional procedure of analysis, were notable to reproduce the X-ray gated TAGS spectrum of the decay of Hg. Additional peaks appearin the X-ray gated experimental TAGS spectrum, that are not accounted for in our conventional5esponse function. The reason lays in the way of calculating the response function where X-rays were not generated and not included in the gamma-ray response. This is conventionallyconsidered unnecessary, because of the low energy of the X-rays involved in most of the β -decay cases studied and their absorption by the layers of dead material in the total absorptiondetectors and materials around the sources. According to the high-resolution study of Porquet et al. [35], the state that receives most of the feeding in the β -decay of Hg is the 1 + state at363.6 keV excitation energy in Au. The total absorption peak associated with this state is aclearly dominant feature in the TAGS spectrum (see Fig. 2). The 363.6 keV state de-excites bya gamma cascade of two gamma rays (112.1 keV (E1) - 251.5 keV (M1)). Both gamma rayshave sizable internal conversion coe ffi cients ( α tot = α tot = β -decayby EC (with the consequent generation of X-rays) or by β + transitions.These additional X-rays, and their large energies ( K α (Au) = ffi cultiesin the conventional analysis. Assuming a pure EC decay to the 363.6 keV state for simplicity,in the case of electron conversion of any gamma transition in the cascade, the resulting X-rayfrom internal conversion can be summed with the unconverted gamma transition of the cascade,thus generating additional peaks in the TAGS spectrum. Thus for example we will have peaksat 112.1 keV plus an X-ray from conversion of the 251.5 keV transition, and 251.5 keV plusan X-ray from conversion of the 112.1 keV transition. In addition, X-rays generated by internalconversion can lead to a β + contamination in the EC spectrum (defined experimentally by the X-ray coincidence, since the 363.6 keV state can be populated also via β + decay and we can detectone of the X-rays generated from the electron conversion of any of the gamma lines de-excitingthe level in the planar detector). To address the complexity of the problem (generation of X-raysbecause of the EC / β + competition depending on the excitation of the level, the generation ofX-rays because of conversion and the summing of gamma transitions with X-rays) a new wayof calculating the response function was developed. The method will be described in full detailin forthcoming publications [24, 36], but essentially what is done is to exploit fully the toolsprovided by the radioactive decay package of the GEANT4 code [37]. The response functionfor each level in the daughter nucleus is obtained by simulating a β -decay (EC + β + ) usingan artificially generated “ β -decay level scheme” that assigns β -feeding to the level for whichthe response is calculated only, and considering that the level (populated in the β -decay) de-excites with a branching ratio matrix B calculated by us. The branching ratio matrix of the levelin the daughter is determined according to our conventional method, by combining the knownbranching ratio matrix from high-resolution studies for the low-lying levels with the added partat higher excitation energy from the statistical model in bins of 40 keV. The response to thelevel is obtained finally by collecting the obtained TAGS spectrum in the GEANT4 simulationin coincidence with the X-rays detected in the planar detector, in exactly the same conditionsas in the experiment. By using this method we employ the tools provided by GEANT4 for thegeneration of X-rays in all the processes and the calculation of the EC / β + ratio for each level.The final response ( R i j ( B )) matrix is obtained by combining the di ff erent responses obtained foreach possible level populated in the decay up to the Q value.The analysis employing the new calculation method of the response function, provided anice reproduction of the X-ray gated TAGS spectrum (see Fig. 2). From the feeding distribu-tion obtained the β strength of the decay is deduced, which is compared with QRPA theoreticalcalculations using the SLy4 force in Fig. 3 [22]. The error bands of the experimental strengthdistribution are determined by the possible solutions of the TAGS inverse problem that reproduce6 nergy [keV]0 500 1000 1500 2000 2500 3000 ] π / A B ( G T ) [ g Σ TAGS resultOblate SLy4Prolate SLy4Mixed solution
Figure 3: Accumulated β strength deduced from the analysis as a function of the level energy compared with the theo-retical calculations using SLy4 force [22] for the decay of Hg. The mixed solution corresponds to ( λ, α ) = (0.46,0.46).For more details see the text. reasonably well the experimental spectrum and by the errors of the Q value and the T / of thedecay used in the calculation of the strength ( Q EC = T / = Hg would be pro-late in its ground state (see the red line in Fig. 3), but this result is in contradiction with theinterpretation of the trend of δ h r i measurements around Hg, which has been explained as arapid shape change from an oblate system (
Hg) to a more deformed odd-A system in
Hg.For that reason, the straightforward interpretation based on the direct comparison of the exper-iment with the results obtained from pure shapes was revised, and more complex deformationscenarios were considered. A simple mixing scenario of the parent (and consequently daughter),such as the one used to explain the Kr case was also discarded, since the variation of δ h r i around Au was interpreted as a sign of
Au being a dominantly prolate nucleus [38].Therefore, a more complex mixing scenario has to be necessarily considered in which theparent and daughter nuclei may both exhibit di ff erent degrees of mixing of the oblate and prolatecomponents that correspond to the prolate ( β = β = -0.18) minima used in theQRPA calculations. This is carried out by the simple model given by Eqs. 1, where parent( | ψ i p ) and daughter ( | φ i d ) states are described by the mixing of two shapes, oblate and prolate,with weights characterized by λ and α , respectively. The idea is to explore whether we canfind independent combinations of prolate and oblate components, for both parent and daughterwavefunctions, that are able to reproduce optimally the experimental GT strength.7 λ A b s . D i ff. A b s . D i ff. Figure 4: Contour plot of the absolute value of the GT exp − GT mix di ff erences in the λ , α surface for the SLy4 force. Energy [keV]0 500 1000 1500 2000 2500 3000 ] π / A B ( G T ) [ g Σ TAGS result)=(0.54,0.0) α , λ ( )=(0.8,0.8) α , λ ( Figure 5: Accumulated β strength deduced from the analysis as a function of the level energy compared with GT mix with( λ, α ) = (0.54,0.0) (black line) and (0.8,0.8) (red line). ψ i p = λ | Oblate i p + √ − λ | Prolate i p | φ i d = α | Oblate i d + √ − α | Prolate i d GT mix = λ α GT Obl . + (1 − λ )(1 − α ) GT Prol . + C . T . (1)It is worth emphasizing here what is meant by GT Obl . and GT Prol . in the formula. GT Obl . stands for the strength corresponding to the GT transition of the pure oblate ground state wavefunction of Hg to the oblate states in
Au and similarly for GT Prol . in the prolate case. Theconsideration of the mixing scenario makes sense in this particular case since the predicted oblateand prolate energy minima for both Hg and
Au are very similar. This is not only true forthe calculations presented here, but also for the results from Hartree-Fock-Bogoliubov modelcalculations based on the Gogny force [39]. In Eqs. 1, C.T. stands for small cross terms thatinvolve phases of the di ff erent components . GT mix is the GT obtained from the assumed mixingof parent and daughter states.As a first step we fitted the experimental GT exp (experimental GT strength) with the GT mix function defined in Eqs. 1 to find the ( λ, α ) parameters that best reproduce the data. The bestfit of the experimental accumulated stregth was obtained with λ = α = Au. The obtained GT mix is presented in Fig. 3 with a blackline. Please note that in this model we are assuming that all states in the daughter nucleus havethe same degree of mixing. This approximation can be considered a natural extension of theone employed in standard QRPA calculations where the shape of the parent nucleus and all thepopulated states in the daughter nucleus are the same.To get a deeper insight into possible additional mixing scenarios, a mesh of α and λ valueswas used to look for minima in the surfaces of the absolute value of the di ff erences between GT mix and GT exp depending on the ( α , λ ) coordinates.The GT-strength di ff erence surface for the SLy4 force shows clearly two well defined min-ima at ( λ, α ) = (0 . , .
46) and (0 . , .
8) (see Fig 4). The two minima are positioned in thediagonal of the ( λ, α ) plane, defining two valleys of quadrant shape. The shape of the valleysis a consequence of the symmetrical dependence of the GT mix function on the λ and α parame-ters. The deepest minimum at (0 . , .
46) corresponds to the values already obtained from thesimple function fit and describes very nicely the pattern of the accumulated strength as seen inFig. 3. The second minimum at (0 . , .
8) describes well the accumulated value of the strengthat E exc = Hg that describes properly theexperimental β -strength pattern. From the surface this value is obtained when α ∼ λ = χ with the one associated with In the studied case the C.T amounts to maximum 5 % of the accumulated strength / [s] ( λ, α )prolate 60.0 (0.0,0.0)oblate 47.9 (1.0,1.0)QRPA-SLy4 mixed 89.1 (0.46,0.46)model mixed 84.5 (0.54,0.0)mixed 93.4 (0.80,0.80)Experiment 82.3(36) Table 1: Comparison of the experimental value of the T / with the results of the calculations assuming di ff erent shapescenarios. The corresponding ( λ, α ) coordinates are provided in the last column. Note that the best description of theground state half-life is provided by the (0 . , .
0) mixed scenario, which maximises the oblate content of the parentground state (see the text for details). the lowest minimum (0 . , . . , .
8) solution has a very poor χ , compared to both (0 . , .
46) and (0 . , .
0) and fails todescribe the decay to the predominant state at 363 keV in
Au.Summarizing, in this article we have presented for the first time the measurement of the β -decay of Hg using the total absorption technique. The complexity of the case requiredthe development of a new approach in the analysis to handle the penetration and summing ofthe X-rays in the total absorption spectrometer that can also be of particular interest for caseswhere the β + component of the β -decay can contaminate the X-ray gated spectra. A doublemixing scenario has been considered for the first time to interpret the results in the framework ofQRPA calculations. From the analysis of the accumulated GT strength assuming a double mixingscenario, clearly the best description of the pattern of the strength is obtained with both parentand daugther nucleus having a dominantly prolate content (1- λ = λ , α ) = (0.46,0.46)).The study of the minimum valleys of the ( λ , α ) surface allowed us to determine the maximumoblate component of Hg in its ground state, that also reproduces nicely the pattern of theaccumulated GT-strength and provides the best description of the half-life of the decay (see Table1) in this framework. This corresponds to the ( λ , α ) = (0.54,0.0) values and to an oblate content of λ = λ , α ) = (0.46,0.46) and ( λ , α ) = (0.54,0.0)) further emphasize what isalready apparent from Figs. 1 and 3, that Hg is located in a transitional region where the shapein the Hg isotopes is changing and the beta transition strengths might be dictated by a fraction ofthe wave function that determines the overlap of parent and daugher wave functions in the caseof di ff erent parent and daughter shapes. Although model dependent, the results presented hererepresent an alternative confirmation of the mixed character of the ground state of Hg.This work was supported by Spanish Ministerio de Econom´ıa y Competitividad under grantsFPA2011-24553, FPA2014-52823-C2-1-P, FPA2017-83946-C2-1-P, Ministerio de Ciencia e In-novacion grant PID2019-104714GB-C21, the program Severo Ochoa (SEV-2014-0398), andgrants RTI 2018-098868-B-100 and ENSAR (grant 262010). S. E. A. O thanks the supportof CPAN Consolider-Ingenio 2010 Programme CSD2007-00042 grant. E. G. acknowledges sup-port from TUBITAK 2219 Abroad Research Fellowship Programme. R. B. C. acknowledgessupport by the Max-Planck-Partner group. Support from the technical sta ff and engineers ofISOLDE-CERN is acknowledged. W.G. acknowledges the support of STFC(UK) council grantST / P005314 /
1. The help of Karl Johnston in the preparation of the Na source is also ac-knowledged. Enlightening discussions with Peter O. Hess, Thomas E. Cocolios and Sophie Peruare also acknowledged. This work was also supported by the National Research, Development10nd Innovation Fund of Hungary, financed under the K18 funding scheme with Projects No. K128729 and NN128072. P. S. acknowledges support from MCI / AEI / FEDER,UE (Spain) undergrant PGC2018-093636-B-I00.
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